Physics Olympiad Papers
Colombian Physics Olympiad Problems
Science Olympiad Blog
Colombian Olympiad Physics Training Problems Problem 1-1 A hinge construction comprises three diamonds whose side lengths are in the proportions 3:2:1. Vertex A 3 is shifted in the horizontal direction with velocity V constant. Determine the velocities of the vertices A 1, A 2, B 2 at all angles of the building are straight.
Problem 1-2 In a movie screen shows the movement of a car. The radius of the front wheels of the car is r = 0.35 m and the rear R of r = 1.5. The front wheels have N 1 = 6 radios. The camera filming the film moves at a speed of 24 frames per second. a) Considering that the wheels of the car move without slipping, determine the minimum speed at which the car must be moved to the front wheels appear to rotate in the screen. b) What is the minimum number of radios N 2 which must be to the rear wheels while the front also appear to not rotate? For the next question considering that the number of spokes of the front and rear wheels is N 1 = N 2 = 6. c) How fast is the car moving from left to right, to a spectator will appear that the spokes of the wheels rotate in a counter clockwise? Problem 1-3 Two tanks are moving on a horizontal ground so that approximate along the same line with constant speed as shown. Each tank fires a shot at the same time in the same vertical plane of the other tank. The speed of each projectile with respect to the tank is u 1 and u 2 and the respective angles with the horizontal 1 2. Both shot tanks impinging upon. a) Find the relative speed of the tanks. b) Find the condition required for u 1, u 2 and 1, 2. Neglecting air resistance constant and assume the value of the acceleration of gravity). What if the above condition is not satisfied?
Problem 1-4 To measure the wind velocity distribution as a function of the height, is rolled up balloon ascends so that constant velocity. When the balloon is released, the dependency was measured elevation angle to the horizon balloon as a function of time as shown in Fig. Assuming that the wind speed at the ground surface is zero and the distance from the observer to the left point where the balloon is L = 1 km, determine the height of the balloon after 7 minutes of being released and the wind speed so high.
Problem 2-1 Determine the force exerted on the wall of a wedge to slip her true body of mass m. The angle of the wedge base The coefficient of friction between the body and the surface of the wedge is between the wedge and the ground. Problem 2-2 A solid is placed on a rough plane and inclined an angle to horizon. One inextensible cord is attached to the solid and its other end passing through a hole made in the plane. Initially, the rope is horizontal and is then pulled slowly until the solid reaches the half circumference having described hole. Find the coefficient of friction and the solid body plane.
Problem 2-3 A cable is placed on a cylinder so that part of it lies on a table and lying on the flat part. After the cable is released it begins to move without friction. Find the speed of the cable after it has established a uniform motion. The height of the table is equal to h.
Problem 2-4 Mass m A wedge is supported on a block of mass M and a stationary wall as shown in Fig. Find the acceleration of each of the blocks. Neglect friction.
Problem 2-5 Determine the accelerations of the bodies of masses m 1, m 2 and m 3 mechanical system of FIG. Is negligible friction between all surfaces in contact.
Problem 2-6 At the end of a table of length L and mass M is located a small block of mass m. The table can move without friction on a horizontal surface. The coefficient of kinetic friction between the body and the table is What minimum speed V is necessary to communicate at once to the table so that it drops the block?
Problem 2-7 For a thread shaped path and of rectangular cross section made on the internal surface of a hollow cylinder and slides a cube infinity. The inner radius of the cylinder is R basis. The thread pitch is h. The coefficient of friction is l. Find the maximum speed (speed limit) reached by the ulna. The dimensions of the cube and the thread profile are much smaller than R.
Problem 2-8 A rope is tied at one end to the lateral surface of a cylinder of radius r at its base and is wound around this k times (k is an integer). A mass m is connected to the other end of the rope and a speed communicates directed along the radius of the cylinder as shown in Fig. How long the rope is wrapped around the cylinder again. The cylinder is located on a smooth horizontal surface.
Problem 2-9 A small metal sphere mass m is skewered on a vertical metal ring of radius R so that it can slide without friction. The ball is connected to a massless spring which has one end fixed to the upper ring. The ball is displaced to point P or so POA = 60 ° and then released. If m = 1kg, k = 50 N / m, R = 50 cm and the natural length of the spring is 50 cm find: a) The conditions to be satisfied by the quantities given above so that when the ball is released from the point P or it reaches the point B. b) The equilibrium positions of the ball along the ring. Point B Is stable equilibrium position?
Problem 2-10 Two bodies of mass m 1 and m 2 are connected by an inextensible string passing over a pulley. The planes in which the bodies are formed with angles the horizontal and The body of the right is higher than the left
a distance h. After a time t starting the movement both bodies are at the same height. The coefficient of friction between the bodies and surfaces is To determine the relationship between the mass of bodies.
Problem 2-11 In the system of the figure, the block of mass M can move without friction. At baseline the suspended body mass m of yarn is separated from an angle the vertical and released. What is the mass of the body, if the angle forms with the vertical thread does not change when moving the system?
Problem 2-12 Two small bodies of masses m 1 and m 2 are joined by an elastic spring constant k. This system is on a smooth horizontal surface. At one point the bodies are released. The bodies begin to oscillate along a straight line. a) What is the period of the oscillations? b) How does each body position relative to the center of mass as a function of time? c) How does the distance between bodies with time? Problem 2-13 A body mass m is placed on another mass M, which is suspended from a spring elastic constant k, fig.9. At first spring body depends only mass M, then both bodies are loosened. Find the maximum force exerted by M on m.
Problem 3-1
A bucket of mass m lies on a horizontal surface. How high strength and low angle relative to the horizon than is necessary to pull the bucket by its upper edge to overturn without slippage, if the friction coefficient is equal to Problem 3-2 A thin sheet of paper is pressed toward the table by a homogeneous mass m bar whose upper end is fastened in an articulated manner. The angle between the bar and the sheet the coefficient of friction between them is There is friction between the table and paper. What minimum horizontal force must be applied to the blade out?
Problem 3-3 A solid cylinder of radius R is supported by two blocks of the same height as shown in Fig. A block is stationary and the other moves with speed V to the left. How the cylinder pressed force on the stationary block at the time when the two blocks are separated by a distance ? Consider that at the initial time the blocks were very close to each other, there is friction between the block and the cylinder.
Problem 3-4 A straight rod, uniform, homogeneous mass m and length L is placed on a horizontal table with its mass center horizontal distance perpendicular to the edge as shown in Fig. The rod is released from rest in its horizontal position and starts to rotate on the edge of the table. If the coefficient of static friction to the initiation of the movement between the bar and the table is μ, find the angle with the horizontal bar starting reached before sliding.
Problem 3-5 A homogeneous uniform circular cylinder rests on the edge of a horizontal step. The cylinder rolls out onto the stage with a negligible initial velocity without slipping. Find the angle that the cylinder rotates before leaving step and the angular velocity of the cylinder after it has rotated. Suppose that the effects of air resistance can be neglected.
Problem 3-6 A homogeneous light stick length L is originally placed horizontally. This is supported so that it can rotate freely around its center in a vertical plane. A spider falls with a vertical speed v o and lands located midway between the center of the bottom and the top. The mass m of the spider is equal to the mass of the stick. Immediately after landing the spider begins to run along this so that the angular velocity of the stick remains constant. Determine the largest value of v or so that when the spider reaches the end of the stick it is vertical. It is assumed that the spider is apparent from the stick when it is in vertical position. Draw a diagram of the path followed by the spider. (Moment of inertia of a bar of length L with respect to a perpendicular axis and passing 2/12). through its center, R = mL Problem 3-7 A homogeneous sphere, solid of radius R and mass m is dropped. Its center of mass is at rest, but the sphere is rotating about a horizontal axis barycentric angular velocity o. The lowest point of the sphere is at a height h from the ground as shown in Fig. When the field is released and hits the floor it bounces a fraction of its original height. The ball and the floor are made of materials such that the deformation of the impact both are considered negligible. Assume that the coefficient of kinetic friction between the ball and the floor is It is assumed that the air resistance is negligible and that the time of impact is very small but finite. (Moment of 2/5). inertia of the sphere about an axis passing through its center, R = 2Mr 1. Assuming that the sphere moves during the impact. Find: a) The rebound tangent angle b) The horizontal distance traveled by the center of mass after the first impact and after the second impact. c) The minimum possible value of
o.
2. Assume now that the slide ceases before the end of the time interval of impact. Reply back questions a) and b). 3. Taking into account the cases 1 and 2 to graph as versus
o.
Problem 4-1 The system of figure consists of two masses m and M together by a light rod of length L. The coefficient of friction between the rod and the edge of the step is μ. There is friction between the mass mand the wall. Find an expression relating the quantities m, M, L and so that the rod remains in equilibrium on the step.
Problem 4-2 Two wedges equal in shape of isosceles triangles, each of mass m 2 and the vertical angle equal are placed one after the other with their bases on a horizontal plane rough. The edges of the wedges are in contact. A mass m smooth sphere of radius r 1 and is positioned between the wedges so that the system is in equilibrium. Prove that there is balance is met:
where is the coefficient of friction and a is the length of each wedge base. Problem 4-3
Two identical blocks parallelepiped (dimensions a, b and c) are arranged as shown in Fig. The mass of the blocks is m and the coefficient of friction between them and the floor is Finding the possible values of the angle so that the system remains in the equilibrium position shown.
Problem 4-4 Three identical cylinders are positioned as shown in Fig. The coefficient of friction between the cylinders is 1 and between the cylinders and the floor is 2. Find the condition to be satisfied 1 and 2 sothat the system remains in balance.
Problem 4-5 Four smooth and equal spheres are placed at the bottom of a hemisphere of radius a. The radius of each sphere is b. A fifth sphere of the same radius and density is placed on them under what conditions there is a balance? There is no contact friction between the bodies. Problem 4-6 Three identical inelastic cords are fixed equidistant from each other a ring of radius r and similarly to a ring of radius 2r. The cords pass through a third ring of radius r as shown in Fig. The ring 1 is fixed in a horizontal plane and the whole system is in equilibrium. Find the distance between the centers of the rings 2 and 3. All rings are made of the same wire.
Problem 4-7
Pliers consist of two identical rigid parts fastened with a pivot at point O. What is the force exerted on the pivot if the edges of the clips are pressed with a force F? Assume there is no friction in the pivot.
Problem 4-8 A rope of length L =
R / 2 is placed on the surface of a fixed cylinder of radius R, with one end located in the upper part thereof as shown in Fig. Find
the acceleration of the cord as soon as it is released. Neglect friction
Problem 4-9 A rope of length L and M is suspended mass of the ends of the points O and O 'of a horizontal roof as shown in the figure below. If the distance from the ceiling to the lowest point of the string is H what is the tension in the rope at the lowest point of this?
Problem 4-10 A small cube of mass m is placed on an incline as shown in Fig. The angle of inclination of the plane is the cube is
= 2tan
and the coefficient of friction between the plane and
Determine the minimum horizontal force required to move the bucket.
Problem 4-11 A light bar length d is secured to the lower ends of two spring constants k 1 and k 2 respectively as shown in Fig. At a distance x from one of them in vertical direction throw applying a slight force F. What spring constant is observed?. Graphing the results
Problem 5-1 A body of mass m 1 = 0.1 kg is suspended from a long wire. He is bound in turn one light string of length L = 0.2 m with one small sphere of mass m 2 = 0.05 kg suspended at the other end as shown in Fig. In the small sphere below is communicated with a very short stroke velocity v or horizontally. What value v or the bodies would be found on the same horizontal?
Problem 5-2 A boy slowly ascends a mountain covered with snow and pulling a sled by a rope as shown in Fig. The rope is always parallel to the tangent at any point on the mountain where the child is located. The mountain top is at a height h and a distance L from its base. What made the boy work to bring the sled to the top of the mountain. The mass of the sled is m and the coefficient of friction μ on snow is.
Problem 5-3 Resting against a system that is on a smooth horizontal surface and consisting of two bodies of mass m, coupled by a spring with spring constant k, the speed V collides true body mass thereof. The collision is elastic. Determine the maximum elongation of the spring.
Problem 5-4
In a thermally insulated flat tube are infinite mass m with two pistons, between which there are n mols of monatomic gas at temperature T o. At the initial instant their velocities are directed in the same direction and is equal to V and pV, where p is a constant. To what maximum temperature will heat the gas? The plungers do not conduct heat. Neglect the mass of gas compared to the mass of the pistons.
Training Problems
Problem 5-5 In the figure shown how high will a sandbag of mass m 2 launched with the help of a very thin board of mass m and length L, if on the other end of the table from the height H drops a sack of mass m 1 ?
Training Problems
Problem 5-6 Two identical balls are linked through a light rope of length L and placed on a table as shown in Fig. Determine the height of the table so that the two balls reach the ground falling at the same time, if the ball is initially at the right edge of the table and about to fall. The friction between the table and the balls like between the string and the edge of the table are neglected.
Problem 5-7 In the initial state the centers of two masses M and spheres with radii R 10 are separated a distance R as indicated below. In one load is distributed evenly + Q and-Q in the second. The first area is connected to a remote wall with a thread which supports a maximum tension T. The second area is released at one time. Determine the velocity of the spheres after colliding if the collision is quite inelastic. The loads are not redistributed.
Problem 5-8 A conductor bar length L and mass m of two rigid bars hanging conductive also negligible mass and length h which are hooked on a horizontal axis. The system is in a vertical homogeneous magnetic field intensity B. A current pulse I or passes through the bar for a short time interval Determine the maximum inclination of the suspension bar relative to the vertical.
Problem 5-9 A satellite moves in a circular orbit of radius R around the earth R = 2 R t (R t = radius of the earth). At one point, the satellite is launched from a ship to a distant planet. The spacecraft is launched tangentially to the circular orbit in the direction of movement of the satellite. As a result, the satellite is in an elliptical orbit that passes close to the earth at a point that is opposite to the launch site of spacecraft. What is the relationship between the mass of the spacecraft and the satellite before launch? How much time elapsed from when the ship is launched until the satellite reaches the opposite point of its orbit? A narrow tube of constant cross-section forms a square of side L, and is in a vertical plane. The tube is filled with two liquids - miscible equal volume and density of 1 and 2. At first, denser liquid occupying the upper tube. At some instant the liquids are set into motion. Find the maximum speed. No friction. The acceleration of gravity is g.
Problem 5-11 A spacecraft in flight explodes into three equal portions. A portion continues along the original line of flight. The other two shoot out in directions forming an angle of 60 ° with the original path. The energy released in the explosion is twice larger than the kinetic energy possessed probe precisely at the time of the explosion. Determine the kinetic energy of each fragment immediately after the explosion. Problem 5-12 Two blocks of equal masses m are joined through an elastic spring constant k, as indicated below. The upper block is lowered so as to compress the spring a distance x or and then released. What is the maximum height of the center of mass of the system after releasing the upper block?
Problem 5-13 In a thermally insulated flat tube are infinite two pistons with mass m and M, between which there is a monatomic gas occupying a volume V or P or pressure. The plungers are freed. Estimate the maximum speeds of the pistons. Underestimate gas mass compared to the mass of the pistons.
Problem 5-14 The piston of mass M, which encloses the volume V or a monatomic gas pressure P or and temperature T or moves at speed u. Determining the temperature and gas volume during maximum compression.The system is thermally insulated. Neglecting the heat capacities of the plunger and the container.
Problem 5-15 On one end of a straw length L and m is mass of mass M a grasshopper. The straw is flat on a horizontal table. What minimum speed must the grasshopper jump to reach the other end of the straw? Problem 5-16 Three bodies of equal mass m are interconnected by a length strings as shown in Fig. Each of the bodies has the same charge q. If one of the threads is cut what is the maximum speed acquired by each of the masses?
Problem 5-17
Two identical particle velocities u and v, and form angles with the joining line, and the distance L from each other as shown in Fig. The charge on each particle is q. Determine the mass of the particles, it is known that the minimum distance which is equal to a close.
Problem 5-18 A meteor moving towards a planet of mass M (along a line through the center of the planet), hitting a spinning artificial satellite by a circular orbit of radius R around the planet. The mass of the satellite is ten times greater than the mass of the meteor. As a result of the crash the meteorite is embedded in the satellite, which in turn passes into a new orbit the planet whose minimum distance is R / 2. Determine the speed or the meteorite before the crash. Problem 5-19 Two identical disks, mass m and radius R, slide on a frictionless ice rink and go to meet with parallel velocities v 1 and v 2, while rotating with angular velocity 1 and 2 in opposite directions. When hitting the edges are glued and their centers are separated by a distance equal to the diameter of both disks. Determine the linear and angular velocities after the collision set.
Problem 6-1 A homogeneous rod, cylindrical, thin and of length L, which is rotatable about an axis O at one end, is introduced slowly into water as indicated in the figure. The density of the rod is less than that of water o can stay upright stick to a certain value of x, it will show as x 1. If x is smaller than x 1, a minor perturbation of the rod is inclined as shown in Figure b. If the axis of rotation remains in the water immersing the rod assumes a position as shown in figure c.
a) Determine the
dependence versus x.
b) Determine the value of x 1. c) Construct a function of x, with-L
Problem 6-3 Determine the density of the alcohol, from the following elements provided. - A test tube. - A 500 ml beaker. - A pipette (unscaled) 3
- Distilled water, whose density is 1 × 10 kg / m
3.
- Alcohol. - Ballast (steel balls). - A millimeter rule. - A piece of cardboard with a hole. - Tape - Graph paper. - Paper towels. a) Describe the procedure chosen clearly indicating both the theoretical and experimental. b) Determine the density of alcohol supplied. c) Evaluate the error of their results.
PRECAUTIONS: - Do not suck any liquid supplied to the mouth when using the pipette. - In case of rupture of a glass element please notify the manager of the test. Problem 6-4 They have two containers of the same shape, height h and attached as shown in the figure below. There is a gap between the two containers at the height x and another of the same cross section in the vessel to the right height and through which the water flows freely. When left container water is supplied such that this is full at every instant of time. What is the height of the water level in the container right after it has been a very big
moment in time? Problem 7-1 A pump piston to perform a cycle draws a volume V or air. By removing this air pump with a container of volume V n cycles are performed. The initial vessel pressure was atmospheric pressure p o. Then, with another pump of the same working volume V or air is introduced from the environment and also n cycles are performed. What pressure is established in the container? Problem 7-2 A specimen of length L is filled with hydrogen at pressure P 'is closed by a movable piston light and dipped into a container of mercury to the depth H. What part of the length of the specimen will be filled with hydrogen under these conditions? For what values of H has a solution this problem? The density of mercury is P and atmospheric pressure hydrogen temperature is kept constant.
Problem 7-3 Perren scientist investigated the dependence of the number of true spherical resin particles according to the height in the water. For particles of radius r 1 = 0.13 micrometers was obtained whose dependency graph shown in Figure 1, (n is the concentration of the particles to the height h and No is the concentration in the bottom of the bucket). The same graph is obtained for particles with radius r = 0.065 microns, only that the vertical scale is magnified by a factor 8. At the same time, it is known that the density of oxygen in the 2
atmosphere decreases with altitude as shown in Figure 2 is the density of oxygen to the height H and oxygen density in the surface of the bucket). Determining the mass of oxygen molecules. As resin density 1.194 g / cm or
3.
Problem 7-4 A parallelepiped-shaped container has a mass M and length L. This container is filled with a gas mass m and also has a thin wall which slides without friction, thereby dividing the gas into two equal parts.At first gas temperature was T. In the right part of the container connects a heater and as a result the temperature is increased to 2T. The gas occupies the left side of the container is kept at temperature T.If the container is on a smooth horizontal surface finding its displacement with respect to the floor.
Problem 7-5 The module of a spacecraft approaching a planet surface with constant speed along a vertical line. This transmits data on external pressure to the module. The time dependence of pressure in arbitrary units is shown in Fig. Data transmitted by the module after landing indicate that the outside temperature is T = 700 K and the free-fall acceleration is g = 10 m/s2. Determine: a) the speed v at which the module falls, if the planet's atmosphere is known that carbon dioxide (CO 2) b) the temperature T h at the height h = 15 km above the earth's surface.
Problem 8-1 A container containing a mixture of water and ice. The water mass is 10 kg. The container is brought into a room after which the temperature of the mixture is measured immediately. The dependence of the temperature T (t) over time t is shown in Fig. The heat capacity of water is C a = 4.2 kJ / (kgK) and the latent heat of fusion of ice is L = 340 kJ / kg. Determining the mass m i of ice the container when it was entered into the room. Neglecting the heat capacity of the container.
Problem 8-2 In a cylindrical vessel under a piston is 1 mol of a monatomic ideal gas. The piston mass is M, and its area is S. What is required amount of heat to the gas communicating unit in time for the piston to move uniformly upward velocity V? Atmospheric pressure is P o. Not considered friction between the piston and the walls. Problem 8-3 A thermally insulated container is divided into two parts by a piston non-conductor of heat which can move without friction by the container. On the left side of the container there is 1 mol of an ideal monatomic gas and the right part is empty. The piston is attached to the right wall with a spring whose average length is equal to the length of the container. To determine the relationship for the system (heat capacity of the system). The heat capacity of the container, the piston and the spring are neglected.
Problem 8-4 A number n of moles of gas, the volume and initial pressure is equal to V and p, is heated twice by one electric coil which passes a current during the same time: the first constant volume V with the particularity that the final pressure p 1, then p constant pressure starting from the same initial state, the final volume being equal to V 2. Find the ratio = from measurements p, p 1, V 2 and V. Problem 8-5 A vertical cylindrical vessel containing air, which is confined by a piston of mass M heavy. The air temperature T o is equal to the temperature of the external environment. The piston is slowly raised to the height H with respect to the equilibrium position thereof and kept there until the temperature of the air is equal to the external environmental temperature again. Then whole thermally insulated system and the piston is released. What will be the displacement of the piston when its oscillations end? Neglecting the heat capacities of the container and piston neglected as the external pressure.
Problem 8-6 A thermally insulated container is divided into two parts by a non-heat conductive piston which can move without friction by the container. In each part of the container are n moles of a gas at the same temperature To. The vessel length is L. If left container is supplied with a quantity of heat Q, find the distance x that as the piston moves from its equilibrium position.
Problem 8-7 With the device of figure below can find the ratio of specific heats at constant pressure and volume = C p / C v) for a gas. It consists of two containers filled with the large volume of gas, air in this case joined by a calibrated glass tube containing a cylindrical magnet therein sufficiently tight, appears. Using two coils placed around the pipe, on both sides of the magnet, conveniently fed with sinusoidal alternating current, can cause the magnet to move with simple harmonic motion of small amplitude and variable frequency and known. Initially the switch is open. To begin the experiment the tap is closed and studied the dependence of the amplitude and the frequency f of the oscillation of the magnet, obtaining as a result the curve in Figure b a) Find the value of b) Suppose the experiment is repeated, but this time, by an oversight, the key is open. Calculate the frequency f 'self oscillating magnet c) Under the conditions of the case b) estimate the value of the amplitude of the oscillations and m for the frequency at which the amplitude was maximal when the key was locked. Consider negligible friction. n
If needed, remember that (1 + x) 1 + nx, if x
2,
The mass of the magnet is 2.0 m = g, the cross sectional area of the tube is A = 1.0 cm the volume of the area of each side of the magnet start to oscillate before it (wrench) is V o = 0.50 L The acceleration of gravity is g = 2 10 9.8 m / s and the atmospheric pressure P o = 1.0. May Pa. Problem 8-8 Determine the numerical value of the change in atmospheric temperature with height. Problem 8-9 Find the change in pressure with height assuming isothermal air stratification. Problem 8-10 Find the change in pressure, temperature, density and height atmosphere atmospheric assuming adiabatic stratification. Problem 8-11 In the diagram of pressure versus volume shown below the lines 1-2 and 3-4 correspond to isotherms, the lines 2-3 and 1-4 correspond to isochoric. The line corresponds to an adiabatic 1-3. When a gas is subjected to cycle through the path 1-2-3-1 cycle efficiency is 1. When this gas is subjected to the same cycle through the path 1-3-4-1 cycle efficiency is 2. If this same gas undergo a cycle through the path 1-2-3-4-1, what is the efficiency of this cycle?
Problem 8-12 The volume of a liquid to a given temperature t, is related to the volume V or t temperature or through the relation V = V or (1 + p) where t = t - t o and is the coefficient of volumetric expansion, which is constant for a certain range of temperature.
The device of the figure is used to measure the coefficient of volumetric expansion of a liquid. This consists of a glass U-tube in which a liquid is deposited. Both branches of the tube are positioned respectively within vessels (shirts) B 1 and B 2 playing the role of thermostats. Through said sleeves is passed water at a given temperature for each branch, thereby establishing a temperature differential between the branches of the tube. The upper branches of the tubes, which are open to the atmosphere, is placed in third shirt B 3 at a temperature equal to that of jacket cooler. As a result of the foregoing establishing a height difference H = h 1 h of liquid columns, which can be measured as the height H. It is evident that depends H t 2
a) According to the scheme shown what the shirt is hotter?. Explain. b) Determine the coefficient of
expansion of the liquid as a function of
H and
t.
c) Given the result of part b), expresses the relative variation of density as a function of graph (qualitatively) in terms of H. HINT: (1 + x)
-1
- x, for x
H
and construct the
1.
d) If H = 0: - What is the ratio between the temperatures of the sleeves B 1 and B 2?. - What is the ratio of the densities of the liquid on shirts B 1 and B 2?. Problem 8-13 One mole of an ideal gas is heated under such conditions that the gas pressure is proportion to its volume: V P = where is a constant. Determine the heat capacity of the gas in such a process. Invent a device in which the gas pressure and the volume it occupies are linked with the indicated relationship. Problem 8-14 A cylinder closed at the top and open at the bottom, is fixed to the wall of the pool that is filled with water. On top of cylinder are n moles of a monoatomic gas separated from water by a plunger which is the depth 2h. The gas is heated by a resistance R causing the piston descend to a depth 3h. Find the time required to achieve this. The resistance r is connected to a battery emf E and internal resistance negligible. Menospréciese plunger mass, friction and thermal conductivity. The pool is wide. The density of water is and the container section is S.
Problem 8-15 In a cylinder which holds the horizontal position to the left of the piston is an ideal gas at the right side of cylinder vacuum has been created. The cylinder is thermally insulated from the environment while the spring located between the plunger and the wall is initially undeformed state. The plunger is released and, after establishing equilibrium, the volume occupied by the gas increases twice. If so, how varying the temperature and pressure of the gas? The heat capacities of the cylinder, the piston and spring are neglected.
Problem 8-16 In a cylindrical container is in equilibrium heavy plunger heat conductor. Above the piston and below it are equal masses identical temperature gas. The relationship between the upper and lower volume n.What will be the ratio of the volumes if we raise the gas temperature T '?
Problem 8-17 This problem is desired to derive the equation of state of a gas in which there is a potential energy of interaction between molecules. The way this energy is assumed to be U = V, where is a negative constant, N is the number of gas molecules and V is the volume occupied by the gas in the container. Similarly,
we want to find the difference between their molar heat capacities and pressure and contante volume obtained in comparison with the case of an ideal gas. Problem 8-18 A bulk container including piston M contains a gas at temperature T or P and atmospheric pressure or, as shown in Fig. The piston is attached to the wall through an elastic spring constant k. Between the container and the surface coefficient of friction exists equal to μ. How many times the initial temperature T should be increased or so that the piston is located at the end of the container.?
Problem 9-1 A point particle mass m is attached to the end of a light rope of length L, which is fixed at its other end to the tip of a cone whose axis is inclined by an angle with the horizontal. The apex of the cone forms an angle equal 2. If the dough is slightly displaced from its equilibrium position, what is the period of small oscillations of the mass? Neglect friction.
Problem 9-2 The system shown in the figure consists of a light rod length L and a body with mass m. One end of the rod is embedded in the wall to a point O, so that it can rotate freely about this point in any direction. The rod is attached to the ceiling through a string of length h light which makes an angle with the vertical and form an with the horizontal. Find the period of small oscillations of the mass when it is moved into the paper (or out of paper).
Problem 9-3 A point lying on the lower generatrix of a horizontal cylindrical channel radius R, is released to the speed vo a small ball, forming a small angle with respect to the generatrix. How often the ball will pass through the lower generatrix of the trough length L?
Problem 9-4 At point O of a wall forming a small angle the vertical is hung by a thread of length L a ball. Then he bent the wire with the ball at a slight angle and released. Considering Elastic absolutely hit the ball against the wall to find the period of the oscillations of the pendulum.
Problem 9-5 For a flat horizontal floor longitudinally slides a rod of length L thin homogeneous. The paddle speed is V o. This comes to a large stretch of rough floor with a coefficient of friction μ How long it takes to stop the bar?
Problem 9-6 Hállese small oscillations period for a mass body M and q load located inside of a smooth sphere of radius R, if the top point of the sphere is fixed leaving a charge Q.
Problem 9-7 Several experiments were conducted to examine the properties of a nonlinear resistance. First, we studied the dependence of the resistance with temperature, and it was found that while the temperature was increased instantly increased resistance R 1 = 50 to 100 at t 1 = 100 ° C (see figure below ). In another experiment, when a constant voltage V = 60 V was applied to the resistor being the temperature was 80 ° C. Finally, when a voltage V 2 = 80 V was applied to the resistor appeared spontaneous oscillations in the stream. The air temperature in the laboratory remained constant and equal to t o = 20 ° C. The rate of heat loss from the resistor is proportional to the difference between its temperature and the temperature of the environment. The heat capacity of the resistor is C = 3 J / K.
Problem 9-8 It has a pair of identical systems moviéndosen on a flat horizontal surface so as to approximate constant velocity V o. Each system comprises two identical blocks each of mass m and joined together by a light spring with spring constant k. When the two half bodies are located at a distance L apart, the springs are unstretched. Find the time elapsed since the central blocks distance L until again meet again at this same distance. Assume that collisions are elastic.
Problem 9-9 A mass m is attached to the end of a horizontal rod length light L and the other end of the rod is held in a ball joint. A vertical inextensible rope length h holds the rod at a distance from the board. Find the period of small oscillations of the system. Neglect friction.
Problem 9-10 At the ends of a rod length of negligible mass of d = 1 m small spheres are fixed two small mass m = 1 g each. The rod is suspended so that it can rotate without friction relative to the vertical axis passing through its center. On the same line with the rod are two large spheres of mass M = 20 kg each. The distance between the centers of each large and small sphere is near L = 16 cm. Determine the period of small oscillations of this pendulum rotational.
Problem 9-11 A train of very long length L constant speed V is suddenly finds a hill, which forms an horizontal. How much time elapsed from the first car begins to rise until it comes to rest?
with the
Problem 9-12 Two parallel cylindrical rollers rotating in opposite directions. The distance between the centers of the rollers is a. A straight bar uniform horizontal length L and weight W rests on the rollers. The coefficient of kinetic friction between the bar and the roller is μ. Taking x as the distance from the center of the bar at the midpoint between the rollers, write the equation of motion of the rod, assuming initially moves from its central position . Finding the resultant oscillatory movement period.
Problem 9-13 A hoop of mass M and radius R is located on a cylindrical support highly rugged and radius r. The ring is displaced slightly from its equilibrium position. Find the period of small oscillations.
Problem 9-14 A support mass M is placed on a flat table. Bracket hangs a sphere of mass m by a string of length L and negligible mass. The yarn is separated by a small angle and released. Draw the graph of velocity versus time support. Consider the collision between the sphere and a perfectly elastic.
Problem 10-1 Two infinite planes that intersect at an angle divide the space in zones I, II, III and IV as shown in Fig. The surface densities cargo planes are + and - Determine the intensity and direction of the electric field in each of the zones.
Problem 10-2
Two identical conductive plates are positioned parallel one opposite the other at a distance d between them. If left plate is placed a charge + Q, show that on the other plate are induced loads right - and + on the left and right surfaces, respectively. Problem 10-3 In a non-conductive rod bent at right angles there are two small spheres (traversed by the rod) that can move without friction along this. The spheres each have a mass m and charge Q and-Q respectively.At baseline spheres are at rest and are at distances d and 2 d of the right angle. If the spheres are released, how come the time difference to the vertex spheres? Find the speed of each of the areas at the time that the separation of the spheres is d? Neglecting the effect of gravity.
Problem 10-4 Two thin sheets of thickness d each are uniformly loaded with bulk densities - y + A negative charge and particle mass m and reaches the positively charged plate speed v at an angle the surface of the sheet.
a) For which values of the particle velocity will not come to the negatively charged plate. b) How long after the point and how far will the particle A positively charged sheet in this case? Problem 10-5 Two electric charges q are joined by two stationary walls rubber elastic cords as illustrated in Fig. The separation of the strands caused by the interaction of the loads is much smaller than its length L. How far x will be found? The constant of elasticity of the rubber cords is and the natural length of each cord is L.
Problem 10-6 A conductive plane has a charge + Q, and each side of it to the distances x 1 and x 2 is placed a conducting plate parallel infinite. Find the potential difference between the plates. Problem 10-7 Two electrons distance r from each other, with the particularity that the speed of one of them is zero velocity and the second is directed under an acute angle to the line joining them. What will be the angle between the velocities of the electrons when they again resulting in the distance r from each other. Problem 10-8 Three small spheres of masses m, 2m and 5m, and charges q, q and 2q respectively are positioned along a straight line. The spheres are at rest at the beginning and the distance of separation between neighboring spheres is. Then, they are released. What are the final velocities of the areas where they are a great distance apart from each other? Consider that the spheres are provided along the same line.
Problem 10-9 Two metal spheres of radii R 1 and R 2 are separated by a distance d R 1, R 1 R 2. Initially, the largest area has a net charge of Q C. It connects to the smaller sphere initially discharged through a very thin conducting wire. Once steady state is reached: a) What is the net charge on each sphere? b) Find the energy of the larger sphere before making the connection. c) What is the energy of the system after connecting the spheres.
d) Show that the load is distributed in the spheres of radii R 1 and R 2 so that density of electric charge.
e) Find the surface electric fields in the fields and show that these satisfy the relation Problem 11-1
Where is the surface
In the circuit shown in Fig find load capacitor C after the circuit has been connected for a long time. Neglecting the internal resistance of the battery.
Problem 11-2 Four identical conductive plates each area S are positioned parallel to one another and equal distance d between them. Initially, the boards are unloaded, then the end plates are connected by a conductor with each other and the two plates are connected to a central battery emf which is E. What is the charge that appears on each plate?
Problem 11-3 A parallel plate capacitor A and B is constructed of square plates each 15 cm side and separated by a distance d = 5 cm apart. The plates are in the air (e o = 8.85.10-12 F / m). A small sphere coated with conductive paint hangs a piece of silk thread length 10 cm which hangs from point A located at the upper end of plate A as shown in Fig. The ball of mass m = 0.1 g and radius r = 0.3 cminitially hits the plate A. Plate A is connected to earth and the plate A is momentarily connected to a Van de Graaf generator charged to a potential of 60,000 volts. The plates are again isolated and the ball is observed that the plate moves to B and back to B several times until it stops being in an equilibrium position with the cord at an angle to the vertical.
a) Explain the behavior of the ball and find the value of. b) Calculate the potential difference between the plates end.
c) Determine the number of times (K) the ball back and forth before coming to rest. d) To a graph of the potential difference between the plates as a function of the number of twists of the ball between the plates, V AB = f (K). Problem 11-4 Given the following list of elements find the capacitance of a capacitor. - A battery of unknown emf. - A capacitor of capacitance C equal to 4.7, which is much less than the value of the unknown capacitance of the capacitor. - An unknown capacitance capacitor. - A galvanometer (whose scale is not calibrated) - Two cables. HELP:
where r is a real number. Problem 11-5 A capacitor of capacitance C o = 20 uF is charged to a potential difference of V o = 400 V and is connected to another capacitor of capacitance C = 1μF, which as a result is loaded. This capacitor is disconnected and the same procedure for loading a second capacitor of the same capacitance (C = 1μF), then a third and so on. Then the capacitors are connected in series. What maximum potential difference can be obtained in this way? Problem 6 Three parallel conductive plates are positioned relative to one another at distances d 1 and d 2. At first in the plate 1 is a charge Q and the plates 2 and 3 are discharged. Then, the plates 2 and 3 are joined by means of a battery voltage U, the plates 1 and 3 are connected with a driver. Finding that each load plate is set.
Problem 11-7 Consider the two situations shown in Fig. In the first situation are the plates of a capacitor with charge Q andQ separated by a distance x. The left plate is fixed. The second situation shown is similar except that the two plates are kept at a constant potential difference E o. The problem is to find the force F required to separate the plates a distance D x (assuming that D x << x) and suggest a method that shows how this device may be used for measuring an electric potential difference.
Problem 12-1 Find the resistance between points a and b of the circuit of Fig. R 1 = R 5 = 1.00 W, R 2 = R 6 = 2.00 W, R 3 = R 7 = 3.00 W and R 4 = R 8 = 4.00 W .
Problem 12-2 To determine the location of damage the insulation between the conductors of a telephone bifiliar line of length L = 4.0 km at one end of this place a source of emf E = 15 V. With this is that if the opposing ends are separated by the battery current is I 1 = 1.0 A, and if they are joined by the battery current is I2 = 1.8A. The resistance per unit length of conductor is r = 1.25 / km. Find the point where it is deteriorating and the insulation resistance at that point. The battery resistance is neglected. Problem 12-3 Find the condition to be satisfied by the resistors R 1, R 2 and R 3, so that the arrangement of the figure on the left is electrically equivalent to the arrangement of the right figure formed by resistors r 1, r2 and r 3.
Problem 12-4 In the circuit shown in Fig a voltmeter is connected between the ends of the resistance r 1 and r 2 taking readings of 6 volts and 4 respectively. When the voltmeter is placed between points A and B it shows 12V. What are the real voltage drops in r 1 and r 2 ? Neglect the internal resistance of the source in the circuit.
Problem 12-5 For the diode D 2 of the circuit shown in Fig a current I 2 = 2 mA. The characteristics of current - voltage of each of the diodes are shown in the attached figure. Finding the currents I 1, I 3 and the electromotive force of the U or source. The resistor values are: R 1 = 100 W and R 2 = 50 W.
Problem 12-6 To charge a battery electromotive force E = 12 V from a voltage source V = 5 V, is built a circuit which consists of an inductor L 1 = H, a diode D and a switch K, which opens and closes periodically at intervals of time t 1 = t 2 = 0.01 s. Determine the average current I p that load to the battery.
Problem 12-7 In the circuit of Fig all voltmeters are equal. The emf of the battery is 5 V and internal resistance is negligible. If the voltmeter indicates higher V 1 = 2.0 V What is the reading of the other two voltmeters?
Problem 12-8 In the scheme shown in the figure, the emf of the battery E, its internal resistance r is the external resistance R. By closing the switch K 1 galvanometer needle tilts to an angle. What angle tilts the galvanometer needle, to be closed if K 1 K 2 is also closed? The inclination of the needle is proportional to the charge passing through the galvanometer.
Problem 12-9 The configuration of the figure consists of constant cross-section wire. The side of the larger square is one meter long and wire has resistance r. Determining the resistance between points A and B.
Problem 12-10 Four equal ammeters and a resistor R are connected as shown in Fig. The ammeter A 1 indicates a current I 1 = 2 A, the ammeter A 2 a current I 2 = 3. What current flows through the ammeter A 3, A4 and resistor R? Find the relationship (r = internal resistance of the ammeter).
Problem 12-11 Two resistors R 1 and R 2 are connected in series to a source of emf E. as indicated in Fig. Find an expression to calculate the theoretical voltage drops in the resistors R 1 and R 2 from experimental measurements with a voltmeter of internal resistance R. Neglecting the internal resistance of the source.
Problem 12-12 50 voltmeters are connected equal and different ammeters 50 as shown in FIG If the first reading voltmeter V 1 = 9.6 V, the first and second ammeters are I 1 = 9.5 mA, I 2 = 9.2 mA respectively .What is the sum of the readings of the voltages indicated by the voltmeters?
Problem 13-1 The flat plates of a capacitor with space d are positioned perpendicularly to the magnetic field intensity B as shown in Fig. In the vicinity of the cathode is a source of slow electrons that break in different directions toward the plates. Holding what? Capacitor voltage electrons gather at the anode?
Problem 13-2
A circular loop of wire in the radius to diameter has a bonding wire thereof, parallel to the horizontal axis OO 'which can rotate around the loop, see figure below. The mass per unit length of the loop and the bridge is the same and equal to r. The current flowing in the loop is equal to I. The loop is in the gravity field and the magnetic field intensity B directed parallel to the gravity field. What angle tothe vertical with respect to the loop deviate?
Problem 13-3 The figure below shows a DC motor which comprises a conductive ring on which moves the end of the rod of length r which is pivotable about a hinge located in the center of the ring. The whole system is in the presence of a constant magnetic field intensity B. Determine the stationary angular speed and the current in the circuit, if the friction force in the movable contact with the ring is F.
Problem 13-4 A ring-shaped wire has a conductive connection along a diameter. The capacitors C 1 and C 2 are connected to the semicircles as found in the figure below. The ring is placed in a linearly increasing magnetic field induction B (t) = B or T / T perpendicular to the ring plane. At some point the connection is removed, then the field keeps changing. Find loads established in capacitors.
Problem 13-5 The circuit shown in the figure below comprises a battery which supplies an emf E, an inductor L, two capacitors C 1 and C 2 and a switch K. If the switch is closed at t = 0 what is the maximum current through the coil?
Problem 13-6 An inductor L is connected in parallel with two resistors R 1 and R 2, as indicated below. Across the windings of the coil and perpendicular to them is a constant magnetic field as shown. If just at the time when the magnetic field is suppressed by the resistance R 1 circulating a current I which is the heat dissipated through each of the resistors?
Problem 13-7 Two coils, which are inductors L 1 and L 2 are connected through the switches K 1 and K 2 with a capacitor C as shown in the figure below. At the initial instant both switches are open and the charged capacitor to a voltage V o. First switch closes K 1, and when the voltage across the capacitor is zero, the switch closes K 2. Determine the maximum and minimum current passing through the coil L 1 after closing the switch K 2. The resistances of the coils are neglected.
Problem 13-8
For a non-conductive surface rolls without slipping a ring uniformly loaded mass m. After connecting an induction magnetic field B perpendicular to the plane of the hoop, the hoop strength of pressure on the halved surface. How fast rolling ring if its charge is q? Problem 13-9 On two parallel metal bars forming an angle with the horizon sliding rod length and mass m b. The two parallel bars are joined at the bottom by a capacitor C. The whole system is in a homogeneous magnetic field of value B directed vertically upwards. Initially the sliding rod is at a distance from the bottom. Determine the time it takes to slide the rod on the bottom. How fast will end?. Neglecting the resistance of the rods.
Problem 13-10 The circuit shown in the figure comprises a battery which supplies an emf E, an inductor L, a capacitor of capacitance C and a switch K. If the switch is closed at t = 0 what is the maximum current through the circuit? What is the maximum voltage that presents the capacitor?
Problem 13-11 In the circuit shown in the figure, the maximum currents hállense in the inductances L 1 and L 2 after closing the switch K. The capacitance is C, and the initial voltage U.
Problem 14-1 In the focus of a parabolic mirror of radius R and focal length f is placed a thin black disc whose size matches the image of the sun at the focus of the mirror. What is the highest possible value of the temperature record? The sun is a good approximation of a black body temperature T = 6000 K. Neglect thermal conduction to the surrounding air. Problem 14-2
Calculate the average surface temperature of the sun and earth. Assume that the sun and the earth can be considered as black bodies and that the energy absorbed by the earth comes from the sun only.The radius of 8 the sun is R s = 7.10 m and the average distance earth sun is R st = 1.5.1011 m. The energy per unit time 2. absorbed by the land area is E o = 1.36.103 W / m Problem 14-3 How sunlight spacecraft orientation relative to the sun if half of the surface of the ship is a reflective surface and the other half is black and absorbs solar radiation completely? The ship is spherical and its center of gravity is located at its center. Problem 14-4 The energy emitted per unit area and time, E, of a body at a temperature T is given by the Stefan-Boltzmann 4, -8 2. law E = s T where s = 5.67.10 W / m It is known that the energy per unit time that reaches the earth per 2. 11 unit area is E o = 1400 W / m The earth-sun distance average is 1.5 · 10 m. A vessel made of iron orbit around the earth. The melting temperature of iron is 1535 ° C. A measure that maximum distance from the sun the ship should be located so that it begins to melt? Problem 14-5 The surface of a space station is a blackened area. The surface is maintained at a temperature T = 500 ° K due to the operation of technical equipment at the station. Determining the temperature T x of the surface of the station if it is enveloped by a thin sheath of black metal almost the same radio station. Problem 15-1 Measurements show that a semitransparent mirror allows passage of 1/5 of the intensity of light impinging on it. If two identical mirror of this kind are placed perpendicular to the incident beam, could be expected that this pair of mirrors dejasen spend 1/25 of the light intensity. But actually about 1/10 of the incident intensity passes through these What is the reason for the above? Problem 15-2 A hemispherical lens radius R = 5 cm and refractive index n = 1.52 is in the air and receives on its flat face perpendicular one cylindrical beam which covers it completely, fig.a. Marginal rays are defined as those which emerge tangentially to the curved surface of the lens. Paraxial rays are defined as those which impinge very close to the optical axis of the lens.
a) Determine the maximum radius of the beam of parallel rays are refracted ball directly in the face of the lens.
b) Determining the minimum radius of the ring of rays parallel to the optical axis after impact the back curve surface, leaving the lens parallel to the optical axis. c) Find the distance along the optical axis between the point where the marginal rays concur and presenting the point where paraxial rays. d) Now a display P is positioned at a distance X from the center of the sphere, parallel to the flat surface of the lens as shown in figure b, for x greater than the focal length determined by the paraxial rays readio of the light spot on the screen as a function of X. Supplementary Problems
1) "Return." Why, a spacecraft returning to Earth's atmosphere its temperature is increased? Why meteors entering the atmosphere may even melt and even evaporate? 2) "Invent yourself". Design and somehow try to photograph physical processes that occur very quickly. Justify the physical value of his photograph. 3) "Skein of wool". A grandmother is a skein of wool ball. How the mass depends on the diameter of the handles of the same? 4) "Nailing tiptoe". Suppose you have to drive 1994 nails (L = 50mm, Ø = 2.5 mm) on a wooden plank. What kind of hammer you choose to do the job with speed and quality? (Hammer type refers to mass and length of the handle). Consider if the board is: a. b.
walnut. oak.
5) "Strange maneuver." Immediately after dropping the atomic bomb on Hiroshima on August 6, 1945, Colonel Tibbets, commander of the B29 Flying Fortress was the following maneuver: turned 60 ° and swooped.With what goal? What should complete the maneuver? Why not turn 180 degrees? Discuss your answers. 6) "Oscillating." A light rod of length L is fastened by one end to a negligible friction hinge, and the other is linked to a spring constant k. Determine the period of small oscillations of the shaft depending on the position of the mass m l.
7) "Viscosity". Determine experimentally how the viscosity varies depending on the vegetal temperature. 8) "Experiences with a cassette." Measure the thickness of a cassette tape of a sound. Calculate the length of a cassette tape of 60 minutes. Measure the speed with which the tape advances.
9) "More with a cassette." Look for the cassette 60 min. an expression showing the distance H in the figure, depending on the length of tape that has passed to the other spool. What, should keep relationship with respect to R and D d What is the minimum value of H?
10) "leveling". The tube as shown in the figure contains water in its branches. Initially there is a difference in the levels H and eventually equalize. Evaluate the speed-leveling for given H and temperature T = const also given. Consider two cases: a. b.
In no air tube. In the tube there is air at atmospheric pressure.
Proposed problems
1) "Two drops which solidify." Two drops of molten tin and zinc are allowed to cool slowly. It turns out that the drop of making spherical tin and zinc defined acquires flattened edges. How can you explain this? 2) "Heat transfer". Investigate cases: T 1 and T 2 T 2.
heat
transfer
through
a
vertical
column
of
water
in
two
3) "inflate pump". Investigate the dependence of the internal pressure of one balloon to inflate (or pump inflation) of its diameter.
4) "Rainbow". Explained by a model the formation of the rainbow. 5) "balloon". A balloon is inflated with helium or oxygen and released, it appears that this begins to rise, to what maximum height the balloon ascends? 6) "Water Sense." How not destroy a tube carrying water, you can determine which way she runs? Assume that you can access only mentioned tube 2m. 7) "Splash". A pebble dropped into water from a height H. What is the maximum height to which water droplets jump? 2
8) "between a hot air pipe." A vertical tube 1m height and cross sectional area of S = 50 cm is open at both ends. At the bottom heater is installed power P = 100 W What is the air velocity in the pipe? What is the cost 3 (in m / s) of air through the tube? 9) "Cone rolling on a table." Cone, with its apex fixed at a point lying wheel without slipping on a horizontal surface. The cone height is h and the base radius is r. What is the total angular velocity full cone if the velocity of the center of the base v constant?
PHYSICAL FUTURE IV TOURNAMENT 1996 Proposed problems 3
1) "A balloon and a crank." A balloon of 1000 m of volume is in equilibrium at a height of H = 300 m on the surface of the Earth. Suddenly he sits on a stork (m = 10 kg). Does he descend the balloon? How? 2) "Volume of a whale." How to determine the volume of a whale swimming in the coasts of Greenland? 3) "Power a small motor." Determine the power of an electric motor toy. Determine also its efficiency. 4) "lunar atmosphere." Suppose that on the moon, it establishes an atmosphere with a composition similar to the Earth. What are its parameters and properties? What happens if I get on with it? 5) "Football in the Moon." Surely the moon could be a resting place for earthlings. Describe and special situations that might occur in the Moon compared to Earth playing a football game. 6) "fragile table." When in the center of a square table placed side by a body whose mass exceeds the value The four legs are broken simultaneously. Find the set of points where you can put a body mass /2 without breaking any leg. 7) "Propose yourself." Propose a theoretical physics problem and solve it. 8) "Propose yourself". Proposes experimental physics problem and solve it. 9) "Sea optometrist." If a person looks good in the water, what type of lenses you need to look good in the air?
10) "Flashlight, holes and screen." Take a flashlight and place it in front of black cardboard with various holes of 1 mm, 2 mm, 3 mm, multiple holes or better experience with the holes you want. Projected onto a screen at various distances. Say observe and explain. 11) "boiling water." Try communicating heat to boil water from above. Explain what it is. 12) "illuminating with economy." We need to save energy, make a parallel between different light sources: common bulb, halogen lamps, mercury, sodium, fluorescent, candles, LED etc.. Mention its working principle, its spectral quality and energy efficiency. V FUTURE PHYSICAL CONTEST 1997 1) "Hot and cold". If fully opens cold water tap, a tub is filled in t 1 = 8 min. If placed at the exit of the key then shower hose with filling time increases to t 2 = 14 min. When the cold water tap is closed and fully open the hot water is filling time t 3 = 12 min, with shower hose and extends time t 4 = 18 min. How soon the tub was filled completely open if the two keys simultaneously without shower and then shower?
2) "Leaving the Moon." What part of a spaceship in circular orbit of radius 2R L around the Moon (Moon 3 radius R L = 1.74 × 10 km) should be fuel, so as result of a short-ignition engine, you can leave the Earth's gravitational field? The exit velocity of the gas jet is u = 4 km / s. The acceleration of gravity at the surface of 2. the moon is L g = 1.64 m / s 3) "Injecting". Investigate factors that depend on the output rate of a liquid from a syringe with the force F applied to the plunger. 4) "Curiosa water pump." In the next figure shows a device used to raise water to a height h of a stream. K 1 and k 2 are two valves that open and close. Investigate factors that determines the amount of water that can be stored in a given time and explain the operating principle of said device
5) "Sifting water." The container has a number of very small holes in a base and depositing nevertheless this water to a certain height, the container empties no. To investigate this phenomenon
6) "artificial gravity." In a space station project aims to create an artificial gravity. Could be a cylinder of radius r = 300 m, rotating with an angular velocity w about the axial shaft linked with an inertial reference systemS. a) What should be the angular velocity w for a body in the inner surface of the cylinder experiences a weight on the surface of the Earth? b) If the station an object falls from a height h = 10 m
Describe qualitatively the motion of the object in the reference system S. Determine the time required for the object arrives at the floor, or drop point.
c) If the object is launched from a ground point with respect to the return on the floor:
Is there a time limit? So that return to t = 2.5 s in which direction and how fast over the season should be released?
7) "Doing donuts." Have you noticed that when preparing donuts, sometimes when they are floating in oil begin to rotate at times significantly faster. Propose a theory to explain the rotation. Experiment if it thinks fit. 8) "Freedom". Proposes interesting experimental problem and solve it. 9) "Tube" U "spinning." In a U-shaped tube are poured two immiscible liquids whose densities relate as 2:1. While the tube is stationary, the area of separation of the liquid passing through the axis of symmetry of the tube. Whither moves and how much the surface of separation if the tube is rotated with respect to the -1? symmetry axis with angular velocity w = 5 s
10) "Helicopter pedal." Someone built a pedal helicopter propeller low mass and diameter d = 8 m. Can a pilot mass M = 80 kg take off on that device? Physical Futures Tournament VI 1998 1 "starting to fly." Early balloons or dirigibles aerostatic were inflated with hydrogen. During the First World War these airships were an easy target as a projectile however small were burnt, thus disappeared from the battlefield. But one day in 1918 over the skies of London received an airship appeared many impacts without fire or fall to the ground, had been inflated with helium. But someone said: "The density of helium is nearly twice that of hydrogen, therefore the lift force of the balloon must be halved." Is this correct? Fundamente.
2 "A paradox." A bogie which has the shape shown in the figure is filled with water. Average pressures on the front and rear walls are equal, since only depend on the height of the liquid column and density. The front wall being larger than the rear area, should also be higher than the fluid force exerted forwards than backwards and exerts itself wagon should move forwards. Where is the error of this reasoning? Fundamente. 3 "playing pool". They are fashionable billiard tables whose edges are heated. What is the benefit? How does this benefit depends on temperature? 4 "Do not panic." Lately there has been speculation about the possibility of an asteroid hitting earth. Describe what would happen if an asteroid 10 km in diameter and density of the Earth collided with the earth. 5 "Resources housewives." Without breaking it is possible to determine if a chicken egg is raw or cooked. Exposing its corresponding theory. 6 "Move granted." Sit in a chair on a fairly smooth surface. Stretching strong feet and then gently picking them up you can move from corner to corner of the room. Apparently this violates the principle that a system can not propel yourself and external force required to accelerate. Since no external force applied on you how does it move? How do you resolve this paradox? 7 "Speaking of football." Estimate the speed with which you can kick a soccer ball. Will there be a maximum limit speed with which to shoot a penalty kick? 8 "Tennis Shoes". Tennis shoes must have certain features such as allowing a rapid increase in speed or braking sharply to a basketball player, which can be determined by the coefficients of static and kinetic friction of such shoes. Measure friction coefficients of different tennis shoes. Do you agree with this there is the maximum speed limit at which an athlete can move forward? PHYSICAL VII FUTURES TOURNAMENT 1999 1. - "Pendulums Pendulums and" One way to demonstrate the rotation of the earth on itself is due to the French Foucault. A pendulum swings on a plane. To make it oscillate but it appears that this plane rotates as time passes. Foucault is assumed as the plane of oscillation of the pendulum that changes should be the rotating earth. Analyze the change of direction of the plane of oscillation of a pendulum in your area as the Earth rotates beneath it. To do this perform the following steps:
Put to swing pendulums of different lengths and observe the variations of the plane of oscillation. Clearly state your conclusions. (Note: It is desirable that the length of the pendulum is large, why?) Measure the angular speed of rotation of the planes of oscillation of several pendulums. Can you state some regularity? Describe it with their conclusions. From previous measurements determine the angular speed of the rotation of the earth on itself. For the above purposes what is most privileged site, the North Pole or Terrestrial Ecuador? Explain and demonstrate.
2. - "For kids" ". Discuss (preferably in digital form) the flight of a soccer ball to be shot by a player from the point of the twelve steps. To do this run the following:
Note many successful launches from penalty kick point and sort from various points of view such as paths, flight times and others that present some interest for physics. For major classifications described in the first paragraph explaining the shape of the path followed by the ball specifically indicating the role of air therein. Measure the flight times and set its analysis and conclusions. Note force considerations mean that the player hits the ball, the contact time between the shoe and the ball caster, size and mass of the ball,
the friction force with the air and other amounts considered material such as whether the ball is fired in Cartagena or in Tunja, or if the ball rotates or not. Based on the analysis performed to determine the maximum initial speed (immediately after the shooting) that a player can print to a soccer ball.
3. - "Human warmth". Determine how much heat energy generated by the human body in a day (in Watts). Describe your method of scoring the theoretical solution on which it is based. 4. - "Jet fly." A bottle lies within a fly on a precision scale. Does it change the scale reading if the fly flies up or down or sideways? Do they change depending readings if the bottle is covered or open? Normally fly flapping fly. If the bottle fly flew by jet method (taking environmental air slowly and violently expelling) what are the answers to the above questions? 5 "See in the dark." What is the maximum distance at which a dark night you can see the light of a match (phosphorus) without using any instruments? The solution of this problem should consist of two parts. First we must carry out the experience and report on the observed, and secondly to do an exhibition in which theoretical aspects are addressed such as luminous intensity of a light source and high power that impresses the human eye . 6. - "Arson remote" Legend has it that the Greeks, led by Archimedes set fire to the Roman ships using mirrors focusing sunlight on them. Analyze the feasibility of both not this company but its effectiveness. Apply your analysis to a real case: a table incinerate dry 10 kg located 10 m from the mirrors in a very sunny day. Analyze the veracity of the story and find the probability of success of the ruse of Syracusan wise. 7. "Speed limit." When an object falls vertically its speed does not increase indefinitely but due to friction with the air reaches a maximum speed limit known generically as speed. Measure the speed limit of a ping-pong ball is released from rest. After fully describe the measurement method for an investigation into the relevant theory. 8. "On your bike". Analyze the motion of a bicycle from two points of view: First, the stability conditions. Second, the effect of air resistance on the maximum possible speed. 9. "Heavy clouds." Clouds are formed by water drops. Water is 800 times denser than air. Why then the clouds will not fall like rocks on earth? Do not just qualitative responses, perform the relevant computations. PHYSICAL VIII FUTURE TOURNAMENT 2000 1. - "Raindrops" is often seen in a wet roof water droplets are formed which eventually break off and fall to the ground. Determine, experimentally and theoretically the dimensions and characteristics with drops of water immediately before falling. What holds the drop before falling? 2. - "How long a battery." Many battery-powered household items. You often hear that the batteries were discharged. Investigate how vary, depending on the usage time, the potential difference and current supplied by a battery. Design and conduct appropriate experiments to test his claims (limit your experiments to A or AA batteries). 3. - "Many photons." Albert Einstein conceived the idea of considering the light as consisting of "photons". Find out how many photons per second standard bulb emits 100 watts of power. Clearly state the assumptions on which it is based to calculate your answer. 4. - "A new orbit." Find the path to change the orbit of a satellite from one circle to another with minimal energy expenditure.
5. - "Prisma in balance." Study the equilibrium conditions on the water surface of a prism of wood density 0.5 3, g / cm the cross section is an equilateral triangle knowing that their length is greater than the side the base of the triangle. Build the prism indicated experimental and test accordingly. 6. - "Sunrise and sunset" Some authors claim that 20 minutes later that "indeed" the sun has set on the horizon we can still receive sunlight. Show the truth or falsity of this statement. If this were true it should not happen we start seeing "leaving" the sun 20 minutes before sunrise the place? 7. "The proper angle." An old game of throwing a stone on the surface of a lake or river not turbulent, so that the stone made several rebounds before finally plunging into the water. Examine how depends on the number of rebounds in terms of launch angle and speed, weight or shape of the stone. Determine under what conditions a stone ball can bounce. Is there a limit on the number of boards that can "optimal" stone? 8. "Like in the movies." In some cowboy movies shows that the wheels turn in the opposite direction to that actually do, ie, the car moves to the right but it is observed that the radii of the rotating wheels counterclockwise.How do you explain this paradox? Confirm your explanation with a similar experiment. 9. - "Delicate walls." Ingéniese a method for measuring the thickness of the walls of a soap bubble and take it to the practice. PHYSICAL IX FUTURE TOURNAMENT 2001 1. - "Aircraft Constructor" With a sheet of legal size paper builds a plane. Win which: a. b. c.
make it fly farther, do fly for longer, and explain how and why these records were achieved.
2. - "Sinking and jump". A tennis ball or similar is kept submerged in a pool. After releasing jump out of the water. Determine the height jumped out of the water in terms of the initial conditions (depth and other parameters).To simplify the calculations can replace the tennis ball on a wooden bucket. Ignore friction. Support your arguments by experiment. 3. - "From snow to snow." Would it be possible from the summit of Nevado del Ruiz see the Sierra Nevada de Santa Marta? And from the Serrania de la Macarena to the previous two? 4. - "Hot and Cold." A cup of hot water freezes first a cold water after placing simultaneously in the fridge freezer? Perform the experiment and explain the different circumstances observed. 5. - "Layer upon layer." When your signature stamp on a piece of paper with a No. 2 pencil you make a small layer of graphite. Calculate the number of atoms that has the height of that layer. 6. - "To get clean" Suppose your bike does not have fenders. What is the maximum speed at which you can move through a wet highway that is not wet ... the back of the body? 7. "Eagle Eye." Einstein postulated that light consists of photons. Can the human eye to "see" a single photon? 8. "Unity is strength". A single strand of yarn breaks easily pulling end. Two, too ... But three previously gimped ... and four? Does it grow the force to break the strings with the number of them? Remember gimped yarn threads. PHYSICAL X FUTURE TOURNAMENT 2002
1. - "Smoking is not good but ...". Determine experimentally and theoretically the temperature from the lit end of a cigarette. Note that there is great variation between the instant of breathing smoke and the normal state. 2. - "Dinosaurs in extinction." Anachronistic and ill-mannered citizen smokes a cigarette in a room 4 mx 5 m by 3 m high where there are 20 people. How many molecules of smoke and ash how many enter each attendee lungs? 3. - "Good winds." What are the ranges of wind speeds that occur on Earth? It is known that not only on Earth but also in some other solar system planets there winds. What are the wind speeds on the different planets in our solar system? What is the speed of sound on these planets? 4. - "... When it dawns." Since when the day is 24 hours? It also should be investigated since when man divided the hour into 60 minutes and a minute into 60 seconds. Where, when and how the man knew that the earth takes about 360 days for a spin around the sun? 5. - "Fattening or thinning." Does the earth mass remains constant or increases or decreases the contrast in significant quantities? Describe what could happen in either case. 6. - "Warming up the ice." On a table are taken at room temperature, a bowl of water and a large plate empty. The fridge freezer will draw two ice cubes equal, one is placed on the plate and the other in the water container. Which of the cubes will melt first? Explain what happened using the appropriate physical principles. 7. "Indurain do not know." May ride a bike without taking the handlebars. Describe how this is possible. In particular, explain how to proceed to describe an "S" on flat land. There is sufficient qualitative description.Quantitatively substantiate their explanations. 8. "Astronomers in action." How are the distances between stars and the distance of the star to the Earth? In particular, how the distances were determined Earth - Sun, Earth - Moon, and the diameters of the Moon and the Earth? 9. "Water world." In the competitions of "diving" is used springboard for the athlete. What is the reason for using this device? What features should have a good trampoline? 10. "Ptolemy or Copernicus?".? Definitely still and the sun is just the solar system revolves around him? PHYSICAL X FUTURE TOURNAMENT 2003 1 - Electron Marathon. Actuating the switch that turns the bulb of a lounge shows that almost instantly begins to illuminate the bulb, which means that there are electrons flowing through its filament. How fast electrons move once you flip the switch? How long did the electrons that were in the terminals of the switch to get to the bulb? 2 - Hole or hole and what will be the minimum size (volume) of a black hole? In these conditions, how much is the gravitational acceleration on its surface? What is the escape velocity from it? Escape velocity is the speed that an object must be to never again fall on the surface of the celestial body that launched 3 - Experimental and theoretical. Usually happens that the smallest angle of inclination of an inclined plane, a cylindrical rough wheel on it. But if placed together two such cylinders in the way suggested in the figure, the case that the angle of inclination of the plane to be increased without sliding cylinders. Explain why this happens and to determine the relationship between the physical variables involved in this. Determine the maximum angle that can take the plane to the cylinders do not move. From the experiment to determine the relationships between the relevant friction coefficients.
4 - Examination for myopic and presbyopic premature. On a white card two circles are painted black radio 1 cm each, so that their centers are far 2cm. Experimentally determining the maximum distance at which the normal human eye individually distinguishes the two circumferences. Explain the observed physical and physiologically. 5 - Go back and play. What is the maximum speed that a football player can print to the ball? An interesting way to find out is to experimentally determine the average speed of the soccer ball in different shots on goal. This can be examined videos of these exciting plays to "measure" the distance traveled and the time used to calculate the average speed. 6 - high and long jump. Knowing the temperature of the solar surface can determine the average speed of the molecules of the bark of the sun. These speeds are enormous. Why these molecules do not escape the sun?That is, since the molecules that make up the Sun collide violently with each other how can the sun not only does not disintegrate but also retains its spherical shape? 7 - up and down. Often heard saying that lightning "falls" from the clouds toward Earth. Do you have full regard this statement? You actually raise or lower the beam? Browse from qualitative insights but physically very accurate, the conditions of production of the rays and their characteristics. 8 - Strong and weak. A Flea, a Man and a jump Elephant virtually the same distance. Will this fact some explanation from the physical point of view? Can it be said that the flea is physically very powerful because it can jump almost a thousand times its own height, while the elephant is a "chicken" because it is not able to jump, but the fourth of his height? 9 - Hoop dancer. Investigate, describe and explain the motion of a ring to descend vertically placed cylindrical rod. If the cylindrical rod moves with a certain speed above the rotating ring remaining at a constant height.Investigate and explain this mechanism. 10 - One on one. Currently is often the foil. If the paper was in fact how many aluminum atoms only fit in the thickness of the leaf? PHYSICAL FUTURE TOURNAMENT XII 2004 1 - In April thousands of water. Determine the speed of raindrops falling on the floor on a rainy day. What the next rain this speed will be different? 2 - Water not drink ... Put the stove a pot lid as shown in the figure, nearly full of water and wait until it boils. Determine the speed of the water vapor out of the mouth of the teapot. Describe the method used in the measurement. Does it change the speed by decreasing the amount of water remaining in the pot? Explain. 3 - Heat with color. Turning on a light bulb filament gets its glow. Determine the temperature of the filament of a tungsten bulb 100 W power line connected to the house at 110 V. Also determine the temperature of the space between the filament and glass bulb. Determine the temperature of the glass bulb. What raises the temperature of the glass of the bulb? Determine the temperature finally a 3 room of 50 m "completely isolated" and illuminated by the bulb. 4 -! Blows and fly! Figure crudely tries to show a seed produced by the famous flower "Dandelion" (Taraxacum officinale). Each seed consists of the seed itself and lots of very thin filaments that serve as a parachute. After observing and describing several flights of these seeds make a study of their movement from the point of view of physics. Under what conditions seeds rise, or fall, what acceleration do, forces acting on them, push paper, its origin and its relation to the weight of the seed, 2.
etc.
5 - Sun, heated slowly. Intensity of solar radiation on the earth's surface is I = 1370 W / m If we expose a
long iron block to this radiation reach what temperature? Determine the intensity of solar radiation and temperature on Saturn will reach beyond that same iron block. 6 - Stargazers lunatics. Suppose we set up a base on the moon astronomical observation and we have the task of describing the rise and the sunset What similarities and differences do you observe about the release and setting of the sun as seen from the Earth? Every day we see the moon rise and set but altered by successive transformations because phases. ? "Day by Day" from the moon as we see the Earth? Do they depend these observations of our location on the lunar surface? 7 - Improvising gravities. If from our land area launched a ball vertically upward with a speed of 10 m / s, after approximately two seconds back in our hands. If now we are located in space far from any star, inside a cylindrical vessel of 10 m radius rotating uniformly with a period of 6.28 s (= 2pi s) and being in the "floor" launched vertically upwards same field with a speed of 10 m / s, how much time after our hands again? What "high" enough? Fully describe the "pseudo gravitational field" that is experienced within the ship and the motion of the sphere.
8 - Is it that they lack money? Currently needed in any school or a voltmeter and an ammeter. But in 1826 when George Simon Ohm enunciated his famous law had none of these instruments. Verify, using only instruments that could have used Ohm, Ohm's law.
1st Secondary Notes:
Read the review and consultation if you have questions. DO NOT put your personal data or the question paper or leaves your solutions!, We will give you a form for that. The conceptual part is worth 40% and 60% practical part. Have a time of 2 hours. Conceptual part
1)
Suggests a way to measure: a.
the thickness of a sheet of paper
b.
the thickness of the film of a soap bubble
c.
the diameter of an atom
2)
3) 4) 1)
Suggests a way to measure: a.
Earth radius
b.
the distance between the Sun and Earth
c.
the radius of the Sun Can be measured along the length of a curved line? If possible how would?
What are the prefixes you know who symbolizes each? Practical part The astronomical distances are so great, compared to land to be used much greater length units to more easily understand the relative distances between astronomical objects. An astronomical unit (AU) is equal to the average distance from the Earth to the Sun, ie around
which
one astronomical
. A parsec is the distance at unitsubtends an
angle (One second). A light year is the distance that light in a year, traveling at a speed in a vacuum, a.
Express the distance from the Sun in tierrra parsecs and light years
b.
Expressing a light year and parsec in miles.
a.
A unit of time that is sometimes used is the microscopic physics tremolo. A tremolo
2)
equals b.
3)
Is there more tremolos in one second than seconds in a year?
Humanity has existed for some years while the universe is around years. If we take the age of the universe as equivalent to a day, how many seconds long has mankind? A spacecraft can travel at a speed of
a. b.
,
What is its speed in light years per century? The nearest star to us is Alpha Centauri and is for
light years away, how long the
ship would take years to get to Alpha Centauri? Discuss your answer.
2nd of Secondary Notes:
Read the review and consultation if you have questions. DO NOT put your personal data or the question paper or leaves your solutions!, We will give you a form for that. The conceptual part is worth 40% and 60% practical part. Have a time of 2 hours.
Conceptual part We can sort the events in time. By example, the event may precede the event b and c
1)
to continue the event, which sets a temporal ordering of events a, b, and c. Hence, there is a sense in time that distinguishes the past from the present and the future. So time is a vector? Explain. 2) a.
3)
Can combine two vectors of different magnitude to give a zero resultant?, Can do three vectors? b. Usually is studied addition, subtraction and multiplication of vectors. Why do you think that is not considered vectors division, is it possible to define such an operation? The wave motion appears almost in all branches of physics. We're all familiar with water waves. There are also sound waves, as well as light waves, radio waves and other electromagnetic waves. And last but not least the mechanics of atoms and subatomic particles
4)
called wave mechanics. How many types of waves you know? Which are? Give some examples. Treatment is suitable geometric surfaces whereas it finds and other discontinuities in the
1)
wave propagation are very large compared to the wavelength. What uses geometrical optics waves?, You can make a geometric study using such acoustic waves or seismic waves? Practical part A motor boat is headed in the direction N30 E to 25 miles per hour in a place where the current is such that the resulting motion is 30 miles per hour in the direction N50 E. Find the current velocity (magnitude and direction)
2) a.
A tuning fork oscillates with a frequency of 440 Hz The speed of sound in air is 350 m / s, determine the wavelength of the sound produced.
b.
c. d. 3)
. Find the wavelength
corresponding to the frequency of , Which is the frequency of the red visible spectrum. Draw two waves specifying its wavelength and amplitude. Obtain the relative wavelength.
Suppose that a certain concave spherical mirror has a focal length of 10 cm. Find the location of the image for object distances a. 25 cm b.
1)
Light propagates in the speed vacuum
10 cm
c. 5 cm Describes the image in each case. 2nd of Secondary PART SOLUTIONS PRACTICE Denoting the boat speed V B, the flow velocity by V C, and the resultant velocity of V, we have V = V B + V C, so that V C = V - V B.
To calculate V C Note that the angle between V and 160 V, thus:
the law of sines is the angle
C
is
. Consequently the
direction of V C is S 42 E. 2) A significant relationship between the wavelength velocity
, The frequency
and the propagation
this is
We then
Once again applying the relationship between the wavelength propagation velocity
, The frequency
and the
we have
When comparing the results of these last two examples, note the difference in the orders of magnitude when it comes to sound waves and light waves. The relative wavelength will
.
3) a.
The mirror equation is:
, Where q = 16.7 cm. The positive sign indicates that
the image is real. The increase is:
b.
c.
, Where M = -0,668 therefore reduced image size
and this inverted. And q is positive then the image is located on the front side of the mirror and is real. The object is located in the focal point. Q = ∞, light rays originating from an object located at the focal point of a reflecting mirror so that the image is formed at an infinite distance from the mirror, ie , the rays traveling parallel to each other after reflection. q = -10 cm, the image is virtual, ie is located behind the mirror. Its increase is M = 2, ie the image is two times larger than the object and is standing. The negative value of q means that the image is behind the mirror is virtual.
3rd of Secondary Notes:
1)
Read the review and consultation if you have questions. DO NOT put your personal data or the question paper or leaves your solutions!, We will give you a form for that. The conceptual part is worth 40% and 60% practical part. Have a time of 2 hours.
Conceptual part We are told that the acceleration of a falling object due to gravity is the same for all bodies. However, that is something that is not met in direct observation. In everyday objects do not fall in the air at the same speed: for example a coin and a piece of paper not reaching the ground at the same time. It is assumed that the cause is air resistance, but are we
2)
sure?. Outside of trying to test in a vacuum, something not readily available, can you think of a simple experiment to give evidence that the acceleration is the same for all bodies? Explain, using the Bernoulli equation, the action of a parachute to slow the free fall.
3)
According to a famous legend, when ships Romans attacked Syracuse in 214 BC Archimedes unless the city. Soldiers stood on the shore, each with a large mirror. At a signal, the soldiers incendiaros the Roman fleet, reflecting the sun's rays on the ships. This story has
1)
any validity practiced? That is the trick of Archimedes might have worked? Practical part The angle at which the sun can be seen from Earth (angular diameter) equals approximately
. The radius of the Earth is
of the average densities of the Earth and the Sun (1 year
. Determine the ratio ,
, V is the
volume of a balloon and R is the radius). 2)
A deposit without lid rectangular (Figure 2) moves with acceleration.
The tank is filled with water to a height h. What should be the acceleration to the water begins to overflow?
3)
A spherical lens has two convex surfaces of radii 0.80 m and 1.20 m. Its refractive index
is . Calculate its focal length and the position of the image of a point 2.00 m from the lens. 4) In the last seconds of free fall, an object travels three-quarters of the way full. How long falls and from that height? 3rd of Secondary CONCEPTUAL PART SOLUTIONS 1) The experiment demonstrates that the doctrine is a surprising simplicity. Take a coin or medallion, on which you will place a piece of paper, making sure it is flush with the edge. Lift and drop the metal object horizontally, with the paper on top. Observe that both, paper and metal, come together on the floor. If the acceleration of the two materials were different, the role left behind. If happen to think it may not be the same acceleration that keeps the piece of paper on the coin, if no air pressure, try again slightly bending the paper. The result will be the same!. 2) The feat of Archimedes is entirely practicable. It was rebuilt in 1973 by a Greek engineer ordered 70 mirrors (each it about 1.5 by 1.2 meters) held by soldiers. That concentrated sunlight on a boat anchored to a 50 meters coast. A few seconds after the mirrors were properly focused, the ship caught fire and was eventually engulfed by the flames. To operate the mirrors must have been slightly concave, with focus placed on the boat. PART SOLUTIONS PRACTICE 1) During the movement of the Earth around the Sun on the Earth's gravitational force acts where M T is the mass of the Earth, M S is the mass of the Sun, L, the radius of the orbit and the constant G of universal gravitation. This force comunicaa Earth centripetal acceleration where T is the period of rotation of the Earth around the Sun According to Newton's second law we have:
but therefore
,
, Or but on the other hand we have
,
and . Combining these two equations we finally obtain the latest
that
.
Now using the relation finally obtain that
,
. 2)
The solution is obtained in the following figure:
3)
The following table reflects the sign convection in spherical mirrors + R Radio Concave Convex Focus f Convergent Divergent Object p Real Virtual Q Picture Real Virtual
According to these convection of signs, we write and It appears that the first surface and the second concave convex seen from the object side which is the Right. Therefore
or The fact that f is positive indicating that it is a convergent lens. To obtain the image position employ Equation Builder wear:
, With
f and the value obtained, which gives
or . Q The negative sign indicates that the image is real and is therefore left lens. Finally, the increase is
In view of the negative sign, the image must be reversed and, as M is less than unity, also be slightly smaller object. 4) t = 2 seconds. H = 19.6 meters.
4th of Secondary Notes:
Read the review and consultation if you have questions. DO NOT put your personal data or the question paper or leaves your solutions!, We will give you a form for that. The conceptual part is worth 40% and 60% practical part. Have a time of 2 hours. Conceptual part
1)
A vessel with water was placed on the end of a table as shown in Figure 1
Will you lose balance on the table if the water surface placing a piece of wood and on the latter, a weight so that both float on the water surface? 2)
Decrease the temperature of the room when we opened the refrigerator door up and running? Explain.
3)
Explains what isothermal and adiabatic processes.
4)
Demonstrates the parallel axis theorem:
, Where I is the inertia around the
axis of rotation arbitrary I cm is the rotational inertia parallel axis passing through the center of mass, Mis the total mass of the object and h is the perpendicular distance between the axes. The two axes are parallel.
1)
Practical part A rectangular tank with no lid (Figure 2) moves with acceleration.
The tank is filled with water to a height h. What should be the acceleration to the water begins to overflow? 2)
A rope, secured at the ends, is extended with the force f. In the middle of the rope is fastened a small weight of mass m.
Determine the period of oscillations small weight attached (Neglect the mass of the rope and not taking into account the force of gravity) 3) A plano-convex lens thin transverse diameter 2r, radius of curvature R, and index of refraction n 0 is positioned such that no air left
(N 1 = 1), and to the right another transparent medium with a refractive index n 2 1 (the convex face side is air). In air at a distance d from the lens on the optical axis is placed a point source of monochromatic light. Demonstrate the relationship between the image position, which is located at a distance f the lens and the source position d. Consider only paraxial rays. F 1 and F 2 are respectively the focal length of the lens in the air and to the situation when one side is in a medium with refractive index n 2. 4th of Secondary CONCEPTUAL PART SOLUTIONS 1)
The balance will not change, since, according to Pascal's law, the pressure on the bottom of the container will be the same in all places.
2)
The temperature in the room increases. The quantity of heat released per unit time is equal to the power consumed by the refrigerator, as the electrical energy is transformed into heat and finally removed from the refrigerator heat back into the room again. PART SOLUTIONS PRACTICE 1)
The solution is obtained in the following figure:
2)
The force F acting on the weight of the inclined position of equilibrium is
As can be
seen in the figure:
As the is small, we can consider that mass m. Therefore
.
while
, Where x is the vertical distance up the
Using this relationship 3)
, We finally obtain that
If to the right of the lens would then air light rays emerging from the source S0 after it is refracted at point S1 concentrate the
distance f1 of the lens.
In correspondence with the lens formula
,
(1).
We then have
.
When filling the space to the right with a medium of refractive index n2 image S0 light source moves to the point S, at a distance f from the lens as seen in Fig. For the proof of the equality sought is needed to show that
We write the law of refraction for both situations:
,
0 is the angle between the incident beam to the limit "lens-air." From the expressions obtained for small values
0,
when
sin obtain:
Because
,
Then
.
Analyzing the course of a beam of rays parallel to the optical axis moving Main can demonstrate the same way that ,
therefore:
,
(2)
From equations (1) and (2) we obtain
that was what we wanted to demonstrate REVIEW of 1 Secondary SOLUTIONS 1.
If a measured person 1782 m , How many miles it measured? a) 1782 Km b) 1782 Km c) MKM 1782 d) 0.0001782 Km ___ Solution
e)
Prefix used: Do not forget the prefixes: TAB LE 1.1 Number 10000000000000000000000000 1000000000000000000000
Decimal Power
Prefix Yotta Zetta
Symbol And Z
Oct. 18 Oct. 15 October 12 Sept. 10 June 10 March 10 February 10 10
1000000000000000000 1000000000000000 1000000000000 1000000000 1000000 1000 100 10 1 0.1 0.01 0.001 0.000001 0.000000001 0.000000000001 0.000000000000001 0.000000000000000001 0.000000000000000000001 0.000000000000000000000001
2.
Exa Peta Tera Jig Mega Kilo Hecto Deca decision centi military service mike nano peak femto ato zepto yocto
E P T G M K H D d c m μ n p F to z and
In one experiment where the temperature was measured according to the length of a body is obtained the following data: TABLE 2.1 T [° 5 C] L [m] 77.3
10
17
29
35
69
110
150
244
350
500
77.3
77.4
77.5
77.7
77.9
78.2
78.9
80.1
82.3
88.2
a) Plot in the Euclidean plane following this phenomenon. Solution What mattered was that the student discovers that the relationship between these variables is not a linear relationship (no points lie on a line)
b) Which of these two quantities is a scalar and what is a vector? Temperature = Scalar Length = Scalar c) If the length of the body 22 ° C voucher (77.48 ± 0.03) m type: Relative error L = 0.0003872 Percent Error = 0.03872% Do not forget the definition of relative error and percentage error: One result is usually expressed as: where
3.
is the average value and
is the error in x, then:
Given two vectors A 6 units making an angle of +36 ° with the axis x, B 7 units and in the negative x direction. The sum of the two vectors and the angle of the direction of the sum vector with the axis x is: Magnitude Sum : 4128 units Steering angle of the vector sum: +121 ° Solution
Let's draw the vectors in a Euclidean plane (Figure 3.1):
The vectors are movable, so that we can transfer notice the beginning "of the vector B at the" end "of the vector A. The vector sum vector will be the one that begins where the vector begins to ends and ends where the vector B:
Magnitudes us note in this graph:
From the law of cosines
get
units.
From the law of sines:
obtain that
and finally the angle
order will be: Do not forget that for any vector e n general we can write V = V or V, where: V: Vector V: Vector Magnitude (Tama no O module) u V: Vector Unit the elements can be seen in Figure 3.4
For example for = S u S u S = 4128.
Task 3: A
= A or A =
6 or A, B
= B u B u B = 7, S
REVIEW of Secondary 2 SOLUTIONS 1. The area of the parallelogram given by the vectors A = 2 or x + 3 u and - u z and B =-u x + u y +z2u is: a) 12.12 units 2 b) 34.03 units 2 c) 9.11 units 2 d) 4.99 units 2 Solution There are two types of multiplication between vectors: Dot or Scalar multiplication (which is named for the result is a scalar and the symbol used is a dot: Cross or vector multiplication (which is named for the result is a vector and a cross symbol used is: Vector Multiplication of vectors A and B is defined as a new vector which is perpendicular to the plane formed by the vectors A and B in the advancing direction of a right-threaded screw which is rotated towards the vector A vector B (Figure 1.1).
The magnitude of the vector A is precisely the searched area and is given by | A | = AB sin ) = Area (1.1) Scalar multiplication of vectors A and B is defined as the amount climbing from: A B = AB cos ) (1.2) Where is the angle between the vector A and vector B when both are starting from the same point (Figure 1.1). The vector A and vector B can be written as: A=Axi+Ayj+Azk = A x u x + A + A and u and u z z (1.3) B = B x i + B and j + B z k = B x u x + B + B and u and u z z (1.4) where i, j, k are the unit vectors (Figure 1.2) and A x, A, and z are the components of the vector A (Figure 1.3).
Note: The figure 1.2 is amplified because the magnitude of the vectors i, j and k unit applies, namely: | i | = i = 1, | j | = j = 1, ... etc.
Note: For the vector B the graph of components B x, B, B z is equivalent to Figure 1.3, which will vary the module, the direction and sense of vector B thus also the magnitudes of its components.
AzBz
Applying the definition given by equation (1.2) yields AB =AxBx+ A and B + (1.5) If A = B then A A = AA cos (0) = AA = A 2 (the angle between the vector A and the same vector A is zero), ie the magnitude of the vector A is given by: (1.6) Likewise it is evident that the magnitude of the vector B is given by: (1.7) From the definition of scalar multiplication, equation (1.2), we can solve and calculate the angle cos 1
(A B / AB) =
Substituting this value in equation (1.1) in addition to calculating the modules of both vectors, using equations (1.6) and (1.7) and similarly replaced in equation (1.1) yields: | A | = AB sin = where finally, Area = | A | = 11.9 square units 2. A simple harmonic oscillator is described by the equation Where all quantities are expressed in MKS units. Find: a. Amplitude: _______ Period: ______ Frequency: _______ Initial Phase: _____
b. The position for a time of 5 s. c. Graphing x vs. t: Solution a. A wave can be expressed according to the following equation (2.1) where A Amplitude [m] Angular frequency or angular speed [rad / s] Initial Phase [rad] t Time [s] x Vertical Variable Distance [m] t + Movement Phase [rad] it holds that: (2.2) where
F Frequency [1 / s = Hz (Hertz)] (Number of repetitions per unit time) P Period [s] (Time at which the function repeats itself) Thus using equation (2.1) can be calculated: Amplitude : A=4 and The angular frequency :
Period P can be calculated from equation (2.2) , and also the frequency f out of the equation (2.2): will eventually initial phase
b.
Position for a time of 5 [s] can be calculated by simply replacing the original equation this time:
Note: Be careful with the units. In your calculator need to enable the option to radians (Rad) so that you find the correct result. Two other options: degrees (Deg [o]) and Grads (Grad). The equivalence is
c.
Figure 2.1
3.
If you see lightning and hear their sound after 12 s, the distance to the lightning that fell this is: a) 276 m b) 6.27 m c) 2761 m d) 39756. M e) 3975.6 m f) 88.2 m Help: The speed of sound in air is: Solution
where 4.
The minimum height of a vertical mirror for a person of 1.68 m height is capable of observing their entire image is: a) 84 cm b) 27 cm c) 61 cm d) 39 cm e) 114 cm f) 100 cm g) ______ Help: Suppose that the eyes are at 10 cm below the top of the head Solution Figure 4.1 shows the trajectories of rays that leave the top of the head of the individual and his toes. These rays chosen so that enter the eye after reflection, affect the vertical mirror in points a and b respectively. The mirror needs to occupy only that region between these two points. Projecting rays reaching the eye towards the place where they form the mirror image is that this should have half the height of the individual, ie 3 ft . Note: The height is independent of the distance at which the person is located in the mirror.
EXAM 3 of secondary SOLUTIONS 1.
The constant force to be exercised by a car engine 1500 Kg mass to increase the speed of 4 Km / h to 40 Km / h in 8 s is: a) 290 N b) 167 N c) 2005 N d) 1909 N e) 1875 N f) ______ The variation of the kinetic energy is a) 9920 J b) 51,167 N c) 5005 N d) 3395 N e) 415 N f) 91,500 J The average power of the engine is a) 1930 W b) 99 W c) 88 505 W d) 895 W e) 11 458 W f) ______ Solution
a) From the basic equations of kinematics (1.1) (1.2) (1.3) where: v Speed [m / s] at any time t v 0 Initial speed [m / s] to Acceleration [m / s 2] x Distance [m] We can use the equation (1.3) to calculate the acceleration of the car:
after the 2nd Law of Newton:
(1.4) force can be calculated:
b) variation of the kinetic energy is given by the equation therefore
c)
2.
Power Motor average is given by
A gas molecule having a speed of 300 m / s resiliently collides against another molecule of the same mass that was initially at rest. After the collision, the first molecule moves at an angle of 30 ° with the initial direction. The speed of the two molecules after collision is: Speed 1: 260 [m / s] Speed 2: 150 [m / s] and the angle formed by the incident direction and the subsequent movement of the target molecule is: Angle: 60 or Solution For the study of collisions needed to use Act Momentum Conservation and Act Conservation Energy. The which indicate that: Initial Momentum = Final Momentum (Vector Equation)
Initial Energy = Final Energy equation) The situation can be schematically in Figure 2.1
(Scalar
For the x component of the movement, we have: (2.1) and for the component, because the collision is elastic can equation conservation of kinetic energy will:
get
the
In this situation: m 1 = m 2, v 1i = 300 [m / s], 1 = 30 Making m 1 = m 2 in equations (2.1), (2.2) and (2.3) get
(2.2) following
(2.3)
or
(2.4) (2.5 ) (2. 6)
From this set of equations we can solve for v 1f v 2f, 2.:
From equation (2.4): (2.7) squaring the equation (2.7) and the equation (2.5): (2.8) (2.9) Adding (2.8) + (2.9), taking into account that: (2.10) get
(2.11 ) Substituting equation (2.6) into equation (2.11), we obtain: where
in equation (2.6):
finally the equation (2.5) calculated
:
The interesting thing is that the two molecules, after the collision, move 3.
perpendicular to each other, ie . What fraction of the volume of an iceberg is discovered? a) 92.1% b) 91.0% c) 93.1% d) 87.0% e) 89.3%
f) 10.7%
Help: , Solution The density of any body of mass m and volume V is: (3.1) The weight of iceberg is: (3.2)
where: P H Ice Weight [N] m H ice mass [kg] V H ice volume [m 3] g Gravity [m / s 2] Note: Weight and mass are different concepts. Let's review The 2nd Act Mechanics : F=ma (3.3) This equation is valid if and only if the mass is a constant. The Force not a consequence of the acceleration, but otherwise, the acceleration is a result of the force The body will communicate acceleration all forces applied to it (although it is possible that some of them cancel each other), ie F indicates "the resultant of all forces." Because Force and Acceleration are vector quantities these are characterized not only by its numerical value (magnitude) but also for his guidance and direction. Taking into account these important observations, we can formulate the 2nd Law Newton as: Acceleration of a body is directly proportional to the resultant of all the forces applied to said body and directed along the result of the Forces. If the mass is not constant (ie the mass of the teacher's chalk, a rocket leaving the Earth, etc..) The 2nd law of Mechanics is given by: (3.4) where q = Momentum is the vector introduced by Isaac Newton in his famous Principia (1678), [Kg m / s] (3.5) Let us return to the concepts of mass m and weight W: U sing the 2nd law of Newton (3.3) we can write P=mg (3.6) where the weight of (vector) P is measured in [kg m / s 2 = N] and mass (scalar) is measured in [kg] For example if a person has a mass m = 66 [kg] weight in the city La Paz is: P = m g = (66 [Kg]) (9.775 [m / s 2]) P = 645.15 [N] Note: The severity in the city of La Paz voucher 9775 [m / s 2] The gravity at sea level it 9810 [m / s 2] Returning to the calculation of the volume fraction of an iceberg is discovered
The calculated weight of the iceberg is: (3.2) and the weight of the volume V A of the seawater is displaced (3.7) but this weight must be equal to the weight of the ice floe (Principle Archimedes) Thereby (3.8) where
4.
This is the submerged part of the iceberg, so the overhang is 10.7% Note: Archimedes Principle: A body wholly or partly immersed in a fluid is pushed upward by a force that equals the weight of the fluid displaced by said body.This force acts vertically through the center of gravity of the body. A straight 60 feet , Weighing 100 lb , Is supported on a wall at a point that is 48 feet above the floor. The center of gravity of the ladder in one third of the length from the floor. A man 160 lb halfway up the ladder. Assuming no friction with the wall and the coefficient of static friction between the floor and the staircase is . How man can climb the ladder before it starts to slip? a) b) c) d) e) f) ______ Help: 3.28 feet = 1 m ; 1 lb = 4448 N Solution First find the forces exerted by the system on the floor and on the wall. The forces acting on the system can be seen in Figure 4.1
Where P PE F1 F 1V F 1H F2 Data
weight man on the stairs [lb] Ladder Weight [lb] Force ground exerts on the ladder [lb] vertical component of F 1 [Lb] horizontal component of F 1 [lb] Force wall exerts on the ladder [lb] P = PE= to = c =
160 [lb] 100 [lb] 48 [feet] 60 [feet]
It is easy to calculate b (Pythagoras): b = 36 [feet] The line of action of P intersects the ground at a distance b / 2 of the wall. The line of action of P and intersects the ground at a distance b 2/3 of the wall. The transnational equilibrium exists if and only if the vector sum of all external forces acting on a body in equilibrium must be zero F=0 (4.1) where F is the resultant of the forces. The rotational equilibrium exists if and only if the vector sum of all external torques acting on a body in equilibrium must be zero: τ=0 (4.2)
where τ is the result of the torques. For there to balance transnational we use equation (4.1) to obtain: (4.3) (4.4) For there to rotational balance, choose an axis passing through the point of contact with the ground, and using equation (4.2) we obtain: (4.5) replacing data in equations (4.3), (4.4) and (4.5) we obtain F 2, F and F 1V 1H:
F 2 = 85 [lb] 1H = F F 2 = 85 [lb] 1V F = P + P E = 260 [lb] Now let us analyze the system, taking into account the coefficient of static friction between the floor and the steps: Let x be the fraction of the total length of the stair before it starts slipping. Then the equilibrium conditions are: (4.3) (4.4) (4.6) replacing data in equations (4.3), (4.4) and (4.6) we obtain F 2 = (120 x + 25) [Lb] (4.7) 1H = + 25) [Lb] (4.8) 1V F = 260 [Lb] (4.9) The maximum force of static friction is given by
F (120 x
(4.1 0) but (4. 11) then (4.12) and (4.12) = (4.8), then: from which we can solve for x:
x = 79/120 Finally the man can climb the ladder 60 x [ft] = 39.5 [feet] before it starts slipping.
EVIEW Secondary 4th SOLUTIONS 1.
The minimum speed necessary for a body of mass m leaves the planet Earth is a) 200 Km / s b) 48 Km / s c) 3 km / s d) 0.9 Km / s e) 1700 km / s f) 11.2 Km / s Help: G = , Solution Let's look at a few lines some fundamental concepts: As an introduction, in 1665 Isaac Newton wrote about Gravitation "... I started to think that gravitation could extend to the orbit of Moon ... having compared and, consequently, the force required to keep Moon in its orbit with the force of gravity on the surface of Earth I found that the agreement was very close ... " Johannes Kepler discovered in 1591 which are now known as Kepler's three laws of planetary motion: i. All planets move in elliptical orbits with the Sun at one focus ii. The line joining a planet to the Sun sweeps out equal areas in equal times. iii. The square of the period of any planet around the Sun is proportional to the cube of the average distance of the planet to the Sun Isaac Newton discovered today known as Act Universal Gravitation : The force between two particles having masses m 1 and m 2 and which are separated by a distance r is an attraction acting along the line joining the particles by size and having: (1.1) G is the gravitational constant and has the same value for all pairs of particles: (1.2) Work Work is defined as force constants:
= F x [N m = J]
(1
.3) Work for nonconstant forces (variables) * is defined as: [N m = J]
(1.4
) * See Appendix at the end of this calculator solucionario. Theorem Variation of Energy T indicates that the work effected by a resultant force F acting on a particle, as it moves from one point to another is equal to the change in kinetic energy E C: (1.5) where: ( 1.6) then (1.7) Conservative force A force is conservative if the work done by her on a particle moving in any round trip is zero. (Eg, the force of gravity) Nonconservative force A force is conservative if the work done by her on a particle moving in any round trip is not zero. (Eg, frictional force)
Note: If there is no change in the kinetic energy of a particle moving in a round trip, then
and equation (1.5)
and the resultant
force acting on the particle must be conservative. Similarly, if , From equation (1.5) we obtain And at least one of the forces acting on the system will be non-conservative. Conservation Energy When forces are conservative total energy E of the particle studied, remains constant. (1.8) where E P this is Potential Energy given by (1.9) relationship valid if and only if the force is conservative. For instance if then E P = mgh. Equation (1.8) means that
(1.10) Therefore, the equation (1.5) becomes: (1.11) or the equation (1.9):
(1.12) Well, in this question the interesting part of the equation (1.12) will where (1.13) When a particle of mass m is at a distance r from the center of Earth , The potential energy of the system is given by equation (1.13) as (1.14) If the particle and Earth are separated by an infinite distance we assign the value zero to the potential energy at zero force this configuration, ie
. So the equation becomes: (1.15)
where is the work done by the conservative force (gravity) on the particle, as it moves from infinity to a distance r from the center of Earth. Assuming that the particle moves towards Earth along a radial line r, the magnitude of the gravitational force F (r) acting on the particle (assuming that r> R T) is: (1.1 6) the minus sign indicates that it is an attractive force, ie a force pulling the particle towards Earth. By Therefore we can calculate Potential Energy of equation (1.15) as (1.17 ) substituting Equation (1.16) into equation (1.17) and integrating *:
(1.18) * See Appendix at the end of this calculator solucionario. The minus sign indicates that the potential energy is negative for any infinite distance, ie, the potential energy is zero at infinity and decreases with decreasing separation distance.This corresponds to the fact that the gravitational force exerted on the particle by Earth Attraction is. Escape Velocity Now we can find the gravitational potential energy of a particle of mass m on the surface Earth using equation (1.18): (1.19) where R T is the radius Earth , M T is its mass. The amount of work required, equation (1.15), to move the body from the surface of Earth to infinity is, using equation (1.19): (1.20) Taking the following data:
(1.21) we can calculate: (1.22) If a projectile which is situated on the surface of Earth we give you more energy than this, then, neglecting the resistance of the atmosphere, would escape Earth never to return. As this happens, its kinetic energy decreases while its potential energy increases, but their speed is never reduced to zero. The speed Escape v 0, so that the projectile does not return to Earth Is given by (1.2 3) of which we can solve equation v 0:
2.
If we consider the planet Earth as a spherical conductor of 6400 Km Radio capacitance is: a) 0.00712 C b) 0.0712 F c) 0.000712 F d) 0.00000712 C e) ______ Help: Solution
3.
From the relation found C = 0.000712 F When 1.00 g of water, which occupies a volume of 1.00 cc, boiling at atmospheric pressure, becomes steam at 1671 cc. The heat of vaporization of water is 539 cal / g at 1atm. Change in internal energy of the system is: a) 2000 cal b) 45,788 cal c) lime 0.0333 d) 498 cal e) 17 cal f) ______ Help: 1 cal = 4186 J Solution Heat of vaporization C V C is the heat required for a unit mass of substance m pass from the liquid to gaseous state holding constant Temperature and Pressure. This is say (3.1) Pressure Pressure is one way to describe Force acting on a fluid. Is defined as the magnitude of Normal Force per unit area. (3.2) Work From equation (1.4) of this solucionario
, We can write (3.
3) then (3.4) if p is a constant
(3.5) 1st Act Thermodynamics If a system state changes from an initial equilibrium i to a final equilibrium state f in a defined way, if the heat absorbed by the system C, the work is done by the system and the change in T Energy inner system is E I then: (3.6) Now if we replace the equations (3.1) and (3.5) in equation (3.6) we get: (3.7) In our case V 2 is the volume of vapor V 1 is the volume of liquid Replacing data:
4.
The fact that this amount is positive means that the internal energy of the system increases during the process. That is the 539 [cal] needed to boil 1 [g] Water 41 [cal]invested in external work of expansion and 498 [cal] as internal energy are added to the system. Consider a solid cylinder of radius R and mass M, which rolls without sliding down an inclined plane, the inertia of the cylinder is . The velocity of its center of mass when the cylinder reaches the lower part of the plane is: a) b) _________ Solution
c)
d)
e)
f)
This is a problem of rotational dynamics. Consider the following: Rigid Body Body where the constituting particles always maintained the same position each. If a rigid body rotates with an angular velocity in each particle of the rotation body has a certain amount of kinetic energy. A particle of mass m, which is at a distance r from the rotation axis moves in a circle of radius r with an angular speed around this axis and has a linear speed given by (4.1)
Therefore its kinetic energy this is (4.2) The kinetic energy Total body is the sum of the kinetic energies of each of its constituent particles. If the body is rigid then all particles have the same angular velocity but each particle may have a different radius r. Therefore Kinetic Energy Total Revolving rigid body is:
(4. 3)
where n indicates the total number of masses which form the system. Rotational Inertia Rotational inertia, denoted by I, plays the same role in rotational motion that performed by Mass M in the transnational movement. Is defined as
(4.4) Note that Rotational Inertia a body depends on the particular axis which is rotating, as well as body shape and the way it is distributed mass. Substituting equation (4.4) in equation (4.3) we obtain Kinetic Energy Rotation E CR:
(4.5) Center of Mass In physics always treat objects as if they were mere particles have mass but not size. Since the translational motion of each particle undergoes the same displacement body which then any movement of a particle represents the movement of the entire body. Even when the body turn to move or vibrate one point in the body called center of mass that moves in the same way you would a particle subject to the same forces.
Position the center of mass of a set of masses that lie on a line or in a plane or in space is given by:
Now consider the problem posed considering Act Conservation Energy : Initially the cylinder is at rest at a height h above the floor leaning against the upper end of the inclined plane (Figure 4.1)
When rolling down the inclined plane loses the cylinder equal to a potential energy (4.6 ) In its motion the cylinder must earn a kinetic energy equal to (4.7) where
v Linear speed of the Center of Mass Angular speed around the center of mass
Hence Conservation of Energy we have: (4.8)
we also know that: equation (4.8):
and
. Then substituting in
(4.9) v clearing where we finally obtain that:
* Appendix Calculation. Calculation Differential calculus is an important mathematical tool for the analysis of physical systems. It's not complicated, just use some familiar ideas (eg and applies them to a small world (eg d, o), infinitely small, or in the words of calculation: infinitesimal. Let your main ideas: Euclidean plane Locus represented by:
Variable changing, which varies, is denoted by x The change that must be considered is the following
Delta:
is a symbol used to denote a difference between a target value
and an initial value, for example
Differential: d is equal to the delta is a delta just super small, infinitely small, infinitesimal. Summation is a mathematical symbol used to denote sum, for example is used to denote the sum of all students college or the amount of bricks with which he has built a house, etc. Integral: Or is a mathematical symbol used to denote sum (like ), Which is used only to denote for example the sum of the number of atoms of oxygen in a room, or the number of drops of water having an ocean, etc. Function Is a relationship between the elements (dots) set x to the elements (points) and assembly. We use the symbol to denote a function. For example in the Euclidean plane a function can be positive:
If we take two points on the x axis, these will correspond to other points on the y axis:
We as:
know
that Delta ,
x and Delta
and are
defined
These Deltas can be represented in the Euclidean plane:
Media Ratio Is defined as the average ratio
that in physics is precisely half the speed.
Limit If we let eg Delta x becomes very but very small, making each horizontal line is but not touching: What we get finally is a point we denote by dx. Obviously at this point corresponds dy point:
Now that the notation has been made is a limit. The threshold applied to the mean ratio or average speed
So d remains
only very small. And
It is known as the instantaneous velocity. And these last two equations define what is referred to as derivative calculation. Viewing FIGURE C.4 Question is: How many points dx between x 1 and x 2? ... Many do not? And what happens if we add? You agree that we obtain Sure! Of course you do. What you have to realize is known as the fundamental theorem of calculus:
Well ... Other useful rules are (without proof, but we hope you've motivated you enough to investigate more about the physics and calculus):
where k is a constant.
REVIEW 3rd of Secondary (20072002) Notes: Read the review and consultation if you have questions. DO NOT put your personal data or the question paper or leaves your solutions!, We will give you a form for that. The conceptual part is worth 40% and 60% practical part. Have a time of 2 hours.
1. 2. 3. 4.
1.
2.
Conceptual part In the street the whole day a cold drizzle falls. In the kitchen is laid much laundry. Do clothes dry faster if you open the window? Because the paper kite tail is placed? As can determine the density of any stone using a dynamometer and water containers? Maximum pressure that can be measured using two U mercury manometer connected in series by a short tube if each of them allows to measure pressure Pa. m? Practical part A hexagonal pencil was pushed along the horizontal plane as shown in Figure 1 With what values of the friction coefficient between the stylus and the stylus slide plane for the roll plane without?
Figure 2 was made from the photograph taken from the tails of smoke trailing advancing two locomotives for railroad rectilinear path with speeds and
. The directions of
movement of trains are marked with arrows. Find the wind speed.
3.
Three bodies with masses m 1, m 2 and m 3 can slide along the frictionless horizontal line (figure 3). Where m 1 >> m 2 and m 3 >> m 2. Determine the maximum speeds of the bodies ends at baseline if they were at rest, while the body was half the speed v. The clashes are considered quite elastic.
SOLUTIONS Conceptual part 1.
Both on the streets and in the kitchen with the window closed the steam is saturated.
But Street temperature is lower than in the premises. Consequently, the steam pressure in the street is lower than in the room. So when you open the window of the kitchen steam will come out of it on the street, due to which the steam is in the kitchen is always unsaturated. The clothes will dry faster. 2. Thanks to the different length of the wires going from main line to points comet paper, the latter is stable with respect to rotation around the axis OO 'and O 1 O 1'. The tail of the comet facilitate stability of paper regarding the rotation around the vertical axis O 2 O 2 '.
3.
To determine the density of the stone is essential to know its mass m and volume V:
. Using the dynamometer can determine the value of the body weight in air P 1 and P 2 in the water. The difference between these values is equal to the force Archimedes acting on the stone water (Archimedes force which acts upon the stone in the air can be underestimated). Knowing the density of water determine the volume dela stone:
,
and density:
4. The manometer mercury U-shaped (Figure 4a) measures the soprepresión , Or indicates how much pressure p at the elbow Left gauge is greater than the atmospheric pressure p 0. The limitation on the range of the pressure values to be measured imposed by the length of the manometer tubes. You can not measure the overpressure greater that with which the mercury reaches the edge of the right side (according to Figure 4a). The limit value of the overpressure measured to the gauge in question is equal to m.
In the case of series connection of two pressure gauges (figure 4b) the overpressure left elbow gauge 1 is greater than
in
Because the pressure p 2 in the elbow
Left gauge 2 is greater than atmospheric in the magnitude thereby . The compressed air in the left elbow gauge 2 occupies the volume
where S is the sectional area of the tubes. First this air volume occupied
right elbow gauge one and the same volume in the left elbow and pressure gauge 2 This air was equal to the Atmospheric (p 0). Assuming isothermal compressed air can be applied is the law of Boyle - Mariotte:
where . Multiplying the numerator and denominator on the right side of this equation by
where
As
Then
, We get
Pa.
Practical part 1. In moving the stylus up side two forces act: the normal reaction force plane N and the friction force F (Figure 1sol). Because the stylus is not displaced in the vertical direction then Friction can annotate Consider the time "critical" when the stylus touches the plane at point A. For the pen not
. For the magnitude of the force
returns the resultant of all the forces must pass through the center of mass of the pencil. Accordingly, for the center of mass must pass the resultant R of the forces N and F. If the coefficient friction force is large and R passes under the center of mass, the pencil will spin. Thus the condition that the pen is not turning shall be recorded as follows: or is obtained where finally .
2.
The plume released by the locomotive at point A at time t will be run by
the wind at point C. Thereby
. Where
is the wind speed (Figure 2a.). But after a time t the locomotive will be located at point B. The progress of the train is equal to , Where is the speed of the train. It is noteworthy that the plume is oriented along Vector , Or what for that matter, along the vector .
Now it's easy to find the wind speed. We draw on an arbitrary scale the vector
. Then from the origin O of
vector we draw from the same scale the vector . The ends of the vectors and we draw straight lines parallel to corresponding columns of smoke (Figure 2b.) At the point M of intersection of these lines with the point O enlasamos. In precisely selected scale OM vector is the wind speed. In effect, the OM-vector v 1 is oriented along plume dela
dragging the first locomotive, while the OM-vector v 2, along the plume of the second. As measured by length of the vector rule module OM will find the wind speed. Equals 3.
.
Collisions of the mass m 2 body with mass bodies m 1 and m 3 continue until the speed becomes the same
less than the speed of one of the bodies (M 1 or M 3). But since m 1 >> m 2 and m 3 >> m 2, momentum and energy of the body mass m 2 is much smaller than the momentum and energy of these bodies of masses m 1 and m 3. Consequently, noting the law conservation of energy and momentum can not take into account the energy and momentum of the body of mass m 2 cease after collision Denoting v 3 v 1 and the velocities of the bodies of masses m 1 and m 3 after cease collisions can be noted:
Solving these equations together and considering >> m 1 m 2 and m 3 >> m 2 found:
and
.
REVIEW 4th of Secondary (20072002) Notes: Read the review and consultation if you have questions. DO NOT put your personal data or the question paper or leaves your solutions!, We will give you a form for that. The conceptual part is worth 40% and 60% practical part. Have a time of 2 hours.
1.
Conceptual part Determine the density of an unknown liquid. You can use: option 1: two vessels with
one liquid glass tube 80 to 100 cm. long, rulers, rubber tubes, funnels. option 2: liquid to be analyzed, graduated cylinder, liquid with known density dynamometer. 2. In a plane mirror is an image of a candle. What will happen to this if between the mirror and the candle is placed parallel plate glass? 3. In the street the whole day a cold drizzle falls. In the kitchen is laid much laundry. Do clothes dry faster if you open the window? 4. In a vase with water that rotates around its axis (figure 1) is released to a ball that floats Awash. What part of the area will be located the ball?
Practical part 1. The foam cube with a mass M = 100 g. is situated on a horizontal support (Figure 2). The hub height is h = 10 cm. Below the cube is pierced by a bullet that flies
vertically and whose mass is m = 10 gr. The speed of the bullet entry in the bucket is
,
to the output
2.
. Toddle onto the cube or not?
From the South Pole and the North Pole of the Earth simultaneously take off two rockets with equal
Initial velocities directed horizontally. Within the time
rockets were
at the maximum distance from one another. Determine the maximum distance between the rockets. The acceleration of fall on Earth is considered known. The radius of the Earth is 3.
.
In the space between the walls of the ampoule in a pressure flask was established
to
ambient temperature. Appreciating the time during which the content in the tea thermos be cooled from 90
0
C to 70 0 C The surface of the blister is
specific heat capacity of water is
. The heat capacity is 1 liter. The , The universal gas constant is
. Not taking into account the heat leakage through the cap. SOLUTIONS Conceptual part 1. By immersing the same in two different liquids load forces acting on Archimedes the same is determined as follows: , where
and
(1)
are the densities of the liquids, one of which is unknown.
Values F 1 and F 2 can be determined by the difference of the indications of the dynamometer which is suspended load in cases when the latter is in the air and in the liquid: ,
(2)
where P Dynamometer is the indication when the load was in the air, P 1 and P 2 the indications dynamometer, when the load is in the density liquids known and unknown. From equations (1) and (2) we find the unknown density of the liquid:
2.
In tracing the course of a few rays is easy to be convinced that, after entering the candle
and the mirror is disposed parallel flat plate glass, the image of the candle will approach the mirror. 3.
See sec Third solutions.
4.
Since the ball floats to flower the water, the density of the material itself is lower than the density
Water . Suppose that the ball is located at a distance R from the axis of a rotating vessel. If the density of the ball is equal to the density of water, it would be an invariable distance axis of rotation. The centripetal acceleration may be communicated to the resulting ball force and gravity forces of the surrounding water pressure. In this resulting module would equal where
is the angular speed of rotation of the container V, the volume of the pellet.
The pellet density Arranged in the same point from the surrounding water acts a Like force the ball now communicates acceleration
This acceleration is greater than that needed for rotation by the circle of radius R. Accordingly, the equilibrium position of the ball is located in the axis of the container. Practical part 1. The cube can jump if the magnitude of the force F, which acts on the same part of the bullet, is greater than the magnitude of the force of gravity
. Let us find this force. For this
examine the bullet. In the same from the bucket acts a force equal in magnitude, but opposite in direction to the force of gravity m g. The speed of the bullet passing through the hub, varies insignificant variation is equal to 5 m / s, which is only 5% of the speed of the bullet to penetrate into the bucket. Therefore we can consider that no force F depends on the speed of the bullet and is constant. The momentum of the bullet passing through the hub, to effect changes in the bullet action of two forces: the force of gravity and the force friction. If the time in which the bullet passes through the whole cube, is denoted by , then (1). Time not hard to find him. Since the forces acting on the hub are constant, the acceleration is constant also Bullet and therefore the speed of the bullet changes linearly with time. Therefore the average speed of movement of the bullet in the cube is equal to . Accordingly, the bullet passes through the hub in time . Substituting this value
in Eq. (1) we find: .
As
is small, the value of
is much smaller than the pulse variation
Bullet and can be neglected. The force F was greater than the strength of the gravity acting on the hub. So skip the bucket. 2. Rockets move by ellipses. The takeoff point corresponds to the distance minimum from the center of the earth, while the point of the orbit that is encime Earth point diametrically opposite to the apogee of the orbit. At these points the rocket velocity is perpendicular to the line drawn from the center of the Earth to orbit. L denote the length of the major axis of the orbit. Then the maximum distance s between rockets will equal
. The period T of the rocket flight orbit equals
to . If the flight period for the circular orbit of radius R t is denoted by T 1, then according to Kepler's third law
where
. Because centripetal acceleration of the satellite moving the circular orbit radius R p is equal to g, then .
Therefore
. Thus
. . 3. Denote temperature T 1 and T 2 tea room temperature. Wall bumping warm air molecules acquire contained in the ampoule kinetic energy
. But upon contacting the cold wall kinetic energy
of the molecules reach equal
Thus the molecule transfers energy .
The number of collisions of the molecules with the walls of surface S at time equals (1) where n is the concentration of molecules and , The mean velocity projection module of the molecules on the X axis perpendicular to the wall. To make the assessment that you can take: The mean square velocity v is determined by the formula
where M is the molar mass of the gas and T, the average temperature in the vial. Since the values of T 1 and T 2 are coming we can take: . From the main equation of the kinetic theory of gases we obtain . Rewriting the formula (1):
meaning that at time
energy is transferred (2).
For
content in the tea thermos cools from the temperature until the temperature energy must be transferred .
Substituting this expression for W in the formula (2), we find the time necessary to cool the tea:
.
REGIONAL PEACE
1st Secondary 1)
Conceptual part List several repetitive phenomena that occur in nature and that could serve as reasonable weather patterns.
2) a.
You can combine two vectors of different magnitude to give a zero resultant?
b.
They can do three vectors?
3)
List several scalar quantities.
4)
Is time a vector? Why?
1)
Practical part Express your height in miles. In your answer using only prefixes.
A plane travels 876.5 [km] in a straight line at an angle of 37.5 to the North
2)
East. How much the plane has traveled both to the North and to the East, from its starting point? . Help: 3)
Two trucks carrying sand. One of these, B, has a small hole in its base through which the sand is falling to the floor. They have taken the following mass versus time for both trucks: Data # Time [min] A forklift Mass [kg] Cart B mass [kg] 1 0.0 8.75 8.75 2 1.0 8.76 7.77 3 2.0 8.75 6.74 4 3.0 8.77 5.76 5 4.0 8.75 4.75 6 5.0 8.75 3.76 7 6.0 8.74 2.73 a) Plot:
The mass versus time for the truck to
The mass versus time for the truck B
b) Because if A mass is constant we have different data? The number of seconds in a year can be replaced conveniently by 10. What is the
4)
percentage error of this figure?. Take = 3.141592653 June 8, 2003
REGIONAL PEACE
2nd of Secondary Conceptual part 1) b.
2)
If a b = 0, does it follow that a and b are perpendicular to each other?
c.
If a = 0, Should be parallel to and b?
d.
Can a dot product between vectors be a negative amount? List several scalar and vector quantities.
3) 4)
What experimental evidence exists to assume that the speed of sound is the same for all wavelengths? What is it that causes mirages? Do you have something to do with the fact that the refractive
1)
index of air is not constant but changes to its density? Draw rays explaining the phenomenon. Practical part A cylindrical vessel containing water has a radius of 2 cm. In 2 hours the water level low 1 mm. Estimate in grams per second, the evaporation rate at which water is evaporating.
2)
The lowest tone that can detect the human ear as sound is about 20 [Hz] and the highest is about 20000 [Hz]. What is the wavelength of each of them in the air?. The speed of sound in air is 331.3 [ms -1]. Indicates a wavelength where the wavelength and amplitude.
3)
What should be the height of a vertical mirror, so that a person 6 feet tall to be able to observe the entire image?. Assume that your eyes are 4 inches below the top is its head
4)
Has been taken following the motion of a body: Data # Time [s] Position [m] Speed [ms -1]
Acceleration [ms 2]
1 2 3 4 5 6
0.0 1.0 2.0 2.5 3.5 4.0
1.0 3.7 4.8 5.0 3.9 1.4
4.0 1.8 0.7 0.0 -3.0 -6.2
-3.8 -1.2 -1.0 -1.9 -4.9 -7.3
Plot:
the position versus time
the speed versus time
acceleration versus time. June 8, 2003
REGIONAL PEACE
3rd of Secondary SOLUTIONS 1)
Conceptual part What is the difference between mass and weight? Much do you weigh?
2)
Everyone knows that when you look in a mirror is an inversion of the left and right. The right hand seems to be a left, left eye seems to be one law, etc.. Is it possible to design a mirror system that would allow to observe an image as the way in which people normally observed? If possible, draw a picture with some typical ray showing that this is true.
3) 4)
Explain: Archimedes Principle, equations of continuity and Bernoulli, As you may know the distance that has been struck by lightning from where you find yourself? Practical part
1) a.
Using the definition of scalar product a b = (a) (b) cos and that a b = a x b x + a and b and b z + z obtaining the angle between the vectors: a = 3 i + 3 j - 3 k and b = 2 i + 3 k
b. 2)
Plot the vectors a = 3 i + 3 j + 3 k, and b = 2 i + 3 k and the vector product a He drops a stone from the top of a building. The sound of the stone to hit the ground is
heard 6.5 s later. If the speed of sound is 1120 ft s -1 Calculate the height of the building.
3)
(Venturi tube) analytically determining the fluid velocity, density known, it travels through the tube shown in the figure, where MP1 and MP2 are two pressure gauges. A 1 and A 2 are the areas perpendicular to the flow in regions 1 and 2 respectively.
Finally with data: = 1 g / cc, p 1 = 1000 N m -2 , P 2 = 800 N m -2, A 1 = 40 cm 2, A 2 = 22 cm 2, calculate v 1 June 8, 2003
REGIONAL PEACE
4th of Secondary 1) 2) 3)
Conceptual part Explain the Steiner theorem, also known as the parallel axis theorem. Explain that the dynamic lifting force is the force acting on a body because of its motion through a fluid. Comment: 1st and 2nd law of thermodynamics, entropy, reversible and irreversible processes, isothermal processes and adiabatic.
4)
Explain what the Doppler effect.
1)
Practical part A disc of 0.5 [m] radius and 20 [kg] of mass can rotate freely about a fixed horizontal axis passing through its center. Applies a force F of 9.8 [N] pulling a cord coiled around the edge of the disc.Find the angular acceleration of the disk and its angular velocity after 2 [s]. Finding the reaction force also exists in the brackets which support the axis of the disc.
2)
A semiquantitative definition of electric flux is: us that: q sphere vectors
3)
. And Gauss's law tells
. Write the electric field of a point charge q taking Gaussian surface as a of
radius r. Help: and
The
total
area
of
a
sphere
is
r 2 and
the
have the same direction.
A boat in motion produces surface waves on a calm lake. The boat runs 12 oscillations in 20 [s]; each oscillation produces a wave crest. The crest of the wave takes 6 [s] to reach the distant shore 12 [m]. Calculate the wavelength of surface waves.
4)
Three capacitors of 1.5 F], 2 F] and 3 F] are connected in a) series, b) are parallel and applies a potential difference of 20 [V]. Determine in each case i) the capacitance of the system, ii) loading and the potential difference of each capacitor, iii) energy of the system.
REGIONAL PEACE
1st Secondary SOLUTIONS 1)
Conceptual part List several repetitive phenomena that occur in nature and that could serve as reasonable weather patterns.
Sun The time when the moon becomes full, the beginning of a season, solar cycles, the movement of the stars, etc.. 2) a.
You can combine two vectors of different magnitude to give a zero resultant?
Sun b.
They can do three vectors?
Sun 3) 4)
1) 2)
No If
List several scalar quantities. Sun - mass, time, density, volume, temperature, electric current, etc.. Is time a vector? Why? Sun - No, that the management and direction of a vector has no restriction on its orientation. Practical part Express your height in miles. In your answer using only prefixes. Sun - If you measure 1.67 meters then say you write 1.67 milli Kilo meters. A plane travels 876.5 [km] in a straight line at an angle of 37.5 to the North East. How much the plane has traveled both to the North and to the East, from its starting point? . Help:
Sun -
Eastbound:
876.5 cos (52.5 = 533.6 [km]
Northbound
876.5 sin (52.5 = 695.4 [km]
Since 90 - 37.5 = 52.5 angle that is taken with respect to the horizontal. 3)
Two trucks carrying sand. One of these, B, has a small hole in its base through which the sand is falling to the floor. They have taken the following mass versus time for both trucks: Data # Time [min] A forklift Mass [kg] Cart B mass [kg] 1 0.0 8.75 8.75 2 1.0 8.76 7.77 3 2.0 8.75 6.74 4 3.0 8.77 5.76 5 4.0 8.75 4.75 6 5.0 8.75 3.76 7 6.0 8.74 2.73 a) Plot:
The mass versus time for the truck to
The mass versus time for the truck B
b) Because if A mass is constant we have different data? Sun - Because when we take measurements random errors always exist, why not find a single result if not several. But note that the difference between them (mass of Cart A) is not great. These differences are known as natural statistical fluctuations. The number of seconds in a year can be replaced conveniently by 10. What is the
4)
percentage error of this figure?. Take = 3.141592653 Sun - 10 = 31415926.53 In a year of 365 days or 8760 hours are 31,536,000 seconds. Therefore the error percentage is 0.38% Remember And This is a rough estimate because in a year when there are actually 365.2 days. June 8, 2003
REGIONAL PEACE
2nd of Secondary SOLUTIONS Conceptual part 5) a.
If a b = 0, does it follow that a and b are perpendicular to each other?
Sun - Yes, since by definition a b = (a) (b) cos as cos = 0 if and only if = 90 then a and b are perpendicular. b.
If a = 0, Should be parallel to and b?
Sun - Yes, since by definition a = (a) (b) sin u and as sin = 0 if and only if = 0 then a and b are parallel. c.
Can a dot product between vectors be a negative amount?
Sun - Yes, you can. Which can not be negative is the magnitude of a vector. 6)
List several scalar and vector quantities. Sun -
7)
8)
Scalar: mass, time, density, volume, temperature, electric current, etc.. Vectors: Strength, Speed, Acceleration, Magnetic Fields, Electric, Gravity; Momentum, Torque, What experimental evidence exists to assume that the speed of sound is the same for all wavelengths? Sun - Any piece of music, which is a collection of different wavelengths of sound waves, could never be heard as we do if the speed was different for certain wavelengths, as certain notes come to us much later or earlier than the other, you think? Would hear at the wrong without understanding anything. What is it that causes mirages? Do you have something to do with the fact that the refractive index of air is not constant but changes to its density? Draw rays explaining the phenomenon. Sun - They did have a lot to do. The refractive index is sensitive to temperature changes. The mirages usually happen in deserts or on paved roads in a region very hot places exceeding 40 C, so ground-level air is hot and have lower density than the cooler air rises
5)
creating a series of strata or layers of different temperature levels. A layer of cold air, another of hot air and cold another produce a lens which bends the light rays and makes an image appear which can not be. Practical part A cylindrical vessel containing water has a radius of 2 cm. In 2 hours the water level low 1 mm. Estimate in grams per second, the evaporation rate at which water is evaporating. [Cc s -1]. 1cc water = 1 g of water. 1 [mm]
Sun - The volume of water that falls is = 0.1 [cm]. Therefore 6)
[G s -1]
The lowest tone that can detect the human ear as sound is about 20 [Hz] and the highest is about 20000 [Hz]. What is the wavelength of each of them in the air?. The speed of sound in air is 331.3 [ms -1]. Indicates a wavelength where the wavelength and amplitude. Sol - As [mm]
and
[Ms -1] then the wavelengths are 16,565 [m] and 16,565
7)
What should be the height of a vertical mirror, so that a person 6 feet tall to be able to observe the entire image?. Assume that your eyes are 4 inches below the top is its head Sun - The figure shows the trajectories of rays that leave the top of the head of the individual and his toes. These rays chosen so that enter the eye after reflection, affect the vertical mirror in points a and b respectively. The mirror needs to occupy only that region between these two points. Projecting rays reaching the eye towards the place where they form the mirror image is that this should have half the height of the individual, ie 3 feet. Note that this height is independent of the distance at which is the person in the mirror.
8)
Has been taken following the motion of a body: Data # Time [s] Position [m] Speed [ms -1]
Acceleration [ms 2]
1 2 3 4 5 6
0.0 1.0 2.0 2.5 3.5 4.0
1.0 3.7 4.8 5.0 3.9 1.4
Plot:
the position versus time
the speed versus time
acceleration versus time.
4.0 1.8 0.7 0.0 -3.0 -6.2
-3.8 -1.2 -1.0 -1.9 -4.9 -7.3
June 8, 2003
REGIONAL PEACE
3rd of Secondary SOLUTIONS 1)
Conceptual part What is the difference between mass and weight? Much do you weigh? Sun - The mass is a scalar, its units are [kg], the weight is a vector, is a force therefore is measured in Newtons [N]. If you say you have a mass of 66 [kg] weights then 66 [kg] [ms -2] = 645.15 [N]. 9775 [ms -2] is gravity in La Paz. 9.81 [ms -2] is the gravity at sea level. 1.67 [ms -2] is the gravity on the moon. How much would you weigh on the moon?
2)
Everyone knows that when you look in a mirror is an inversion of the left and right. The right hand seems to be a left, left eye seems to be one law, etc.. Is it possible to design a mirror system that would allow to observe an image as the way in which people normally observed? If possible, draw a picture with some typical ray showing that this is true. Sun - If possible, be requires two mirrors that are joined at an angle of 90 between
3)
them. Each image in a mirror will be reflected in the other mirror as to achieve reverse what we usually see as a result finding the desired image. Explain: Archimedes Principle, equations of continuity and Bernoulli,
Sol - A body wholly or partly immersed in a fluid is pushed upward by a force that equals the weight of the fluid displaced by said body (Archimedes). The principle that expresses the conservation of mass in a fluid movement is known as the
Where is the fluid density, is the area through which the fluid at a given time and is the fluid velocity. That the product of these three quantities remain constant is a fancy way of saying that the mass does not change in the fluid. continuity equation:
The principle that expresses the conservation of energy in the movement of a fluid is known as
4)
Bernoulli's equation:
Where
and
and
the height at which the fluid moves,
is the pressure,
the severity
continue to express the density and
velocity of fluid. The first term is the kinetic energy per unit volume [J m -3], the second and third terms express the potential energy per unit volume [N m -2 = J m -3] due to internal forces (pressure) and external forces respectively. Therefore the total energy per unit volume remains constant. As you may know the distance that has been struck by lightning from where you find yourself? Sun - First "see" the beam. Light travels at a speed of approximately
[Ms -1] so we
can say that lightning emits light reaches us instantly. Then we have the time
that comes to
us in the "sound" of the beam. The speed of sound in air is worth
[Ms -1]. Then
using the relationship
the distance found. Practical part
1) a.
Using the definition of scalar product a b = (a) (b) cos and that a b = a x b x + a and b and b z + z obtaining the angle between the vectors: a = 3 i + 3 j - 3 k and b = 2 i + 3 k
Sun - The angle will b. Sun -
2)
Plot the vectors a = 3 i + 3 j + 3 k, and b = 2 i + 3 k and the vector product a a = 9i - 3 j - 6 k, which must be stressed is that both a and b form a
plane
in space which is perpendicular to the vector to the graph is easily accomplished by locating the points in space (3,3,3), (2,0,2) and (9, -3, -6 ) indicating the end of each vector starting at the origin (0,0,0). He drops a stone from the top of a building. The sound of the stone to hit the ground is heard 6.5 s later. If the speed of sound is 1120 ft s -1 Calculate the height of the building. Sun - The total displacement covered by the stone and the sound is:
where g = -32.2 [ft / s 2] also
then
[S]
where
solution: 3)
cleared
[S]. Finally
staying
only
with
the
positive
[Feet].
(Venturi tube) analytically determining the fluid velocity, density known, it travels through the tube shown in the figure, where MP1 and MP2 are two pressure gauges. A 1 and A 2 are the areas perpendicular to the flow in regions 1 and 2 respectively.
Finally with data: = 1 g / cc, p 1 = 1000 N m -2 , P 2 = 800 N m -2, A 1 = 40 cm 2, A 2 = 22 cm 2, calculate v 1 Sun - From the continuity equation:
(A) And the Bernoulli equation when the system is in a horizontal position: (B)
If we replace (A) in (B) and then solve for
we obtain:
Replacing the data provided we find that:
13.16 [ms -1]
4)
Verify that when a wave hits a certain angle and passes through half limited by flat faces parallel, the direction of propagation of the beam emerging is parallel to the incident beam. Sun Consider the following figure:
Using the law of refraction or Snell's law we find: Similarly:
n 1 sin i) = n 2 sin t)
n 2 sin = n 2 sin
Now within the medium 2 is true also that i =
t.
Combining these equations is reached t = i, which is what we wanted to prove. June 8, 2003
REGIONAL PEACE CONTEST II
4th of Secondary SOLUTIONS 5)
6)
7)
Conceptual part Explain the Steiner theorem, also known as the parallel axis theorem. Sun - The parallel axis theorem is given by the relationship: , Where I is the inertia around the axis of rotation arbitrary I cm is the rotational inertia parallel axis passing through the center of mass, M is the total mass of the object and h is the perpendicular distance between the axes. The two axes are parallel. The moments of inertia with respect to the parallel axes relate in this simple way. Explain that the dynamic lifting force is the force acting on a body because of its motion through a fluid. Sun - These bodies are the wings of an airplane or a helicopter propellers. The streamlines of air around the wing of an aircraft for example cause the air speed above the wing has a greater magnitude than the air velocity below this, which means that the pressure above the wing is less than pressure below which must occur if there is to be a push upward. Comment: 1st and 2nd law of thermodynamics, entropy, reversible and irreversible processes, isothermal processes and adiabatic. Sun All thermodynamic system in an equilibrium state has a state variable, called the internal energy of the system is such that its change
where
Energy is added to
is the energy supplied by the system when performing work. (1st Law) the system by heat transfer and
It is impossible for a cycler not produce another effect that continuously transfer heat from one body to another at a higher temperature than this. It is also possible to reformulate the 2nd law in terms of entropy: A natural process that begins in an equilibrium state and ends in another place at the direction that causes the entropy of the system and its environment increases. Entropy is a thermodynamic variable that measures the disorder. If a change occurs very slowly so that at each moment the system is in an equilibrium position then the process is reversible. And if the system away from its equilibrium state then the process is irreversible. When there is a change in system pressure or volume but the temperature is kept constant is spoken of an isothermal process. When there are non-heat exchange between the system and the environment comes to an adiabatic process. An adiabatic process can be reversible or irreversible. 8)
Explain what the Doppler effect. When a person hears a sound is moving toward the stationary source that produces it, the frequency of the sound heard is greater than when at rest. If the person is moving away from the stationary source, less frequently heard when this than when at rest. Similarly is the
5)
equivalent when both source and person move away from or towards. This effect applies to all waves in general. Practical part A disc of 0.5 [m] radius and 20 [kg] of mass can rotate freely about a fixed horizontal axis passing through its center. Applies a force F of 9.8 [N] pulling a cord coiled around the edge of
the disc.Find the angular acceleration of the disk and its angular velocity after 2 [s]. Finding the reaction force also exists in the brackets which support the axis of the disc. Sun 6)
A semiquantitative definition of electric flux is: us that: q sphere
7)
. Write the electric field of a point charge q taking Gaussian surface as a of
vectors
. And Gauss's law tells
radius r. Help: and
The
total
area
of
a
sphere
r 2 and
is
the
have the same direction.
A boat in motion produces surface waves on a calm lake. The boat runs 12 oscillations in 20 [s]; each oscillation produces a wave crest. The crest of the wave takes 6 [s] to reach the distant shore 12 [m]. Calculate the wavelength of surface waves.
8)
Three capacitors of 1.5 F], 2 F] and 3 F] are connected in a) series, b) are parallel and applies a potential difference of 20 [V]. Determine in each case i) the capacitance of the system, ii) loading and the potential difference of each capacitor, iii) energy of the system.
REGIONAL PEACE
3rd of Secondary SOLUTIONS 1)
Conceptual part What is the difference between mass and weight? Much do you weigh? Sun - The mass is a scalar, its units are [kg], the weight is a vector, is a force therefore is measured in Newtons [N]. If you say you have a mass of 66 [kg] weights then 66 [kg] [ms -2] = 645.15 [N]. 9775 [ms -2] is gravity in La Paz. 9.81 [ms -2] is the gravity at sea level. 1.67 [ms -2] is the gravity on the moon. How much would you weigh on the moon?
2)
Everyone knows that when you look in a mirror is an inversion of the left and right. The right hand seems to be a left, left eye seems to be one law, etc.. Is it possible to design a mirror system that would allow to observe an image as the way in which people normally observed? If possible, draw a picture with some typical ray showing that this is true. Sun - If possible, be requires two mirrors that are joined at an angle of 90 between
3)
them. Each image in a mirror will be reflected in the other mirror as to achieve reverse what we usually see as a result finding the desired image. Explain: Archimedes Principle, equations of continuity and Bernoulli, Sol - A body wholly or partly immersed in a fluid is pushed upward by a force that equals the weight of the fluid displaced by said body (Archimedes). The principle that expresses the conservation of mass in a fluid movement is known as the
Where is the fluid density, is the area through which the fluid at a given time and is the fluid velocity. That the product of these three quantities remain constant is a fancy way of saying that the mass does not change in the fluid. continuity equation:
The principle that expresses the conservation of energy in the movement of a fluid is known as Bernoulli's equation:
Where
and
and
the height at which the fluid moves,
is the pressure,
the severity
continue to express the density and
velocity of fluid. The first term is the kinetic energy per unit volume [J m -3], the second and third terms express the potential energy per unit volume [N m -2 = J m -3] due to internal forces
4)
(pressure) and external forces respectively. Therefore the total energy per unit volume remains constant. As you may know the distance that has been struck by lightning from where you find yourself? Sun - First "see" the beam. Light travels at a speed of approximately
[Ms -1] so we
can say that lightning emits light reaches us instantly. Then we have the time
that comes to
us in the "sound" of the beam. The speed of sound in air is worth
[Ms -1]. Then
using the relationship
the distance found. Practical part
1) a.
Using the definition of scalar product a b = (a) (b) cos and that a b = a x b x + a and b and b z + z obtaining the angle between the vectors: a = 3 i + 3 j - 3 k and b = 2 i + 3 k
Sun - The angle will b.
Plot the vectors a = 3 i + 3 j + 3 k, and b = 2 i + 3 k and the vector product a
Sun -
2)
a = 9i - 3 j - 6 k, which must be stressed is that both a and b form a
plane
in space which is perpendicular to the vector to the graph is easily accomplished by locating the points in space (3,3,3), (2,0,2) and (9, -3, -6 ) indicating the end of each vector starting at the origin (0,0,0). He drops a stone from the top of a building. The sound of the stone to hit the ground is heard 6.5 s later. If the speed of sound is 1120 ft s -1 Calculate the height of the building. Sun - The total displacement covered by the stone and the sound is:
where g = -32.2 [ft / s 2] also
[S]
then
where
solution: 3)
[S]. Finally
cleared
staying
only
with
the
positive
[Feet].
(Venturi tube) analytically determining the fluid velocity, density known, it travels through the tube shown in the figure, where MP1 and MP2 are two pressure gauges. A 1 and A 2 are the areas perpendicular to the flow in regions 1 and 2 respectively.
Finally with data: = 1 g / cc, p 1 = 1000 N m -2 , P 2 = 800 N m -2, A 1 = 40 cm 2, A 2 = 22 cm 2, calculate v 1 Sun - From the continuity equation:
(A) And the Bernoulli equation when the system is in a horizontal position: (B)
If we replace (A) in (B) and then solve for
we obtain:
Replacing the data provided we find that:
13.16 [ms -1]
4)
Verify that when a wave hits a certain angle and passes through half limited by flat faces parallel, the direction of propagation of the beam emerging is parallel to the incident beam. Sun Consider the following figure:
Using the law of refraction or Snell's law we find: Similarly:
n 1 sin i) = n 2 sin t)
n 2 sin = n 2 sin
Now within the medium 2 is true also that i =
t.
Combining these equations is reached t = i, which is what we wanted to prove. June 8, 2003
REGIONAL PEACE CONTEST II
4th of Secondary SOLUTIONS 5)
Conceptual part Explain the Steiner theorem, also known as the parallel axis theorem. Sun - The parallel axis theorem is given by the relationship: , Where I is the inertia around the axis of rotation arbitrary I cm is the rotational inertia parallel axis passing through the center of mass, M is the total mass of the object and h is the perpendicular distance
6)
7)
between the axes. The two axes are parallel. The moments of inertia with respect to the parallel axes relate in this simple way. Explain that the dynamic lifting force is the force acting on a body because of its motion through a fluid. Sun - These bodies are the wings of an airplane or a helicopter propellers. The streamlines of air around the wing of an aircraft for example cause the air speed above the wing has a greater magnitude than the air velocity below this, which means that the pressure above the wing is less than pressure below which must occur if there is to be a push upward. Comment: 1st and 2nd law of thermodynamics, entropy, reversible and irreversible processes, isothermal processes and adiabatic. Sun All thermodynamic system in an equilibrium state has a state variable, called the internal energy of the system is such that its change
where
Energy is added to
is the energy supplied by the system when performing work. (1st Law) the system by heat transfer and
It is impossible for a cycler not produce another effect that continuously transfer heat from one body to another at a higher temperature than this. It is also possible to reformulate the 2nd law in terms of entropy: A natural process that begins in an equilibrium state and ends in another place at the direction that causes the entropy of the system and its environment increases. Entropy is a thermodynamic variable that measures the disorder. If a change occurs very slowly so that at each moment the system is in an equilibrium position then the process is reversible. And if the system away from its equilibrium state then the process is irreversible. When there is a change in system pressure or volume but the temperature is kept constant is spoken of an isothermal process. When there are non-heat exchange between the system and the environment comes to an adiabatic process. An adiabatic process can be reversible or irreversible. 8)
Explain what the Doppler effect. When a person hears a sound is moving toward the stationary source that produces it, the frequency of the sound heard is greater than when at rest. If the person is moving away from the stationary source, less frequently heard when this than when at rest. Similarly is the
5)
equivalent when both source and person move away from or towards. This effect applies to all waves in general. Practical part A disc of 0.5 [m] radius and 20 [kg] of mass can rotate freely about a fixed horizontal axis passing through its center. Applies a force F of 9.8 [N] pulling a cord coiled around the edge of the disc.Find the angular acceleration of the disk and its angular velocity after 2 [s]. Finding the reaction force also exists in the brackets which support the axis of the disc. Sun -
6)
A semiquantitative definition of electric flux is: us that: q sphere vectors
7)
. And Gauss's law tells
. Write the electric field of a point charge q taking Gaussian surface as a of
radius r. Help: and
The
total
area
of
a
sphere
is
r 2 and
the
have the same direction.
A boat in motion produces surface waves on a calm lake. The boat runs 12 oscillations in 20 [s]; each oscillation produces a wave crest. The crest of the wave takes 6 [s] to reach the distant shore 12 [m]. Calculate the wavelength of surface waves.
Three capacitors of 1.5 F], 2 F] and 3 F] are connected in a) series, b) are parallel
8)
and applies a potential difference of 20 [V]. Determine in each case i) the capacitance of the system, ii) loading and the potential difference of each capacitor, iii) energy of the system.
REGIONAL PEACE
3rd of Secondary SOLUTIONS 1)
Conceptual part What is the difference between mass and weight? Much do you weigh? Sun - The mass is a scalar, its units are [kg], the weight is a vector, is a force therefore is measured in Newtons [N]. If you say you have a mass of 66 [kg] weights then 66 [kg] [ms -2] = 645.15 [N]. 9775 [ms -2] is gravity in La Paz. 9.81 [ms -2] is the gravity at sea level. 1.67 [ms -2] is the gravity on the moon. How much would you weigh on the moon?
2)
Everyone knows that when you look in a mirror is an inversion of the left and right. The right hand seems to be a left, left eye seems to be one law, etc.. Is it possible to design a mirror system that would allow to observe an image as the way in which people normally observed? If possible, draw a picture with some typical ray showing that this is true. Sun - If possible, be requires two mirrors that are joined at an angle of 90 between
3)
them. Each image in a mirror will be reflected in the other mirror as to achieve reverse what we usually see as a result finding the desired image. Explain: Archimedes Principle, equations of continuity and Bernoulli, Sol - A body wholly or partly immersed in a fluid is pushed upward by a force that equals the weight of the fluid displaced by said body (Archimedes). The principle that expresses the conservation of mass in a fluid movement is known as the
Where is the fluid density, is the area through which the fluid at a given time and is the fluid velocity. That the product of these three quantities remain constant is a fancy way of saying that the mass does not change in the fluid. continuity equation:
The principle that expresses the conservation of energy in the movement of a fluid is known as
4)
Bernoulli's equation:
Where
and
and
the height at which the fluid moves,
is the pressure,
the severity
continue to express the density and
velocity of fluid. The first term is the kinetic energy per unit volume [J m -3], the second and third terms express the potential energy per unit volume [N m -2 = J m -3] due to internal forces (pressure) and external forces respectively. Therefore the total energy per unit volume remains constant. As you may know the distance that has been struck by lightning from where you find yourself? Sun - First "see" the beam. Light travels at a speed of approximately
[Ms -1] so we
can say that lightning emits light reaches us instantly. Then we have the time
that comes to
us in the "sound" of the beam. The speed of sound in air is worth
[Ms -1]. Then
using the relationship
the distance found. Practical part
1) a.
Using the definition of scalar product a b = (a) (b) cos and that
a b = a x b x + a and b and b z + z obtaining the angle between the vectors: a = 3 i + 3 j - 3 k and b = 2 i + 3 k
Sun - The angle will b.
Plot the vectors a = 3 i + 3 j + 3 k, and b = 2 i + 3 k and the vector product a
Sun -
2)
a = 9i - 3 j - 6 k, which must be stressed is that both a and b form a
plane
in space which is perpendicular to the vector to the graph is easily accomplished by locating the points in space (3,3,3), (2,0,2) and (9, -3, -6 ) indicating the end of each vector starting at the origin (0,0,0). He drops a stone from the top of a building. The sound of the stone to hit the ground is heard 6.5 s later. If the speed of sound is 1120 ft s -1 Calculate the height of the building. Sun - The total displacement covered by the stone and the sound is:
where g = -32.2 [ft / s 2] also
[S]
then
where
solution: 3)
[S]. Finally
cleared
staying
only
with
the
positive
[Feet].
(Venturi tube) analytically determining the fluid velocity, density known, it travels through the tube shown in the figure, where MP1 and MP2 are two pressure gauges. A 1 and A 2 are the areas perpendicular to the flow in regions 1 and 2 respectively.
Finally with data: = 1 g / cc, p 1 = 1000 N m -2 , P 2 = 800 N m -2, A 1 = 40 cm 2, A 2 = 22 cm 2, calculate v 1 Sun - From the continuity equation:
(A) And the Bernoulli equation when the system is in a horizontal position: (B)
If we replace (A) in (B) and then solve for
we obtain:
Replacing the data provided we find that:
13.16 [ms -1]
4)
Verify that when a wave hits a certain angle and passes through half limited by flat faces parallel, the direction of propagation of the beam emerging is parallel to the incident beam. Sun Consider the following figure:
Using the law of refraction or Snell's law we find: Similarly:
n 1 sin i) = n 2 sin t)
n 2 sin = n 2 sin
Now within the medium 2 is true also that i =
t.
Combining these equations is reached t = i, which is what we wanted to prove. June 8, 2003
REGIONAL PEACE CONTEST II
4th of Secondary SOLUTIONS 5)
6)
7)
Conceptual part Explain the Steiner theorem, also known as the parallel axis theorem. Sun - The parallel axis theorem is given by the relationship: , Where I is the inertia around the axis of rotation arbitrary I cm is the rotational inertia parallel axis passing through the center of mass, M is the total mass of the object and h is the perpendicular distance between the axes. The two axes are parallel. The moments of inertia with respect to the parallel axes relate in this simple way. Explain that the dynamic lifting force is the force acting on a body because of its motion through a fluid. Sun - These bodies are the wings of an airplane or a helicopter propellers. The streamlines of air around the wing of an aircraft for example cause the air speed above the wing has a greater magnitude than the air velocity below this, which means that the pressure above the wing is less than pressure below which must occur if there is to be a push upward. Comment: 1st and 2nd law of thermodynamics, entropy, reversible and irreversible processes, isothermal processes and adiabatic. Sun -
All thermodynamic system in an equilibrium state has a state variable, called the internal energy of the system is such that its change
where
Energy is added to
is the energy supplied by the system when performing work. (1st Law) the system by heat transfer and
It is impossible for a cycler not produce another effect that continuously transfer heat from one body to another at a higher temperature than this. It is also possible to reformulate the 2nd law in terms of entropy: A natural process that begins in an equilibrium state and ends in another place at the direction that causes the entropy of the system and its environment increases. Entropy is a thermodynamic variable that measures the disorder. If a change occurs very slowly so that at each moment the system is in an equilibrium position then the process is reversible. And if the system away from its equilibrium state then the process is irreversible. When there is a change in system pressure or volume but the temperature is kept constant is spoken of an isothermal process. When there are non-heat exchange between the system and the environment comes to an adiabatic process. An adiabatic process can be reversible or irreversible. 8)
Explain what the Doppler effect. When a person hears a sound is moving toward the stationary source that produces it, the frequency of the sound heard is greater than when at rest. If the person is moving away from the stationary source, less frequently heard when this than when at rest. Similarly is the
5)
equivalent when both source and person move away from or towards. This effect applies to all waves in general. Practical part A disc of 0.5 [m] radius and 20 [kg] of mass can rotate freely about a fixed horizontal axis passing through its center. Applies a force F of 9.8 [N] pulling a cord coiled around the edge of the disc.Find the angular acceleration of the disk and its angular velocity after 2 [s]. Finding the reaction force also exists in the brackets which support the axis of the disc. Sun -
6)
A semiquantitative definition of electric flux is: us that: q sphere vectors
7)
. And Gauss's law tells
. Write the electric field of a point charge q taking Gaussian surface as a of
radius r. Help: and
The
total
area
of
a
sphere
is
r 2 and
the
have the same direction.
A boat in motion produces surface waves on a calm lake. The boat runs 12 oscillations in 20 [s]; each oscillation produces a wave crest. The crest of the wave takes 6 [s] to reach the distant shore 12 [m]. Calculate the wavelength of surface waves.
8)
Three capacitors of 1.5 F], 2 F] and 3 F] are connected in a) series, b) are parallel and applies a potential difference of 20 [V]. Determine in each case i) the capacitance of the system, ii) loading and the potential difference of each capacitor, iii) energy of the system.
REGIONAL PEACE
3rd of Secondary SOLUTIONS 1)
Conceptual part What is the difference between mass and weight? Much do you weigh? Sun - The mass is a scalar, its units are [kg], the weight is a vector, is a force therefore is measured in Newtons [N]. If you say you have a mass of 66 [kg] weights then 66 [kg] [ms -2] = 645.15 [N].
9775 [ms -2] is gravity in La Paz. 9.81 [ms -2] is the gravity at sea level. 1.67 [ms -2] is the gravity on the moon. How much would you weigh on the moon? 2)
Everyone knows that when you look in a mirror is an inversion of the left and right. The right hand seems to be a left, left eye seems to be one law, etc.. Is it possible to design a mirror system that would allow to observe an image as the way in which people normally observed? If possible, draw a picture with some typical ray showing that this is true. Sun - If possible, be requires two mirrors that are joined at an angle of 90 between
3)
them. Each image in a mirror will be reflected in the other mirror as to achieve reverse what we usually see as a result finding the desired image. Explain: Archimedes Principle, equations of continuity and Bernoulli, Sol - A body wholly or partly immersed in a fluid is pushed upward by a force that equals the weight of the fluid displaced by said body (Archimedes). The principle that expresses the conservation of mass in a fluid movement is known as the
Where is the fluid density, is the area through which the fluid at a given time and is the fluid velocity. That the product of these three quantities remain constant is a fancy way of saying that the mass does not change in the fluid. continuity equation:
The principle that expresses the conservation of energy in the movement of a fluid is known as
4)
Bernoulli's equation:
Where
and
and
the height at which the fluid moves,
is the pressure,
the severity
continue to express the density and
velocity of fluid. The first term is the kinetic energy per unit volume [J m -3], the second and third terms express the potential energy per unit volume [N m -2 = J m -3] due to internal forces (pressure) and external forces respectively. Therefore the total energy per unit volume remains constant. As you may know the distance that has been struck by lightning from where you find yourself? Sun - First "see" the beam. Light travels at a speed of approximately
[Ms -1] so we
can say that lightning emits light reaches us instantly. Then we have the time
that comes to
us in the "sound" of the beam. The speed of sound in air is worth
[Ms -1]. Then
using the relationship
the distance found. Practical part
1) a.
Using the definition of scalar product a b = (a) (b) cos and that a b = a x b x + a and b and b z + z obtaining the angle between the vectors: a = 3 i + 3 j - 3 k and b = 2 i + 3 k
Sun - The angle will b. Sun -
Plot the vectors a = 3 i + 3 j + 3 k, and b = 2 i + 3 k and the vector product a a = 9i - 3 j - 6 k, which must be stressed is that both a and b form a
plane
in space which is perpendicular to the vector to the graph is easily accomplished by locating the points in space (3,3,3), (2,0,2) and (9, -3, -6 ) indicating the end of each vector starting at the origin (0,0,0).
2)
He drops a stone from the top of a building. The sound of the stone to hit the ground is heard 6.5 s later. If the speed of sound is 1120 ft s -1 Calculate the height of the building. Sun - The total displacement covered by the stone and the sound is:
where g = -32.2 [ft / s 2] also
[S]
then
where
solution: 3)
cleared
[S]. Finally
staying
only
with
the
positive
[Feet].
(Venturi tube) analytically determining the fluid velocity, density known, it travels through the tube shown in the figure, where MP1 and MP2 are two pressure gauges. A 1 and A 2 are the areas perpendicular to the flow in regions 1 and 2 respectively.
Finally with data: = 1 g / cc, p 1 = 1000 N m -2 , P 2 = 800 N m -2, A 1 = 40 cm 2, A 2 = 22 cm 2, calculate v 1 Sun - From the continuity equation:
(A) And the Bernoulli equation when the system is in a horizontal position: (B)
If we replace (A) in (B) and then solve for Replacing the data provided we find that: 4)
we obtain: 13.16 [ms -1]
Verify that when a wave hits a certain angle and passes through half limited by flat faces parallel, the direction of propagation of the beam emerging is parallel to the incident beam. Sun Consider the following figure:
Using the law of refraction or Snell's law we find: Similarly:
n 1 sin i) = n 2 sin t)
n 2 sin = n 2 sin
Now within the medium 2 is true also that i =
t.
Combining these equations is reached t = i, which is what we wanted to prove. June 8, 2003
REGIONAL PEACE CONTEST II
4th of Secondary SOLUTIONS 5)
6)
7)
Conceptual part Explain the Steiner theorem, also known as the parallel axis theorem. Sun - The parallel axis theorem is given by the relationship: , Where I is the inertia around the axis of rotation arbitrary I cm is the rotational inertia parallel axis passing through the center of mass, M is the total mass of the object and h is the perpendicular distance between the axes. The two axes are parallel. The moments of inertia with respect to the parallel axes relate in this simple way. Explain that the dynamic lifting force is the force acting on a body because of its motion through a fluid. Sun - These bodies are the wings of an airplane or a helicopter propellers. The streamlines of air around the wing of an aircraft for example cause the air speed above the wing has a greater magnitude than the air velocity below this, which means that the pressure above the wing is less than pressure below which must occur if there is to be a push upward. Comment: 1st and 2nd law of thermodynamics, entropy, reversible and irreversible processes, isothermal processes and adiabatic. Sun All thermodynamic system in an equilibrium state has a state variable, called the internal energy of the system is such that its change
where
Energy is added to
is the energy supplied by the system when performing work. (1st Law) the system by heat transfer and
It is impossible for a cycler not produce another effect that continuously transfer heat from one body to another at a higher temperature than this. It is also possible to reformulate the 2nd law in terms of entropy: A natural process that begins in an equilibrium state and ends in another place at the direction that causes the entropy of the system and its environment increases. Entropy is a thermodynamic variable that measures the disorder.
If a change occurs very slowly so that at each moment the system is in an equilibrium position then the process is reversible. And if the system away from its equilibrium state then the process is irreversible. When there is a change in system pressure or volume but the temperature is kept constant is spoken of an isothermal process. When there are non-heat exchange between the system and the environment comes to an adiabatic process. An adiabatic process can be reversible or irreversible. 8)
Explain what the Doppler effect. When a person hears a sound is moving toward the stationary source that produces it, the frequency of the sound heard is greater than when at rest. If the person is moving away from the stationary source, less frequently heard when this than when at rest. Similarly is the
5)
equivalent when both source and person move away from or towards. This effect applies to all waves in general. Practical part A disc of 0.5 [m] radius and 20 [kg] of mass can rotate freely about a fixed horizontal axis passing through its center. Applies a force F of 9.8 [N] pulling a cord coiled around the edge of the disc.Find the angular acceleration of the disk and its angular velocity after 2 [s]. Finding the reaction force also exists in the brackets which support the axis of the disc. Sun -
6)
A semiquantitative definition of electric flux is: us that: q sphere vectors
7)
. And Gauss's law tells
. Write the electric field of a point charge q taking Gaussian surface as a of
radius r. Help: and
The
total
area
of
a
sphere
is
r 2 and
the
have the same direction.
A boat in motion produces surface waves on a calm lake. The boat runs 12 oscillations in 20 [s]; each oscillation produces a wave crest. The crest of the wave takes 6 [s] to reach the distant shore 12 [m]. Calculate the wavelength of surface waves.
8)
Three capacitors of 1.5 F], 2 F] and 3 F] are connected in a) series, b) are parallel and applies a potential difference of 20 [V]. Determine in each case i) the capacitance of the system, ii) loading and the potential difference of each capacitor, iii) energy of the system.
