2.1 LINEAR MOTION Physical Quantity Distance, l
Definition, Quantity, Symbol and unit Distance is the total path length traveled from one location to another. Quantity: scalar SI unit: meter (m)
(a) The distance in a specified direction. (b)the distance between two locations measured along Displacement, the shortest path connecting them in a specific l direction. (c) The distance of its final position from its initial position in a specified direction. Quantity: vector
SI unit: meter (m)
Speed is the rate of change of distance Speed,v Speed = Distance traveled Time taken Quantity: scalar
SI unit: m s-1
Velocity is the rate of change of displacement. Velocity, v Velocity = Displacement Time taken Direction of velocity is the direction of displacement Quantity : Vector SI unit: m s-1 Average speed
v = Total distant traveled, s Total time taken , t
Average velocity
v = Displacement, s Time taken, t
Example: A car moves at an average speed / velocity of 20 ms-1 On average, the car moves a distance / displacement of 20 m in 1 second for the whole journey. 1
Uniform speed
Speed that remains the same in magnitude regardless of its direction.
Uniform velocity
Velocity that remains the same in magnitude and direction.
An object has a non-uniform velocity if: Acceleration, a
a=
v−u t
unit : ms-2
(a) the direction of motion changes or the motion is not linear. (b)The magnitude of its velocity changes. When the velocity of an object changes, the object is said to be accelerating. Acceleration is defined as the rate of change of velocity. Acceleration = Change in velocity Time taken = final velocity, v – initial velocity, u Time taken, t
acceleration is positive
• The velocity of an object increases from an initial velocity, u, to a higher final velocity, v
Deceleration
The rate of decrease in speed in a specified direction.
acceleration is negative.
The velocity of an object decreases from an initial velocity, u, to a lower final velocity, v.
Zero acceleration
An object moving at a constants velocity, that is, the magnitude and direction of its velocity remain unchanged – is not accelerating Velocity increases at a uniform rate. When a car moves at a constant or uniform acceleration of 5 ms-2, its velocity increases by 5 ms-1 for every second that the car is in motion.
Constant acceleration
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1. 2. 3. 4. 5.
Constant = uniform increasing velocity = acceleration decreasing velocity = deceleration zero velocity = object at stationary / at rest negative velocity = object moves at opposite direction 6. zero acceleration = constant velocity 7. negative acceleration = deceleration Comparisons between distance and displacement. Distance Total path length traveled from one location to another
Scalar quantity It has magnitude but no direction SI unit meter
Displacement The distance between two locations measured along the shortest path connecting them in specific direction Vector quantity
Comparisons between speed and velocity Speed The rate of change of distance Scalar quantity
Velocity The rate of change of displacement Vector quantity
It has magnitude but no direction
It has both magnitude and direction SI unit : m s-1
SI unit : m s-1
It has both magnitude and direction SI unit : meter
Fill in the blanks: 1. A steady speed of 10 m/s = A distance of .. ……….is traveled every ……….. 2. A steady velocity of -10 m/s = A …………. Of 10 m is traveled every ………..to the left. 3. A steady acceleration of 4 ms-2 = Speed goes up by 4 m/s every ………. 4. A steady deceleration of 4 ms-2 = speed goes ……….. by 4 m/s every ………. 5. A steady velocity of 10 m/s = …………………………………………… …………………………………………………………………………………
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Example 1 Every day Rahim walks from his house to the junction which is 1.5 km from his house. Then he turns back and stops at warung Pak Din which is 0.5 km from his house.
(a) What is Rahim’s displacement from his house • when he reaches the junction.
Example 2 Every morning Amirul walks to Ahmad’s house which is situated 80 m to the east of Amirul’s house. They then walk towards their school which is 60 m to the south of Ahmad’s house. (a) What is the distance traveled by Amirul and his displacement from his house? (b)If the total time taken by Amirul to travel from his house to Ahmad’s house and then to school is 15 minutes, what is his speed and velocity?
• When he is at warung Pak Din. (b)After breakfast, Rahim walks back to his house. When he reaches home, (i) what is the total distance traveled by Rahim? (ii)
what is Rahim’s total displacement from his house?
Example 3 Syafiq running in a race covers 60 m in 12 s. (a) What is his speed in m/s (b) If he takes 40 s to complete the race, what is his distance covered? 4
Example 4 An aeroplane flys towards the north with a velocity 300 km/hr in one hour. Then, the plane moves to the east with the velocity 400 km / hr in one hour. (a) What is the average speed of the plane? (b)What is the average velocity of the plane? (c) What is the difference between average speed and average velocity of the plane? Example 5 The speedometer reading for a car traveling north shows 80 km/hr. Another car traveling at 80 km/hr towards south. Is the speed of both cars same? Is the velocity of both cars same? A ticker timer ¾ Use: 12 V a.c power supply ¾ 1 tick = time interval between two dots. ¾ The time taken to make 50 ticks on the ticker tape is 1 second.
Hence, the time interval between 2 consecutive dots is 1/50 = 0.02 s. ¾ 1 tick = 0.02 s
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Relating displacement, velocity, acceleration and time using ticker tape. VELOCITY
FORMULA Time, t = 10 dots x 0.02 s = 0.2 s displacement, s = x cm velocity = s = x cm t 0.2 s
ACCELERATION
elapse time, t = (5 – 1) x 0.2 s = 0.8 s or t = (50 – 10) ticks x 0.02 s = 0.8 s
TICKER TAPE AND CHARTS
Initial velocity, u = x1 0.2 final velocity, v = x2 0.2 acceleration, a=v–u t
TYPE OF MOTION Constant velocity – slow moving Constant velocity – fast moving
¾ Distance between the dots
increases uniformly ¾ the velocity is of the object is increasing uniformly ¾ The object is moving at a uniform / constant acceleration.
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¾ Distance between the dots
decrease uniformly ¾ The velocity of the object is decreasing uniformly ¾ The object is experiencing uniform / constant deceleration Example 6 The diagram above shows a ticker tape chart for a moving trolley. The frequency of the ticker-timer used is 50 Hz. Each section has 10 dots-spacing. (a) What is the time between two dots. (b) What is the time for one strips. (c) What is the initial velocity (d) What is the final velocity. (e) What is the time interval to change from initial velocity to final velocity? (f) What is the acceleration of the object.
THE EQUATIONS OF MOTION u = initial velocity v = final velocity t = time taken s = displacement a = constant accleration
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2.2 MOTION GRAPHS DISPLACEMENT – TIME GRAPH
Velocity is obtained from the gradient of the graph. A – B : gradient of the graph is +ve and constant ∴ velocity is constant. B – C : gradient of the graph = 0 ∴ the velocity = 0, object at rest. C – D : gradient of the graph –ve and constant. The velocity is negative and object moves in the opposite direction.
VELOCITY-TIME GRAPH
GRAPH Zero velocity
s versus t
Area below graph Positive gradient Negative gradient Zero gradient
v versus t
Distance / displacement Constant Acceleration (A – B) Constant Deceleration (C – D) Constant velocity / zero acceleration (B – C) a versus t
Negative velocity
Constant velocity
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GRAPH Constant acceleration
s versus t
v versus t
a versus t
Constant deceleration
Example 7
Example 6 Contoh 11
Based on the s – t graph above: (a) Calculate the velocity at (i) AB (ii) BC (iii)
CD
(a) Calculate the acceleration at: (i) JK (ii) KL (iii) LM
(b) Describe the motion of the object at: (i) AB (ii) BC (iii) CD (b) Describe the motion of the object at: (i) JK (ii) KL (iii) LM (c)Find: (i) total distance (ii) total displacement
Calculate the total displacement.
(d) Calculate (i) the average speed (c) Calculate the average velocity. (ii)
the average velocity of the moving particle. 9
2.3 INERTIA Inertia
The inertia of an object is the tendency of the object to remain at rest or, if moving, to continue its motion.
Newton’s first law
Every object continues in its state of rest or of uniform motion unless it is acted upon by an external force. The larger the mass, the larger the inertia
Relation between inertia and mass SITUATION
SITUATIONS INVOLVING INERTIA EXPLAINATION When the cardboard is pulled away quickly, the coin drops straight into the glass. The inertia of the coin maintains its state at rest. The coin falls into the glass due to gravity.
Chili sauce in the bottle can be easily poured out if the bottle is moved down fast with a sudden stop. The sauce inside the bottle moves together with the bottle. When the bottle stops suddenly, the sauce continue in its state of motion due to the effect of its inertia. Body moves forward when the car stops suddenly The passengers were in a state of motion when the car was moving. When the car stopped suddenly, the inertia in the passengers made them maintain their state of motion. Thus when the car stop, the passengers moved forward. A boy runs away from a cow in a zig zag motion. The cow has a large inertia making it difficult to change direction.
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• The head of hammer is secured tightly to its handle by knocking one end of the handle, held vertically, on a hard surface. • This causes the hammer head to continue on its downward motion when the handle has been stopped, so that the top end of the handle is slotted deeper into the hammer head.
Ways to reduce the negative effects of inertia
Relationship between mass and inertia
• The drop of water on a wet umbrella will fall when the boy rotates the umbrella. • This is because the drop of water on the surface of the umbrella moves simultaneously as the umbrella is rotated. • When the umbrella stops rotating, the inertia of the drop of water will continue to maintain its motion. 1. Safety in a car: (a) Safety belt secure the driver to their seats. When the car stops suddenly, the seat belt provides the external force that prevents the driver from being thrown forward. (b)Headrest to prevent injuries to the neck during rear-end collisions. The inertia of the head tends to keep in its state of rest when the body is moved suddenly. (c) An air bag is fitted inside the steering wheel. It provides a cushion to prevent the driver from hitting the steering wheel or dashboard during a collision. 2. Furniture carried by a lorry normally are tied up together by string. When the lorry starts to move suddenly, the furniture are more difficult to fall off due to their inertia because their combined mass has increased. • Two empty buckets which are hung with rope from a the ceiling. • One bucket is filled with sand while the other bucket is empty. • Then, both pails are pushed. • It is found that the empty bucket is easier to 11
• •
• •
push compared to the bucket with sand. The bucket filled with sand offers more resistance to movement. When both buckets are oscillating and an attempt is made to stop them, the bucket filled with sand offers more resistance to the hand (more difficult to bring to a standstill once it has started moving) This shows that the heavier bucket offers a greater resistance to change from its state of rest or from its state of motion. An object with a larger mass has a larger inertia.
2.4 MOMENTUM Definition
Momentum = Mass x velocity = mv SI unit: kg ms-1
Principle of Conservation of Momentum
In the absence of an external force, the total momentum of a system remains unchanged.
Elastic Collision
Both objects move independently at their respective velocities after the collision. Momentum is conserved. Kinetic energy is conserved. Total energy is conserved.
Inelastic collision
The two objects combine and move together with a common velocity after the collision. Momentum is conserved. Kinetic energy is not conserved. Total energy is conserved. 12
Total Momentum Before = total momentum After m1u1 + m2u2 = m1v1 + m2v2
Total Momentum Before = Total Momentum After m1u1 + m2u2 = (m1 + m2) v Explosion Before explosion both object stick together and at rest. After collision, both object move at opposite direction. Total Momentum Total Momentum before collision after collision : Is zero m1v1 + m2v2 From the law of conservation of momentum: Total Momentum = Total Momentum Before collision after collision 0 = m1v1 + m2v2 m1v1 = - m2v2
-ve sign means opposite direction EXAMPLES OF EXPLOSION (Principle Of Conservation Of Momentum) ¾ When a rifle is fired, the bullet of mass m, moves with a high velocity, v. This creates a momentum in the forward direction. ¾ From the principle of conservation of momentum, an equal but opposite momentum is produced to recoil the riffle backward. Application in the jet engine: A high-speed hot gases are ejected from the back with high momentum. This produces an equal and opposite momentum to propel the jet plane forward. 13
The launching of rocket ¾ Mixture of hydrogen and oxygen fuels burn explosively in the combustion chamber. Jets of hot gases are expelled at very high speed through the exhaust. ¾ These high speed hot gases produce a large amount of momentum downward. ¾ By conservation of momentum, an equal but opposite momentum is produced and acted on the rocket, propelling the rocket upwards. In a swamp area, a fan boat is used. ¾ The fan produces a high speed movement of air backward. This produces a large momentum backward. ¾ By conservation of momentum, an equal but opposite momentum is produced and acted on the boat. So the boat will move forward. A squid propels by expelling water at high velocity. Water enters through a large opening and exits through a small tube. The water is forced out at a high speed backward. Total Mom. before= Total Mom. after 0 =Mom water + Mom squid 0 = mwvw + msvs -mwvw = msvs The magnitude of the momentum of water and squid are equal but opposite direction. This causes the squid to jet forward.
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Example
Car A of mass 1000 kg moving at 20 ms-1 collides with a car B of mass 1200 kg moving at 10 m s-1 in same direction. If the car B is shunted forwards at 15 m s-1 by the impact, what is the velocity, v, of the car A immediately after the crash?
Example
A truck of mass 1200 kg moving at 30 m/s collides with a car of mass 1000 kg which is traveling in the opposite direction at 20 m/s. After the collision, the two vehicles move together. What is the velocity of both vehicles immediately after collision?
Example
Before collision
After collision
MA = 4 kg MB = 2 kg UA = 10 m/s to the left UB = 8 m/s to the right VB = 4 m/s to the left. Calculate the value of VA .
Example
A man fires a pistol which has a mass of 1.5 kg. If the mass of the bullet is 10 g and it reaches a velocity of 300 m/s after shooting, what is the recoil velocity of the pistol?
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2.5 FORCE Example: Balanced Force When the forces acting on an object are balanced, they cancel each other out. The net force is zero. Effect : the object at is at rest [ velocity = 0] or moves at constant velocity [ a = 0]
Weight, W = Lift, U Unbalanced Force/ Resultant Force
Thrust, F = drag, G
When the forces acting on an object are not balanced, there must be a net force acting on it. The net force is known as the unbalanced force or the resultant force. Effect : Can cause a body to - change it state at rest (an object will accelerate - change it state of motion (a moving object will decelerate or change its direction)
Force, Mass & Acceleration The acceleration produced by a force on an object Newton’s Second is directly proportional to the magnitude of the net Law of Motion force applied and is inversely proportional to the mass of the object. The direction of the acceleration is the same as that of the net force. When a net force, F, acts on a mass, m it causes an acceleration, a.
Force = Mass x Acceleration F = ma 16
Relationship between a & F
Relationship between a and m
aαF The acceleration, a, is directly proportional to the applied force, F. a∝
1 m
The acceleration of an object is inversely proportional to the mass,
Experiment to Find The Relationship between Force, Mass & Acceleration Relationship between Situation
Inference
Hypothesis
a&F
a&m
Both men are pushing the same mass but man A puts greater effort. So he moves faster. The acceleration produced by an object depends on the net force applied to it.
Both men exerted the same strength. But man B moves faster than man A.
The acceleration of the object increases when the force applied increases
The acceleration of the object decreases when the mass of the object increases
Variables: Manipulated : Force Responding : Acceleration Constant : Mass Apparatus and Material
The acceleration produced by an object depends on the mass
Mass Acceleration Force
Ticker tape and elastic cords, ticker timer, trolleys, power supply and friction compensated runway and meter ruler. 17
Procedure : - Controlling manipulated variables.
An elastic cord is hooked over the trolley. The elastic cord is stretched until the end of the trolley. The trolley is pulled down the runway with the elastic cord being kept stretched by the same amount of force
An elastic cord is hooked over a trolley. The elastic cord is stretched until the end of the trolley. The trolley is pulled down the runway with the elastic cord being kept stretched by the same amount of force
- Controlling responding variables.
Determine the acceleration by analyzing the ticker tape.
Determine the acceleration by analyzing the ticker tape.
Acceleration a =
Acceleration a =
- Repeating experiment.
v−u t
v−u t
Repeat the experiment by Repeat the experiment by using two , three, four using two, three, four and and five elastic cords five trolleys.
Recording data
Analysing data
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1. What force is required to move a 2 kg object with an acceleration of 3 m s-2, if (a) the object is on a smooth surface? (b) The object is on a surface where the average force of friction acting on the object is 2 N?
2. Ali applies a force of 50 N to move a 10 kg table at a constant velocity. What is the frictional force acting on the table?
3. A car of mass 1200 kg traveling at 20 m/s is brought to rest over a distance of 30 m. Find (a) the average deceleration, (b) the average braking force.
4. Which of the following systems will produce maximum acceleration?
2.6 IMPULSE AND IMPULSIVE FORCE Impulse
The change of momentum mv - mu Unit : kgms-1 or Ns Impulsive The rate of change of momentum in a Force collision or explosion
Effect of time
Unit = N Impulsive force is inversely proportional to time of contact
m = mass u = initial velocity v = final velocity t = time
Longer period of time →Impulsive force decrease Shorter period of time →Impulsive force increase 19
Situations for Reducing Impulsive Force in Sports Situations Explanation Thick mattress with soft surfaces are used in events such as high jump so that the time interval of impact on landing is extended, thus reducing the impulsive force. This can prevent injuries to the participants.
Goal keepers will wear gloves to increase the collision time. This will reduce the impulsive force. A high jumper will bend his legs upon landing. This is to increase the time of impact in order to reduce the impulsive force acting on his legs. This will reduce the chance of getting serious injury. A baseball player must catch the ball in the direction of the motion of the ball. Moving his hand backwards when catching the ball prolongs the time for the momentum to change so as to reduce the impulsive force. Situation of Increasing Impulsive Force Situations Explanation A karate expert can break a thick wooden slab with his bare hand that moves at a very fast speed. The short impact time results in a large impulsive force on the wooden slab. A massive hammer head moving at a fast speed is brought to rest upon hitting the nail. The large change in momentum within a short time interval produces a large impulsive force which drives the nail into the wood.
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A football must have enough air pressure in it so the contact time is short. The impulsive force acted on the ball will be bigger and the ball will move faster and further.
Pestle and mortar are made of stone. When a pestle is used to pound chilies the hard surfaces of both the pestle and mortar cause the pestle to be stopped in a very short time. A large impulsive force is resulted and thus causes these spices to be crushed easily. Example 1 A 60 kg resident jumps from the first floor of a burning house. His velocity just before landing on the ground is 6 ms-1. (a) Calculate the impulse when his legs hit the ground. (b) What is the impulsive force on the resident’s legs if he bends upon landing and takes 0.5 s to stop? (c) What is the impulsive force on the resident’s legs if he does not bend and stops in 0.05 s? (d) What is the advantage of bending his legs upon landing? Example 2 Rooney kicks a ball with a force of 1500 N. The time of contact of his boot with the ball is 0.01 s. What is the impulse delivered to the ball? If the mass of the ball is 0.5 kg, what is the velocity of the ball?
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2.7 SAFETY VEHICLE
Component Function Headrest To reduce the inertia effect of the driver’s head. Air bag Absorbing impact by increasing the amount of time the driver’s head to come to the steering. So that the impulsive force can be reduce Windscreen The protect the driver Crumple Can be compressed during accident. So it can increase zone the amount of time the car takes to come to a complete stop. So it can reduce the impulsive force. Front Absorb the shock from the accident. Made from steel, bumper aluminium, plastic or rubber. ABS Enables drivers to quickly stop the car without causing the brakes to lock. Side impact Can be compressed during accident. So it can increase bar the amount of time the car takes to come to a complete stop. So it can reduce the impulsive force. Seat belt To reduce the inertia effect by avoiding the driver from thrown forward.
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2.8 GRAVITY Gravitational Objects fall because they are pulled towards the Earth Force by the force of gravity. This force is known as the pull of gravity or the earth’s gravitational force. The earth’s gravitational force tends to pull everything towards its centre. Free fall
¾ An object is falling freely when it is falling under the ¾ ¾
¾
Acceleration due to gravity, g
¾ ¾ ¾
¾
force of gravity only. A piece of paper does not fall freely because its fall is affected by air resistance. An object falls freely only in vacuum. The absence of air means there is no air resistance to oppose the motion of the object. In vacuum, both light and heavy objects fall freely. They fall with the same acceleration ie. The acceleration due to gravity, g. Objects dropped under the influence of the pull of gravity with constant acceleration. This acceleration is known as the gravitational acceleration, g. The standard value of the gravitational acceleration, g is 9.81 m s-2. The value of g is often taken to be 10 m s-2 for simplicity. The magnitude of the acceleration due to gravity depends on the strength of the gravitational field.
Gravitational The gravitational field is the region around the earth in field which an object experiences a force towards the centre of the earth. This force is the gravitational attraction between the object and the earth. The gravitational field strength is defined as the gravitational force which acts on a mass of 1 kilogram. g=
F m
Its unit is N kg-1. 23
Gravitational field strength, g = 10 N kg-1 Acceleration due to gravity, g = 10 m s-2 The approximate value of g can therefore be written either as 10 m s-2 or as 10 N kg-1. Weight
Comparison between weight & mass
The gravitational force acting on the object. Weight = mass x gravitational acceleration W = mg SI unit : Newton, N and it is a vector quantity Mass The mass of an object is the amount of matter in the object Constant everywhere A scalar quantity A base quantity SI unit: kg
Weight The weight of an object is the force of gravity acting on the object. Varies with the magnitude of gravitational field strength, g of the location A vector quantity A derived quantity SI unit : Newton, N
The difference between a fall in air and a free fall in a vacuum of a coin and a feather. Both the coin and the feather are released simultaneously from the same height.
At vacuum state: There is no air resistance. The coin and the feather will fall freely. Only gravitational force acted on the objects. Both will fall at the same time.
At normal state: Both coin and feather will fall because of gravitational force. Air resistance effected by the surface area of a fallen object. The feather that has large area will have more air resistance. The coin will fall at first. 24
(a) The two sphere are falling with an acceleration.
Two steel spheres are falling under gravity. The two spheres are dropped at the same time from the same height.
The distance between two successive images of the sphere increases showing that the two spheres are falling with increasing velocity; falling with an acceleration.
(b)The two spheres are falling down with the same acceleration The two spheres are at the same level at all times. Thus, a heavy object and a light object fall with the same gravitational acceleration. Gravitational acceleration is independent of mass.
Motion graph for free fall object Free fall object Object thrown upward
Object thrown upward and fall
Example 1 A coconut takes 2.0 s to fall to the ground. What is (a) its speed when it strikes the ground (b) the height of the coconut tree.
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2.9 FORCES IN EQUILIBRIUM Forces in When an object is in equilibrium, the resultant force acting Equilibrium on it is zero. The object will either be 1. at rest 2. move with constant velocity. Newton’s 3rd Law Examples( Label the forces acted on the objects)
Resultant Force
A single force that represents the combined effect of two of more forces in magnitude and direction.
Addition of Forces Resultant force, F = ____ + ____
Resultant force, F = ____ + ____
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Two forces acting at a point at an angle [Parallelogram method]
STEP 1 : Using ruler and protractor, draw the two forces F1 and F2 from a point.
STEP 3 Draw the diagonal of the parallelogram. The diagonal represent the resultant force, F in magnitude and direction.
STEP 2 Complete the parallelogram
scale: 1 cm = ……
Resolution of Forces
Fx = F cos θ Fy = F sin θ
A force F can be resolved into components which are perpendicular to each other: (a) horizontal component , FX (b) vertical component, FY Inclined Plane
Component of weight parallel to the plane = mg sin θ Component of weight normal to the plane = mg cos θ 27
find the resultant force
(d)
(e)
Lift Stationary Lift
Lift accelerate upward
Lift accelerate downward
Resultant Force =
Resultant Force =
Resultant Force =
The reading of weighing scale =
The reading of weighing scale =
The reading of weighing scale = 28
Pulley
1. Find the resultant force, F 2. Find the moving mass,m 3. Find the acceleration,a 4. Find string tension, T
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2.10 WORK, ENERGY, POWER & EFFICIENCY Work
Work done is the product of an applied force and the displacement of an object in the direction of the applied force W = Fs
The SI unit of work is the joule, J
W = work, F = force s = displacement
1 joule of work is done when a force of 1 N moves an object 1 m in the direction of the force
Calculation of Work The displacement, s of the object is in the direction of the force, F
W = Fs
s
The displacement , s of the object is not in the direction of the force, F
F
W = (F cos θ) s W=Fs Example 1 A boy pushing his bicycle with a force of 25 N through a distance of 3 m.
Calculate the work done by the boy.
Example 2 A girl is lifting up a 3 kg flower pot steadily to a height of 0.4 m.
What is the work done by the girl?
Example 3 A man is pulling a crate of fish along the floor with a force of 40 N through a distance of 6 m.
What is the work done in pulling the crate?
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No work is done when: The object is stationary
A student carrying his bag while waiting at the bus stop
Concept Power
Energy
The direction of motion of the object is perpendicular to that of the applied force.
A waiter is carrying a tray of food and walking
Definition The rate at which work is done, or the amount of work done per second.
No force is applied on the object in the direction of displacement (the object moves because of its own inertia) A satellite orbiting in space. There is no friction in space. No force is acting in the direction of movement of the satellite.
Formula & Unit
P=
W t
p = power, W = work / energy t = time
¾ Energy is the capacity to do work. ¾ An object that can do work has energy ¾ Work is done because a force is applied and the
objects move. This is accompanied by the transfer of energy from one object to another object. ¾ Therefore, when work is done, energy is transferred from one object to another. ¾ The work done is equal to the amount of energy transferred. Potential Energy
Gravitational potential energy is the energy of an object due to its higher position in the gravitational field.
m = mass h = height g = gravitational acceleration E = mgh
Kinetic Energy
Kinetic energy is the energy of m = mass an object due to its motion. v = velocity E = ½ mv2
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Principle of Conservation of Energy
Energy can be changed from one form to another, but it cannot be created or destroyed. The energy can be transformed from one form to another, total energy in a system is constant. Total energy before = total energy after
Example 4 A worker is pulling a wooden block of weight,W,with a force of P along a fritionless plank at height of h. The distance traveled by the block is x. Calculate the work done by the worker to pull the block.
Example 5 A student of mass m is climbing up a flight of stairs which has the height of h. He takes t seconds..
What is the power of the student?
Example 6 A stone is thrown upward with initial -1 velocity of 20 ms . What is the maximum height which can be reached by the stone?
Example 7
A boll is released from point A of height 0.8 m so that it can roll along a curve frictionless track. What is the velocity of the ball when it reaches point B?
Example 8
Example 9
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A trolley is released from rest at point X along a frictionless track. What is the velocity of the trolley at point Y?
A ball moves upwards along a frictionless track of height 1.5 m with a velocity of -1 6 ms . What is its velocity at point B?
Example 10 A boy of mass 20 kg sits at the top of a concrete slide of height 2.5 m. When he slides down the slope, he does work to overcome friction of 140 J. What is his velocity at the end of the slope?
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2.12 ELASTICITY Elasticity
A property of matter that enables an object to return to its original size and shape when the force that was acting on it is removed. No external force is applied. Molecules are at their equilibrium separation. Intermolecular force is equal zero.
Compressing a solid causes its molecules to be displaced closer to each other. Repulsive intermolecular force acts to push the molecules back to their original positions.
Stretching a solid causes its molecules to be displaced away from each other. Attractive intermolecular force acts to pull back the molecules to their original positions.
Stretching a wire by an external force:
¾ Its molecules are slightly displaced away from
one another. ¾ Strong attractive forces act between the molecules to oppose the stretching When the external force is removed: ¾ The attractive intermolecular forces bring the molecules back to their equilibrium separation. ¾ The wire returns to its original position
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Hooke’s Law
The extension of a spring is directly proportional to the applied force provided the elastic limit is not exceeded. F = kx F= force on the spring x = extension k = force constant of the spring
Force extension graph
Based on the graph: Relationship between F & x : F is directly proportional to x The gradient of the graph represent = force constant of the spring, k Area under the graph equal to the work done to extent the spring: = elastic potential energy = ½ Fx = ½ kx2
The elastic limit of a spring
The maximum force that can be applied to a spring such that the spring will be able to be restored to its original length when the force is removed. If a force stretches a spring beyond its elastic limit, the spring cannot return to its original length even though the force no longer acts on it. The Hooke’s law is not obeyed anymore.
Force constant of the spring, k
The force required to produce one unit of extension of the spring. k=
F x
unit N m-1 or N cm-1 or N mm-1
k is a measurement of the stiffness of the spring ¾ The spring with a larger force constant is harder to extend and is said to be more stiff. ¾ A spring with a smaller force constant is easier to extend and is said to be less stiff or softer. 35
Factors that effect elasticity Factor Change in factor
How does it affects the elasticity Length Shorter spring Less elastic Longer spring More elastic Diameter of spring Smaller diameter More elastic wire Larger diameter Less elastic Diameter spring Smaller diameter Less elastic Larger diameter More elastic Type of material Springs made of different materials Elasticity changes according to the type of material Arrangement of the spring In series
In parallel
The same load is applied to each The load is shared equally among the spring. springs. W Tension in each spring = W Tension in each spring = 2 Extension of each spring = x x Total extension = 2x Extension of each spring = 2 If n springs are used: If n springs are used: The total extension = nx x The total extension = n
Example 1 The original length of each spring is 10 cm. With a load of 10 g, the extension of each spring is 2 cm. What is the length of the spring system for (a), (b) and (c)?
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SECTION A QUESTION 1 Figure 1.1 shows a car moving along a straight line but hilly road. Figure 1.1 Figure 1.2 shows how the velocity of the car varies with time as it travels from A to E. The car travels at 60 kmh-1 from A to B for two minutes. (a)
(b)
Figure 1.2 Describe the acceleration of the car as it travels from A to E. ………………………………………………… ……………………………. Compare the resultant force as it travels along AB and CD.
(c)
………………………………………………… …………………………… Give a reason to your answer in (b)
(d)
………………………………………………… ………………………… Calculate the distance AB
2 m
1 m
1 m
2 m (e)
The velocity of a car increases if the force exerted on the accelerator of a car increases. Explain why the velocity of the car increases from D to E although the force on the accelerator of the car is the same as a long C to D. …………………………………………………
2 m 38
…………………………… ………………………………………………… …………………………...
QUESTION 2 (SPM 1999)
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QUESTION 3 ( SPM 2000) Figure 2 Figure 2 shows a car of mass 1 000kg moving a straight but hilly road. QRST and TU is the part of the hill that have constant slope where the slope of QRST is higher that the slope of TU. The frictional force that acts along QRSTU is 2 000N. The velocity if the car at P is 80kmh-1 and takes 3 minutes to move from point P to Q. The motion of the car along PQRSTU represent by a velocity-time graph in Figure 3.
(e) Why is it necessary to ha capacity limit for the safe A bus traveled from Kota the bus? Lumpur at 9:00 pm. The cap passenger in the bus is 40 ……………………………… mass…………………………… of the bus with the ca and the average frictional fo bus tire and the road for the jo ……………………………… The bus moves at average sp …………………………… Kota Bharu before stopover a at 12:00 mid night on the s hour later the bus continue Kuala Lumpur with average The bus arrived at 6:00 am on (a) Put in a table all the phys involved in the informatio two groups.
(b) Calculate the total distanc the bus.
(c) Sketch a distance-time gr the motion of the bus.
(d) (i) What is the value of the tr the bus when it moves at speed?
(ii) ……………………………… …………………………… Give a reason for the ans
……………………………… 40 ……………………………
(a) Classify the physical quantity into two groups. 2m (b) From the graph in Figure 3, explain the acceleration of the car from point P to S. ………………………………………………………………………………………… ………………………………………………………………………………………… 2m (c) (i) Compare the resultant force of the car when the move along PQ and ST. 1m …………………………………………………………………………………….. (ii) State a reason for your answer in c(i) 1m ……………………………………………………………………………………... (d) Calculate the distance form point P to Q
2m QUESTION 4 (SPM 2002) Figure 3(i) Figure 3(ii) Figure 3(i) shows a sky diver start to make a jump from an aircraft at a certain height. Figure 3(ii) shows a velocity-time graph for the skydiver at position S, T, U, V and W from the earth surface. (a) (i) At which point the parachute start to open? …………………………………………………………………………………… (ii) Give a reason for your answer in (a)(i)
1m
…………………………………………………………………………………… (b) Calculate the acceleration of the diver at ST.
1m
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2m (c) Sketch an acceleration-time graph for the motion of the skydiver at point S, T, U, V and W at the space below.
3m (d) Suggest one way that can the skydiver apply to reduce injuries on his leg during landing. Explain your answer. ………………………………………………………………………………………... ………………………………………………………………………………………..
QUESTION 5 (SPM 1988)
Figure 4(i) 42
2m
Figure 4(i) show a gun fires a bullet of mass 5g to an object. (a) (i) What happen to the gun during the shot? 1m ………………………………………………………………………………….. (ii) Explain your answer in (a)(i) 1m …………………………………………………………………………………... (b) The bullet shot the object of mass 0.495kg. (i) If the bullet speed is 400ms-1, what is the momentum of the bullet? 2m (ii) What is speed of the object after the bullet obscured into the object after the gunshot? 2m (c) The object and the bullet that obscured in the object aloft at a maximum height of H, as shown in Figure 4(ii).
Figure 4(ii) (i) What is the value of kinetic energy of the object together with the bullet 2m inside the object?
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(ii) Calculate maximum height, H achieved by the object? 2m
1m (iii) In real situation it is possible to achieved maximum height, H. Why? …………………………………………………………………………………… …………………………………………………………………………………… QUESTION 6 (SPM 1994) Figure 5 shows a man standing on a stationary boat. He then jumps out of the boat onto the jetty. The boat moves a way from the jetty as he jumps. Figure 5 (a) State the physics principle that is involved in the movement of the boat as the man jumps onto the jetty.
………………………………………………………………………………………… 1m (b) Explain why the boat moves away from the jetty when the man jumps.
………………………………………………………………………………………… 1m (c) The mass of the man is 50 kg and he jumps at a velocity 2ms-1. The mass of the boat is 20kg. Calculate the velocity of the boat as the man jumps.
2m (d) Name one application of the physics principle stated in (a) in an exploration of outer space. ………………………………………………………………………………………… m 44
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