Excel Review Center 1.
2.
3.
4.
5.
6.
7.
8.
9.
An 8-gram object is attached to a spring that requires a force of 1000 dynes to extend its length 5 cm greater than its natural length. What is the period of the spring’s simple harmonic motion? Ans. 1.26 s A simple pendulum has a period of 1 2 s in Manila, where g is exactly 32 ft/s . This pendulum is taken to Cebu where it is found to lose 20 oscillations per day. What is the acceleration due to gravity in Cebu? Ans. 32.185 ft/s2 A string 100 cm long has a frequency of 200 vibrations per second. What is the frequency of this string under the same tension but cut to half in length? Ans. 400 vps A 1-m string has a mass of 4 grams and frequency of 250 vibrations per second. Another string, same length but mass is 1 g, is put to the same tension as the first. What is the frequency of vibration? Ans. 500 vps
ECE Refresher Course 13. How many nuclei are there in 1 kg of aluminum if the atomic mass of aluminum is 26.98 g/mol? Ans. 25 2.35x10 14. If the average distance the free electrons travel between collisions in copper is 4x10-8 m, in a span of 1 second, what is the time between collisions? The average electron 6 speed in copper is 1.21x10 m/s. Ans. 3.3x10-14 s 15. Find the deBroglie wavelength corresponding to an electron with energy 1, 104 or 105 eV. Neglect any corrections connected with the theory of relativity. Ans. 16. Calculate the wavelength of the first line in the visible (Balmer) series of the hydrogen spectrum, for which the electron transition is from orbit 3 to orbit 2. Ans. 6560 A 17. At what velocity is the mass of a particle twice its rest mass? Ans. 2.664x1010 cm/s
Sound with a frequency of 1000 Hz is produced when the air temperature is 15 degrees centigrade. What is the wavelength of this sound? Ans. 1.12 ft/cycle
18. An observer moves past a meter stick at a velocity that is one-half the velocity of light. What length does he measure for the meter stick? Ans. 86.6 cm
Compute the speed of sound in the steel rails of a railroad track. The weight density of steel is 490 lb/ft 3. Modulus of elasticity for steel is 29x106 psi. Ans. 1.6x104 ft/s
19. A man planned of building a house. The cost of construction is P500,000 while annual maintenance cost is estimated at P10,000. If the interest is 6%, what is the capitalized cost of the house? Ans. P666,667
A researcher notices that the frequency of a note emitted by a car horn appears to drop from 284 Hz to 266 Hz as the car passes by him. From this observation, he is able to calculate the speed of the car. What value does he obtain for the speed (in mph) if the speed of sound is said to be 1100 ft/s? Ans. 24.5 mph A man has a concave shaving mirror whose focal length is 20 in. How far should the mirror be held from his face in order to give an image of twohold magnification? Ans. 10 in A flat bottom swimming pool is 8 ft deep. How deep does it appear to be filled with water whose refractive index is 4/3? Ans. 6 ft
10. The length of a microscope tube is 10 cm. The focal length of the objective lens is 0.5 cm and the focal length of the eyepiece is 2 cm. What is the magnifying power of the microscope? Ans. 250 11. A certain farsighted person has a minimum distance of distinct vision of 150 cm. He wishes to read type at a distance of 25 cm. What focal length glasses should he use? Ans. 30 cm 12. What is the energy content of 1 gram 13 of water? Ans. 9x10 J
20. At 6% per annum, find the capitalized cost of a bridge whose cost is P250M and life is 20 years, if the bridge must be partially rebuilt at a cost of P100M at the end of each 20 years. Ans. P295,308,323.10 21. An investment, consisting of deposits of P1000, P1500 and P2000 are made at the end of the 2nd year, 3rd year and 4th year, respectively. If money is worth 10%, what is the equivalent present worth of the investment? Ans. 3319.45 22. Carmelo Anthony is earning an annual salary of $5M for 10 years from the Knicks. The Lakers would like to acquire his services as a replacement for Kobe Bryant. They offered Anthony an initial annual salary of $3M but is increasing at the rate of $600,000 annually. If he can still play in the NBA for 10 years and money is worth 10%, where should he play and why? Ans. Lakers, $235,276 more annually. 23. A machine costing P720,000 is estimated to have a book value of P40,545.73 at the end of 10 years. Depreciation cost is computed using a constant percentage of the declining book value. What is the annual rate of depreciation? Ans. 25%
Baguio: PiRC Building, Gapuz Centrum II, 80 T. Alonso St., New Lucban CP: 0928 934 1637
GEAS 24. An equipment cost P10,000 with a salvage value of P500 at the end of 10 years. Calculate the annual depreciation cost by sinking fund method at 4% interest? Ans. P791.26 25. If you borrowed money from your friend with simple interest of 12%, find the present worth of P50,000 which is due at the end of 7 months. Ans. P46,728.97 26. What nominal rate, compounded semi-annually, yields the same amount as 16% compounded bimonthly Ans. 16.32% 27. In year 0, you invest P10,000.00 in a 15% security for 5 years. During that time, the average inflation is 6%. How much, in terms of year 0 pesos will be in the account at maturity? Ans. 15,030.03 28. Money is deposited in a certain account for which the interest is compounded continuously. If the balance doubles in 6 years, what is the annual percentage rate? Ans. 11.55% 29. The mass of a rectangular bar of iron is 320 g. It is 2x2x10 cm in dimensions. What is its specific gravity? Ans. 8 30. Find the force acting on the bottom of an aquarium having a base 1 ft by 2 ft and containing water to a depth of 1 ft? Ans. 124.8 lb 31. How much pressure is needed to raise water to the top of the Empire State Building, which is 1250 ft high? Ans. 542 psi 32. A steel shaft 12 ft long and 8 in in diameter is part of a hydraulic press used to raise up cars in a garage. When it is supporting a car weighing 3200 lb, what is the decrease in length of the shaft? E for steel is 29x106 psi. Ans. 0.000316 in 33. A ship is being towed by a tug by means of a steel wire. If the drag on the ship is equivalent to 2x106 lb and if the breaking strain of the wire is 0.025, what is the smallest permissible diameter of wire that may be used? Ans. 1.87 in 34. By how much will the de Broglie wavelength of a particle increase if the momentum of a de Broglie wavelength of the particle is decreased by 30%?
h mv
'
h h 1.429 1.42 mv 0.70 mv
' 0.429 Ans Note: Answer is 43%, closest to 0.429 35. An particle with a mass of 4 kg is initially at rest. How much kinetic energy does this particle will have if a force of 10 N is applied to it for 10 second?
Manila: CMFFI Bldg. R. Papa St. Tel. 7365291
Excel Review Center
ECE Refresher Course
Ft mv
m2 s v' = 10 2
10 N10 s 4 kgv; v = 25 m/s
KE =
80 kg
2
m 1 2 1 mv 4 kg 25 1250 J 2 2 s
T' = T' =
40. A solid sphere with a mass of 12 kg and radius of 8 cm rolls without slipping down an inclined plane, starting from rest, from a height of 2 m to ground level. Assuming no frictional losses, what is the translational velocity of the sphere when it is rolling across the ground?
m 15.3 kg Ans 38. A compound microscope has a focal length of its objective and eyepiece of 3.5 cm and 6.5 cm, respectively. What is the angular magnification of the microscope if a person using it has a near point of 30 cm?
M mo me
16 25 18x Ans 3.5 6.5
39. A ball of mass 10 kg is attached to the end of a string and is swung in a circle of radius 4 m with a constant linear velocity o 2 m/s. While the ball is in motion, the string is shortened to 2 m. What is the change in the period of the motion? Get the initial angular momentum:
L = mvr L = 10 2 4 L = 80 kg
m2 s
Solve for the initial period:
T= T=
2 r v 2 4
2 T = 12.56 s Since the angular momentum is conserved, after shortening the string:
Use the Law of Conservation of Energy:
PE KE translational KE rotational 1 1 mv 2 I2 2 2 1 12 2 mgh mv mr 2 2 2 25 1 2 1 2 2 gh v r 2 5 mgh
1 2 1 2 v v r 2 5 r 1 2 1 2 gh v v 2 5 7 2 gh v 10
2
gh
v
10 m 9.81 2 2 m 7 s
m2 s
Solve for the new velocity:
44. What is the energy in electronvolts of a photon of green light of wavelength 546 nm? E hf Eh
c
E 6.63 1034
3 10 546 10 8
9
1 eV E 3.64 1019 J 1.6 1019 J E 2.28 eV Ans
45. What is the fractional part of the iceberg that is above the seawater surface if its specific gravity is 0.90 and that of seawater 1.03? Note: The portion of the iceberg that is underwater must displace enough seawater to support its own weight
Wsubmerged Wseawater mgsubmerged mgseawater submerged Vg seawater Vg submerged seawater submerged seawater
0.90 87.4% 1.03
Since 87.4% is submerged, 12.6% is above the seawater.
v 5.29 m/s Ans 41. Suppose we have two charges, 4 x 10-4 C and – 8 x 10-4 C, with an initial separation of 3 m. What is the change in potential energy if we increase the separation to 8 m?
1 1 PE Kq1q2 r2 r1
PE 600 J Ans 42. Calculate the wavelength of the line in the Balmer series with the longest wavelength. Johann Balmer’s Formula:
R = 1.097 107 / m
1 1 1 1.097 107 / m 2 2 3 2 656 nm Ans
46. A stone (density is 1500 kg/m3) has a volume of 1500 cu. cm. It is dropped into a swimming pool with maximum depth of 6 feet. When the stone is lying on the bottom of the pool, what is the magnitude of the normal force on the stone?
Fbuoy fluid Vsubmerged g
1 1 PE 9 109 4 104 8 104 8 3
1 1 1 R 2 2 n = 3,4,5,6 n 2
L' = L L' = 80 kg
From 12.56 s, the period decreased to 3.14 s, which is a decrease by a factor of 4.
2 r ' v' 2 2
4 T' = 3.14 s
37. A machine part can be made of either steel (density = 7800 kg/m3) or magnesium-aluminum alloy (density = 2600 kg/m3). If steel is used, the mass of this machine part will be 46 kg. What will be the mass of this machine part if magnesium-aluminum alloy is used?
c hc E 6.63 1034 3 108 3.05 1019 652 nm Ans
Eh
Solve for the new period:
1 1 1 2R i o 1 1 1 ; R = 8 cm Ans 0.5R 4 2
m m 46 kg ;v= 5.9 103 m3 kg v 7800 3 m m kg ; m = v = 2600 3 5.9 103 m3 v m
E hf
v' = 4 m/s
36. What is the radius of curvature of a mirror that will produce an image twice the normal size when a person stands 2 feet in front of it?
GEAS 43. What is the wavelength of a quantum radiation whose energy is 3.05 x 10-19 J?
L' = mv'r'
Baguio: PiRC Building, Gapuz Centrum II, 80 T. Alonso St., New Lucban CP: 0928 934 1637
1 m3 9.81N kg Fbuoy 1000 3 1500 cm 3 3 3 m 100 cm kg Fbuoy 14.7 N
Weight brick Vg 1 m3 9.81N kg 1500 3 1500 cm3 3 3 m 100 cm kg 22.05 N Fnormal 22.05 14.7 7.35 N Ans
47. The light meter in your camera indicates that your film is properly exposed at a shutter speed of 1/50 s and an aperture setting of f/16. However, to photograph a bird flying across the part, you must shorten the exposure time to 1/200 s to avoid blurring. What should the new aperture setting be?
Manila: CMFFI Bldg. R. Papa St. Tel. 7365291
Excel Review Center
ECE Refresher Course
For a photographic camera, light is prevented from getting in the camera by means of a shutter. When you press the button, the shutter momentarily opens and image is captured. The shutter needs to be open only a small fraction of a second to record an image. Shutter speed is the length of the time during which the shutter is open. The faster the shutter speed (shorter time the shutter is open), the faster the object can be moving and still produce a sharp image.
F hA
Relativistic Doppler Effect: Another effect of time dilation is the shift in the frequency found for light emitted by atoms in motion as opposed to light emitted by atoms at rest.
F 941.76 N Ans
F 9810 12 8 0.001
55. A steel rod with a cross-sectional area of 150 mm2 is stretched between two fixed points. The tensile load at 20°C is 5000 N. What will be the stress at -20°C if the coefficient of linear expansion is 11.7x10-6/°C?
v c v 1 c
1 fobserved fsource
Aperture refers to the lens opening. The size of the aperture is often measured by the f-value or the f-number.
fobserved 5 1014
fobserved 5.5 1014
focal length lens diameter f f number d
GEAS
the light if their velocity relative to the star is 0.095c?
thermal tensile
1 0.095 1 0.095 Hz Ans
ET
P A
11.7 106
200 10 40
f number
Therefore, if the aperture setting is f-16 it means that the diameter is 1/16 of the focal length:
50. A rectangular drinking trough for animals is 1.9 m long, 53.1 cm wide and 30.7 cm deep. A 1.95x105 g sample of liquid with density of 1.55 kg/dm3 is placed in it. Calculate the height of the liquid in the trough. 3
1.55
f f number d f f 16 16 f 16
f d
f f 2 16 f f number f 8 f number 8 f number
f - 8 Ans
48. Find the ratio of the momentum of a muon traveling at a speed of 0.990c to the value computed from the nonrelativistic definition of momentum.
Prelativistic Pnonrelativistic Prelativistic Pnonrelativistic Prelativistic Pnonrelativistic
2
v c2 mv
1
1
Pb
F 15 N A 0.0001 m
1.9 105 Pa Ans
2
2
v2 c2 1
4.8 108 Pa Ans
16P 0.075 0.02 1 3 4 0.075 0.02 64PR3 n Gd4 64 2748.9 0.075 n 3
0.1
4 9 N 83 10 0.02 m2 n 18 turns Ans
57. What is the maximum thickness of a steel plate in which a 4.2-in diameter hole can be drilled? Assume that for this material, the maximum shearing strength is 50 ksi and the maximum compressive strength is 60 ksi. Solve for force P using normal/axial stress given:
52. What is the fluid pressure at the bottom of the ocean where the depth is 8000 m?
Note: The density of sea water is 1.025x103 kg/m3
FG
0.990c
2
c2
60,000
7.09 Ans
49. A spacecraft exploring a distant galaxy is moving very rapidly toward a strange star that emits a yellow light of frequency 5.0x1014 Hz, measured in a net frame of the planet. What frequency does the spacecraft crew observe for
m1m2 d2
132 lb
Nm F 6.67 1011 kg2 2
F 6 10
8
2
1 kg 2.2 lb
2 m
d 1 4R
P 2748.9 N
51. A thumbtack is pushed into a piece of wood by applying a force of 15 N to the head of the tack. The radius of the point is 0.1 mm and the radius of the head is 5 mm. What is (a) the pressure applied to the head of the tack and (b) the pressure exerted by the point on the wood.
F 15 N A 0.005 m
16PR3 d3
3
140 106
height 12.5 cm Ans
53. Two persons both 132 lb stand 2 m apart. What is the gravitational attraction between them?
1 1
max
kg m P gh 1.025 103 3 9.81 2 8000 m m s P 8.04 107 Pa Ans
mv Prelativistic Pnonrelativistic
56. A helical spring is made by wrapping steel wire 20 mm in diameter around a forming cylinder 150 mm in diameter. Compute the number of turns required to permit an elongation of 100 mm without exceeding a shearing stress of 140 MPa. G = 83 GPa.
1.26 105 cm3 190cm 53.1cm height
Pa
1 150 1000
127 MPa Ans
1 cm3 5 3 V 1.95 105 g 1.26 10 cm 1.55 g V length width height
If the shutter speed is adjusted from 1/50 s (20 ms) to 1/200 s (5 ms) means shortening the exposure by a factor of 4. Therefore, the aperture should be increased to 4 times its original area to have proper exposure. Since area is a function of the square of the diameter, diameter will be doubled to quadruple the area. Hence: f number
kg 1000g 1 dm g 1.55 1 kg 10 cm dm3 cm3
5000
9
2
P A
lb P 2 in2 4.2 4 lb 2 P 60,000 2 4.2 in 4
Use this force P in getting the shear stress: P A lb 2 60,000 2 4 4.2 lb in 50,000 2 4.2 t in t 1.26 in Ans
2
N Ans
54. A water tank is 8 m in diameter and 12 m high. If the tank is completely filled, determine the tangential force on the tank.
Baguio: PiRC Building, Gapuz Centrum II, 80 T. Alonso St., New Lucban CP: 0928 934 1637
P A lb 2 60,000 2 4 4.2 lb in 50,000 2 d 0.5 in in
t 1.67 in Ans
Manila: CMFFI Bldg. R. Papa St. Tel. 7365291
2
Excel Review Center
ECE Refresher Course
58. A 3-meter solid steel shaft, with an unknown diameter, twists by 5 degrees as it is stressed by 60 MPa. What is the diameter of the solid steel shaft? Assume that G = 83 GPa. 5
TL JG
61. A steel wire has a diameter of 10 mm. It is suspended vertically from one end and carries only its own weight. What is the maximum length of the wire that is capable of carrying a maximum axial stress of 50 MPa?
180 4 d 32
T 5 m
wire L water SG L 50 106
59. For a heavy spring supporting a load of 3.5 kN, solve for the maximum shearing stress if it is made from a 30-mm diameter wire and is turned 35 times with a radius of 100 mm. Assume that G = 83 GPa.
16 3500 0.1 4 6.67 1 0.615 3 0.03 4 6.67 4 6.67 808 kPa Ans 3
21,000 12,000,000 0.00175 radians Ans. 63. A single rivet is used to join two plates. If the diameter of the rivet is 20 mm and the load is 30 kN, what is the average shearing stress developed in the rivet? Note: The rivet hole is usually 1.5 mm larger in diameter than the rivet.
60. A structure is made up of a steel rod 1.5 m high and 100 mm in diameter and is wrapped by an iron shell that is 15 mm thick. What is the compressive force needed if the structure is to be compressed by 1.5 mm? For iron, E = 100 GPa. The force needed to compress the entire structure is the sum of forces needed to compress the steel rod and the iron shell. Solve for the force needed to compress the iron shell: iron 0.015 Piron
Piron L AE
Piron 1.5 m
0.132 0.12 4 172,500 N
0.015
100 10 9
Psteel
AE Psteel 1.5 m
64. A 0.6-m diameter flat circular manhole cover on a level street was 5 feet below the rainwater surface during the flood that hit Manila due to the southern monsoon rain. Determine the force exerted by the water on the manhole cover.
4
100 (80000) 0.285 degrees Ans 67. A block of lead is placed in a container filled with liquid and is subjected to a gauge pressure of 800 atom. What is the fractional change in density of the lead? (Bulk modulus of lead is 5.2x102 N/m2) N 800 1.103 105 2 P m N B 5.2 1010 2 m 0.0016 16% increase Ans 68. Given a copper wire of length 2 m and diameter of 1 mm. How long will the wire be stretched if a 15 kg mass is suspended at its end. Young’s modulus of copper = 10 x 1010 N/m2
PL AE
15 kg 9.81
m 2 m s2 2 10 N 4 0.001 m 10 10 m2 3.75 mm Ans
69. A man standing at the foot of a tower throws a ball vertically upward at a certain velocity. On its way up, the time for the ball to reach the top of the tower is 1 sec while on its way down, the time for the ball to reach the top of the tower is 2 sec. Find the height of the tower.
1 gt1t 2 2 1 h 32.2 1 2 32.2 s Ans 2 h
70. A man throws an apple vertically upward at the foot of a cliff 40 m high while his wife simultaneously drops another apple from the top of the same cliff. The two F gh A apples collide at an altitude of 20 2 kg N m 2 meters. What was the initial speed of F 1000 3 9.81 5ftx 0.3 m kg 3.28ft m the apple that was thrown upward? F 4228.2 N Ans
Use the formula for the power transmitted of a short shaft
P
Get the sum of the two forces: Ptotal 172,500 N + 1570796.33 N Ptotal 2113 kN Ans
584 3 x 106 (1300)
F A F pA
65. What power would a short shaft, 50 mm in diameter transmit at 400 rpm?
PsteelL
0.12 200 109 4 1570796.33 N
30,000N 0.0215 m2 4 N 8.26 x 107 2 m 82.6 MPa Ans.
584TL D4 G
p
Solve for the force needed to compress the steel rod: steel
G
3
max
N N 9810 3 7.85 L 2 m m L 650 m Ans
62. Low-carbon structural steel has a shearing ultimate strength of approximately 45,000 lb/in2. A 1-inch hole is punched through a plate of this steel 3/8 in thick. If the modulus of elasticity in shear for this material is 12 x 106 lb/in2, find the shear strain at the edge of this hole when the shear stress is 21,000 lb/in2.
16PR3 4m 1 0.615 max m d3 4m 4 2R D 200 mm m 6.67 d d 30 mm 16 3500 0.1 4 6.67 1 0.615 3 4 6.67 4 6.67 0.03
For wires suspended at one end and carries only its own weight:
9 N 83 10 m2 6 4 T 237.03 10 d
max
66. Given a solid steel shaft, 100 mm in diameter and 1300 mm long, subjected to twisting moment of 3x106 N-mm. The torsional modulus of elasticity of this shaft is 80,000 N/mm2. What is the torsional deflection?
Specific gravity of steel = 7.85
16T 3 d 16 237.03 106 d4 N 60 106 2 m d3 d 49.7 mm Ans
max
GEAS
D3 N 0.83 x 106
503 (400) 0.83 x 106 P 60 kW Ans P
Baguio: PiRC Building, Gapuz Centrum II, 80 T. Alonso St., New Lucban CP: 0928 934 1637
y Vo t
1 2 at 2
1 9.81 t 2 2 t 2.019 s
20
y Vo t
1 2 at 2
1 2 9.81 2.019 2 Vo 19.81 m/s Ans 20 Vo 2.019
71. A ball is swung in a vertical circle with constant speed at the end of a 1-m
Manila: CMFFI Bldg. R. Papa St. Tel. 7365291
Excel Review Center
ECE Refresher Course
rope. What must be the period of the motion for the ball to be “weightless” at the top of the swing? Note: “weightlessness” means that there would be zero tension un the rope and yet it would remain straight.
Vo 2 Voy 2 V 2ox
If there is no head/tail wind, how far can he travel and return without running out of fuel? Ans: 150 miles
Vox 552 40.122
If there is head/tail wind, it should be less than 150 miles:
F = ma T + W = ma 0 + mg = m
t1 t 2 3 hr
v2 r
v gr
9.81 1
v = 3.13 m/s Get the period:
T= T=
2 r v 2 1
3.13 T=2s 72. A ball is thrown with an initial horizontal velocity of 30 m/s from a height of 3 m above the ground and 40 m from a vertical wall/. How far from the wall will the ball rebound for the first time? Analyze first the vertical component of the motion: y Voy t
1 ay t 2 2
1 9.81 t 2 2 t 0.782 s
3 0
Get the horizontal distance traveled by the ball in this time (t = 0.782 s) by analyzing the horizontal component of the motion: 1 ax t 2 2 x 30 0.782 0
d1 d2 d
Since it has traveled by 23.46 m, it means that it is 16.54 m from the wall the first time it bounces. 73. A racing car passes one end of the grandstand at a speed of 50 ft/s. It slows down at a constant acceleration a, such that it’s speed as it passes the other end of the grandstand is 10 ft/s. If this process takes 20 s, what is the length of the grandstand?
ft ft v 10 s 50 s a t 20s ft a 2 s2 1 x Vo t at 2 2 1 2 x 50 20 2 20 2 x 600 ft Ans 74. A plane can travel 100 mph without any wind. Its fuel supply is 3 hours, which means that it can fly 300 miles without a wind. The pilot now proposed to fly east with a tail wind of 10 mph and to return with, of course, a head wind of 10 mph.
Vox 37.62 ft/s
1 ax t 2 2 80 37.62 t 0 s Vox t
y Voy t
d d 3 hr 100 10 100 10 d = 148.5 miles Ans
75. What is the distance travelled by a car for 30 s if it has an initial speed of 60 kph and is decelerating at 9 m/min/sec? v o 60 kph = 16.67 m/s m 1 min min 60 s 0.15 m a s s2 1 2 s v o t at 2 1 2 s 16.67 30 0.15 30 2 s 432.6 m Ans 9
76. A flywheel, in the form of a uniform disk 4 ft in diameter, weighs 600 lb. What will be its angular acceleration if it is acted upon by a net torque of 225 lb-ft? The rotational inertia of the wheel is 0.5mr2.
1 ay t 2 2
y 40.12 2.13
1 2 32.2 2.13 2
y 12.41 y T 12.41 5 y T 17.41 ft Ans
78. A skier is filmed by a motion-picture photographer who notices him traveling down a ski run. The skier travels 36 ft during the fourth second of the filming and 48 ft during the sixth second. What distance did he cover in the eight seconds of filming? Assume that the acceleration is uniform throughout. a
v Vf Vo t tf to
4th second is from t = 3s to t = 4s. Get the velocity when t = 3s and consider this as the initial velocity during the 4th second 1 2 at 2 1 2 36 v o 1 a 1 2 36 v o 0.5a eq 1 s vo t
W mg m
Vo 2 V 2oy
t 2.13 s
W 600 lb 18.63 slugs ft g 32.2 2 s
x Vox t
x 23.46 m
Vox
d1 d2 3 hr v1 v 2
2
v=
GEAS
How far can he fly and return without running out of fuel?
6th second is from t = 5s to t = 6s. Get the velocity when t = 5s and name this as the “final” velocity (even though this is actually the initial velocity during the 6th second)
1 1 2 I mr 2 18.63 2 2 2 I 37.3 slugs ft 2 T I
225 lb ft = 37.3 slugs ft 2 6
rad s2
Ans
Ft P Ft mv f mv i
F 3 0 6000 55.55 F 111.11 kN Ans
77. In a gymnasium with a ceiling 30 ft high, a player throws a ball towards a wall 80 ft away. If he releases the ball 5 ft above the floor with initial velocity of 55 ft/s, determine the highest point at which the ball could strike the wall. At the highest point: Vfy 2 Voy 2 2ay 0 Voy 2 2 32.2 ymax Voy 2 32.2 25 Voy 40.12 ft/s
Baguio: PiRC Building, Gapuz Centrum II, 80 T. Alonso St., New Lucban CP: 0928 934 1637
1 2 at 2 1 2 48 v f 1 a 1 2 48 v f 0.5a eq 2 s vo t
At this point, you have vo which is the velocity at t = 3s and you also have v f which the velocity at t = 5s. From t = 3s to t = 5s, the total time difference is 2s. 0.5a 36 Vo 0.5a 48 Vf 36 Vo 48 Vf Vf Vo 12 a
v Vf Vo t tf to
Vo 12 Vo 2 a 6 ft/s 2 a
You have now the value of the constant acceleration. This time, get the exact
Manila: CMFFI Bldg. R. Papa St. Tel. 7365291
Excel Review Center
ECE Refresher Course
GEAS
Fx ma
value of the velocity when t = 3s. This is your vo from equation 1.
T m1gsin30 N1 m1a Fy 0
36 v o 0.5a
36 v o 0.5 6
N1 m1gcos30
v o 33 ft/s
T m1gsin30 m1gcos30 m1a 2
At this point, get the velocity when t = 0 and assign this as vo’. Assign vo (which is the velocity when t = 3s) as the “final” velocity for the period from t = 0 to t = 3s.
Add equation 1 and 2: T m1gsin30 m1gcos30 m2gsin60 T m2gcos 60 m1a m2a
v f v o at
T m1gsin30 m1gcos30
v o v o ' at
m2gsin60 T m2gcos 60 m1 m2 a
33 v o ' 6 3
m1gsin30 m1gcos30
v o ' 15 ft/s
m gsin60 m2gcos 60 a 2 m1 m2
Solve for the distance after 8s. 1 s v o 't at 2 2 1 s 15 8 6 8 2 s 312 ft Ans
a 5.9 ft/s2 Ans
80. Two bodies having masses 30 g and 40 g are attached to the ends of a string of negligible mass and suspended from a light frictionless pulley. Find the acceleration of the lighter body.
2
79. Two rough planes A and B, inclined, respectively, at 30º and 60º to the horizontal and of the same vertical height, are placed back to back. A smooth pulley is fixed to the top of the planes and a string passed over it connecting two masses, the first of 0.2 slug resting on plane A and the other of mass 0.6 slug resting on plane B. The coefficient of kinetic friction on both planes is
1 3
T T
. Find
m 1
the acceleration of the system.
m
g
2
nd
Use Newton’s 2
Law (F=ma) g
For the first box, take the upward direction as the positive direction Fy ma T m1g m1a 1
For the second box, take the downward direction as the positive direction Box
Box 1
Fy ma
2
W 1
T
m2g T m2a 2
W
T
2
Add equation 1 and 2: T m1g m2g T m1a m2a
F
m2g m1g m1a m2a
1
Box 2:
N
N
3 0 °
1
6 2
F 0 °
m
2
2
m a
m1 g m1 m2 a m1 g 2
m1 m2
40g 30g9.81
Fx ma
a
m2gsin60 T N2 m2a
a 1.4 m/s2 Ans
Fy 0
30g 40g
N2 m2gcos 60 m2gsin60 T m2gcos 60 m2a 1
Never stop learning.
Box 1:
Baguio: PiRC Building, Gapuz Centrum II, 80 T. Alonso St., New Lucban CP: 0928 934 1637
Manila: CMFFI Bldg. R. Papa St. Tel. 7365291
