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Physics 12 Exam Review Problems
1. A hammer slides down a roof sloped at 35o reaching a speed
of 4.6. m/s before falling off. How long does it take to hit the
ground? (1.5s)
2. A 65 kg man is 3.0 m up a 5.0 m, 16 kg ladder leaning against a
smooth wall at an angle of 72o as shown below. Assuming
there is no friction between the ladder and wall, what is the
minimum required frictional force between the ladder and the
ground? (150N)
3. An experiment was performed on the surface of an asteroid. A
mass was dropped from various heights and the time taken to fall
was recorded. Determine the rate of acceleration due to gravity
on the surface of the asteroid. (0.56m/s/s)
4. A 2.5 kg projectile is launched towards a brick
wall as shown.
a. What are the horizontal and vertical
components of its initial velocity?
(Vx=11m/s, Vy=9.0m/s)
b. How much time does it take for the
projectile to reach the wall? (1.4s)
c. What is its impact speed with the wall?
(12m/s)
5. A 5.30 kg wagon is moving at 2.00 m/s to the right. A 0.180 kg blob of putty moving at 32.0 m/s
also to the right strikes the wagon and sticks to it. With what speed will the wagon and the putty
move after the collision? (2.99m/s)
6. A 4.0 m long uniform pole with a mass of 15 kg is
pivoted at one end and held in position by a horizontal
cable at the other end. If a 25 kg mass is suspended from
the end of the pole, what is the tension in the horizontal
cable? (270N)
7. A 4300 kg truck travelling at 21 m/s in the direction of 31o north of east collides with a stationary
1500 kg car. After the collision, the car has a speed of 15 m/s due east. What is the resulting speed
of the truck? (17 m/s)
8. A sign is suspended from the end of a 6.0 m long
uniform pole of mass 25 kg as shown. If the mass of
the sign is 36 kg, what is the tension in the horizontal
restraining cable? (680N)
9. A 4.20*104 kg satellite orbits the earth at an altitude of 700. km. What is its orbital speed?
(7510m/s)
10. A small plastic ball carrying a positive charge is held
near a fixed large positively charged sphere as shown
below. It is then released. Explain how and why the
acceleration of the plastic ball changes as it moves
away from the sphere.
11. A uniform 4.0 m long beam
with a mass of 15 kg rests on
a pivot at one end and is kept
horizontal by a cable at the
other end. The beam is
supporting a 25 kg mass as
shown. What is the tension
in the cable? (280N)
12. A beam of electrons travels perpendicular to a magnetic field of 0.011T. The electrons are initially
ravelling at 4.7*107m/s. What is the acceleration of the electrons in this field? (9.1*1016m/s/s/)
13. A 1500 kg satellite orbits the moon at an altitude of 2.3*106 m. What is its orbital period? (23000s)
14. A 6.0 kg ball having a kinetic energy of 192 J was travelling due east when it underwent an oblique
collision with a stationary 2.3 kg ball. The 2.3 kg ball travelled at 3.6 m/s at an angle of 47o north of
east after the collision. What was the velocity (magnitude and direction) of the 6.0kg ball after the
collision? (7.1m/s @ 8.1o S of E)
15. Electrons with a speed of 3.3*107 m/s are directed between charged parallel plates as shown.
a. What are the magnitude and direction of the electrostatic force on the electron while it is
between the plates? (1.04*10-15N downward)
b. What is the magnitude of the acceleration of the electron while it is between the plates?
(1.1*1015m/s/s)
16. A blue ball rolls off the cliff shown below at 10 m/s
and hits the ground with a speed of 30 m/s.
a. What is the vertical component of the ball’s
impact velocity? (-28.3m/s)
b. How high is the cliff? (41m)
17. A 3.00 kg object initially at rest explodes into three
fragments as shown in the diagram. What are the
speed and direction of the 0.80kg fragment? (33m/s
@ 47o)
18. An alpha particle (a helium nucleus) is travelling with high velocity when it enters a set of charged
plates as shown. Find the magnitude of its acceleration. (9.2*1010m/s/s)
19. A space station of radius 90 m is rotating to
simulate a gravitational field. What is the
period of the space station’s rotation so that a
70 kg astronaut will experience a normal
force by the outer wall equal to 60% of his
weight on the surface of the earth? (T=25s)
20. During their physics field trip to the amusement park, Tyler and Maria took a rider on the Whirligig.
The Whirligig ride consists of long swings that spin in a circle at relatively high speeds. As part of
their lab, Tyler and Maria estimate that the riders travel through a circle with a radius of 6.5 m and
make one turn every 5.8 seconds. Determine the speed of the riders on the Whirligig. (7.04 m/s)
21. During the spin cycle of a washing machine, the clothes stick to the outer wall of the barrel as it
spins at a rate as high as 1800 revolutions per minute. The radius of the barrel is 26 cm.
a. Determine the speed of the clothes (in m/s) that are located on the wall of the spin barrel.
(2940 m/s)
b. Determine the acceleration of the clothes. (3.33*107m/s2)
22. In the display window of the toy store at the local mall, a battery-powered plane is suspended from
a string and flying in a horizontal circle. The 631-gram plane makes a complete circle every 2.15
seconds. The radius of the circle is 0.950 m. Determine the velocity of, acceleration of, and net
force acting upon the plane. (2.78 m/s, 8.11 m/s2, 5.12 N)
23. In an effort to rev up his class, Mr. H does a demonstration with a bucket of water tied to a 1.3meter long string. The bucket and water have a mass of 1.8 kg. Mr. H whirls the bucket in a vertical
circle such that it has a speed of 3.9 m/s at the top of the loop and 6.4 m/s at the bottom of the loop.
a. Determine the acceleration of the bucket at each location. (11.7 m/s2 top, 31.5 m/s2 bottom)
b. Determine the net force experienced by the bucket at each location. (21.1N, 56.7N)
c. Draw a free body diagram for the bucket for each location and determine the tension force in
the string for the two locations. (3.44N, 74.4N)
24. A 76-kg pilot at an air show performs a loop de loop with his plane. At the bottom of the 52-m
radius loop, the plane is moving at 48 m/s. Determine the normal force acting upon the pilot.
(4110N)
25. Alexis is in her Toyota Camry and trying to make a turn off an expressway at 19.0 m/s. The turning
radius of the level curve is 35.0 m. Her car has a mass of 1240 kg. Determine the acceleration, net
force and minimum value of the coefficient of friction that is required to keep the car on the road.
(1.05)
26. Sheila (m=62 kg) is riding the Demon roller coaster ride. The turning radius of the top of the loop is
12 m. Sheila is upside down at the top of the loop and experiencing a normal force that is one-half
of her weight. Draw a free body diagram and determine Sheila's speed. (13.3m/s)
27. In 2002, professional skateboarder Bob Burnquist became the first to successfully navigate a 360°
full pipe turn. Determine the minimum speed that would be required at the top of the circular loop
to make it through the 1.8-m radius pipe. (4.20m/s)
28. Tyrone and Mia have masses of 84 kg and 59 kg respectively. They sit 1.0 m apart in the front
center of Mr. H's Physics class. For some time, they each have been sensing a sort of electricity in
their growing relationship. And now, six units into their Physics course, they have learned that they
are gravitationally attracted to each other. Determine the magnitude of this force of gravitational
attraction. (3.31*10-7N)
29. Determine the force of gravitational attraction between the Earth and the moon. Their masses are
5.98 x 1024 kg and 7.26 x 1022 kg, respectively. The average distance separating the Earth and the
moon is 3.84 x 108 m. Determine the force of gravitational attraction between the Earth and the
moon. (1.96*1020N)
30. Determine the acceleration of the moon about the Earth. (GIVEN: MEarth = 5.98 x 1024 kg and Earthmoon distance = 3.84 x 108 m) (2.70*10-3m/s2)
31. Determine the orbital speed of the International Space Station - orbiting at 350 km above the
surface of the Earth. (7698 m/s)
32. Hercules is hoping to put a baseball in orbit by throwing it horizontally (tangent to the Earth) from
the top of Mount Newton - 97 km above Earth's surface. With what speed must he throw the ball in
order to put it into orbit? (7847 m/s)
33. Scientists determine the masses of planets by observing the effect of the gravitational field of those
planets on nearby objects - mainly upon their moons. By measuring the orbital period and orbital
radius of a moon about a planet, Newton's laws of motion can be used to determine the mass of the
planet. Phobos, a moon of the planet Mars, was discovered in 1877. Its orbital radius is 9380 km
and its orbital period is 0.319 days (2.77 x 104 seconds). Determine the mass of Mars based on this
data. (6.37*1023kg)
34. A 720 kg communication satellite is in synchronous orbit around an unknown planet. This
synchronous orbit matches the period of rotation so that the satellite appears to be stationary over a
position on the equator of the planet. What is the orbital radius of this satellite? Assume the planet
has a mass of 6.42*1023kg and a period of rotation of 8.86*104s. (2.0*107m)
35. Geostationary satellites are satellites that are orbiting the Earth above the equator and make one
complete orbit every 24 hours. Because their orbital period is synchronized with the Earth's
rotational period, a geostationary satellite can always be found in the same position in the sky
relative to an observer on Earth. (GIVEN: MEarth = 5.98 x 1024 kg)
a. Determine the orbital radius of a geostationary satellite. (4.225*107m)
b. Determine the orbital speed of a geostationary satellite. (3073m/s)
c. Determine the acceleration of a geostationary satellite. (0.223m/s2)
36. A Styrofoam plate with a negative charge of -4.86x10-7 C is placed near an aluminum dish that has
been charged positively by induction to a charge of +8.29x10-8 C. The centers of positive and
negative charge are positioned 1.85 cm apart. Determine the magnitude of the force of attraction
between the Styrofoam plate and the aluminum dish. (1.06N)
37. Two metallic balls have charges of -3.1x10-7 C and -3.7x10-7 C. Determine the force of electrical
repulsion when held a distance of 42 cm apart. (5.85*10-3N)
38. Two vinyl balloons with an identical charge are given a separation distance of 52 cm. The balloons
experience a repulsive force of 2.74x10-3 N. Determine the magnitude of charge on each one of the
balloons. (2.87*10-7C)
39. What mass would a pair of electrons have in order for their gravitational force of attraction to be
equal to the electrical force of repulsion? (1.86*10-9kg)
40. An electron has a mass of 9.11x10-31 kg. In the Bohr model of the hydrogen atom, the electron was
viewed as orbiting the lone proton of the nucleus; the centripetal force requirement was met by the
electrical attraction between the oppositely charged proton and electron. The radius of orbit was
5.29x10-11 m. Use circular motion and electrostatic principles to determine the speed at which the
electron moves as it orbits the proton. (2.19*106m/s)
41. Two bowling balls with a mass of 7.25 kg are positioned in a vertical cylinder such that they fit one
above the other. What quantity of charge must the two bowling balls have such that the electrical
force of repulsion causes the top ball to levitate above the bottom ball such that their nearest
surfaces are distanced 25 cm apart? The diameter of a bowling ball is 21.8 cm. Assume the bowling
balls have an identical charge. (4.16*10-5C)
42. Two objects with charges Q1 and Q2 experience an electrical force of attraction of 8.0x10-4 N when
separated by a distance of d. Determine the force of attraction if the same objects are separated by
…
a. … a distance of 2•d. (2.0*10-4N)
b. … a distance of 3•d. (8.89*10-5N)
c. … a distance of 2d and each object having double the charge. (8.0*10-4N)
43. There is an electric field in the atmosphere surrounding the Earth that has a magnitude of roughly
150 N/C and a direction pointing towards the center of the Earth. Determine the magnitude and the
direction of the force experienced by a dust particle having a negative charge of 9.2x10-16 C.
(1.38*10-13N away from the centre of earth)
44. A test charge with a negative charge of 2.18x10-8 C experiences a northward force of 4.50x10-5 N
when placed a distance of 25.0 cm from a source charge.
a. Determine the magnitude and direction of the electric field at this location. (2.064*103N/C
South)
b. Determine the magnitude and type of charge on the source. (1.433*10-8C)
c. Determine the strength of the electric field at a distance of 75.0 cm from the source.
(229N/C)
45. A small balloon with a 4.36x10-9 C charge is placed a distance of 41 cm from a 1.28*10-6C charge.
a. Determine the electric field intensity at the location where the balloon is. (6.853*104N/C)
b. Determine the electrical force experienced by the balloon at this location. (2.99*10-4N)
46. The electric field between the positive and negative plates of the cathode ray tube of an older
television set can be as high as 2.5x104 N/C. Determine the force and resulting acceleration of an
electron as it travels through this electric field towards the television
screen. (2.915*1015m/s2)
47. Two identical balloons are inflated and charged in the same manner.
They are tied by threads and hung from the same pivot point on the
ceiling. The balloons hang down, with the threads making an angle of
14° with each other and the balloons being separated by a distance of 58
cm (center-to-center). Each balloon has a charge of -3.5x10-7 C. Draw a
free-body diagram for the balloons and consider them to act as point
objects.
a. Calculate the force of electrical repulsion between the balloons. (3.277*10-3N)
b. What is the horizontal component of force in the thread that supports either one of the
balloons? (3.994*10-4N)
c. What is the vertical component of force in the thread that supports either one of the
balloons? (3.253*10-7N)
d. What is the mass of either one of the balloons? (3.32*10-4kg)
48. Three charges are arranged as shown in the diagram at the
right. GIVEN:
Q1 = -15 nC
Q2 = +14 nC
Q3 = +11 nC
a. Determine the magnitude and direction of the force
exerted by Q1 upon Q2. (3.857*10-6N down)
b. Determine the magnitude and direction of the force
exerted by Q3 upon Q2. (1.54*10-5N left)
c. Determine the magnitude and direction of the net
electrostatic force on Q2. (1.588*10-5N W14.1oS)
49. Determine the strength of the net electric field at a location midway between two point charges. The
charges are Q1 = +8.32x10-9 C and Q2 = +6.04x10-9 C. The separation distance is 24.6 cm.
Suggestion: construct a diagram of the arrangement of two charges and compute each individual
electric field. Then compute the vector sum of these field vectors to determine the net electric field.
(1.356*103N/C right)
50. Four positive charges are positioned in such a
manner than they form a square with sides that
are 5.0 cm long. A 3.0 microC charge is placed
at the (0 cm, 0 cm) mark. A 9.0 microC charge is
placed at the (0 cm, 5 cm) mark, a 3.0 microC
charge is placed at the (5 cm, 5 cm) mark, and a
6.0 microC charge is placed at the (5 cm, 0cm)
mark. Determine the magnitude and direction of
the electric field at the exact center of the square.
(2.159*107N/C E45oS)
51. The diagram at the right shows three charges
positioned to form an equilateral triangle. Each side
has a length of 46 cm and each charge has a
positive charge of 7.8 nC. Determine the magnitude
and direction of the net electric force exerted upon
the charge at point P at the top of the triangle.
(4.48*10-6N North)
52. In an effort to create a cannonball-style splash, eight-year old Matthew runs off the edge of the
board of the high dive at 4.6 m/s and falls 2.3 m to the water below.
a. Determine the time for Matthew to fall the 2.3 m to the water. (0.685s)
b. What horizontal distance from the edge of the board will Matthew plunge into the water?
(3.15 m)
c. With what speed does Matthew enter the water? (8.14m/s)
53. Jacob wishes to throw a 2.8-kg pumpkin horizontally off the top of the school roof in order to hit
Mr. B's car. The car is parked a distance of 13.4 m away from the base of the building below the
point where Jacob is standing. The building's roof is 10.4 m high. Assuming no air resistance, with
what horizontal speed must Jacob toss the pumpkin in order to hit Mr. B's car? (9.20m/s)
54. Two students, Sharon and Al, are participating in an egg toss. In their winning toss, Sharon gave
the egg an underhand toss, releasing it with a velocity of 8.06 m/s at an angle of 30° to the
horizontal. To the pleasure of the crowd, Al caught the egg at the same height as the toss without
even a fracture to its shell.
a. Calculate the horizontal and vertical components of the initial velocity. (6.98m/s, 4.03m/s)
b. Calculate the time for the egg to reach the midpoint of the trajectory. (0.411s)
c. Calculate the total time the egg is in the air. (0.822s)
d. Calculate the horizontal distance that the egg traveled. (5.74m)
e. Calculate the height of the egg (relative to the release point) when it was at the peak of its
trajectory. (0.828m)
55. On New Year’s eve of 2007, Robbie Maddison set the world record for the longest motorcycle
jump, traveling 98.3 m through the air from ramp to ramp. (The record has since been broken
several times by Maddision himself.) Assuming a launch angle of 45°, insignificant air resistance
and a landing location at the same height as the launch height, determine the speed with which
Maddison left the ramp. (31.1m/s)
56. Billy is a star punter for the varsity football team. His best hang time this past season was for a punt
which he kicked at 74° above the horizontal. The punt had a 6.2-second hang time.
a. Determine the speed at which the ball was punted. (31.6m/s)
b. Determine the horizontal distance that the ball traveled. (54.1m)
57. As a spaceship flies past with speed ‘v’, you observe that 1.0000s elapses on the ship’s clock in the
same time that 1.0000 min elapses on Earth. How fast is the ship traveling, relative to the Earth?
(0.99986c)
58. Astronaut Benny travels to Vega, the fifth brightest star in the night sky, leaving his 35.0-year-old
twin sister Jenny behind on Earth. Benny travels with a speed of 0.990C, and Vega is 25.3 light
years away from Earth.
a. How long does the trip take from Jenny’s perspective? (25.6y)
b. How much has Benny aged when he arrives at Vega? Hint: use Benny’s frame of reference
(3.61y)
59. Find the speed for which the length of a metre stick is 0.500m. (0.866c)
60. A portion of the Fermilab particle accelerator contains a tube 64m long. If protons travel through
the tube at a speed of 0.65c, how long is the tube in the proton’s frame of reference? (49m)
61. A beam of white light containing frequencies between 4.00*1014Hz and 7.90*1014Hz is incident on
a sodium surface, which has a work function of 2.28eV.
a. What is the range of frequencies in this beam of light for which electrons are ejected from
the sodium surface? (5.50*1014Hz to 7.90*1014Hz)
b. Find the maximum kinetic energy of the ejected electrons. (1.59*10-19J)
62. Calculate the momentum of a photon of yellow light with a frequency of 5.25*1014Hz. (1.16*1027kgm/s)
63. How fast is an electron moving if its deBroglie wavelength is 3.50*10-7m? (2080m/s)
64. If the momentum of a particle with finite mass (like a proton) is doubled, its kinetic energy
increases by a factor f 4. If the momentum of a photon is doubled, by what factor does its energy
increase? (it doubles)
65. An electron in a hydrogen atom drops from the third energy level to the second. Calculate the
energy emitted. (3.0*10-19J)
66. A player kicks a soccer ball toward the goalkeeper at an initial speed of 14.7m/s @ 37o from the
horizontal. The kicker is 26.0m from the goalkeeper. How far from the goal keeper will the ball hit
the ground? (4.8m)
67. A satellite is 5.0*106m above the surface of Jupiter. The radius of Jupiter is 7.18*107m and its mass
is 1.90*1027kg.
a. Find its orbital speed. (41000m/s)
b. Find its orbital period. (12000s)
68. Three friends experiment with a large seesaw. A 65.0kg person sits 1.00m from the pivot. A
42.5kg person sits on the same side at the 2.00m position. What is the minimum length of the other
side of the seesaw if a 75.0kg person perfectly balances the other two? (2.00m)
69. Determine the net force on charged particle C in the diagram below. Assume it is a right angle
triangle. (19000N @ 15.8o N of W)
QA = +45.0 microC
QB = +36.0 microC
QC = –55.0 microC
A
0.0320m
B
0.0470m
C
70. Two cars collide at an intersection. The first car has a mass of 925kg and was travelling North.
The second car gas a mass of 1075kg and was travelling West. Immediately after the impact, the
first car had a velocity of 52.0km/h, 40.0o N of W, and the 2nd car had a velocity of 40.0km/h, 50.0o
N of W. what was the speed of each car prior to the collision? (60.0km/h W, 69.0km/h N)
71. In a Millikan apparatus, an experimenter used a potential difference of 4.20*103V, a plate
separation of 1.60*10-2m, and an oil drop of mass 3.00*10-12kg. Assuming the drop is in a state of
equilibrium when observed, what is the charge on the oil drop? (1.12*10-16C)
72. A child standing on a small hill throws a snowball horizontally at a tree 15m away. When the
snowball is released, it is 4.0m above the height of the ground on which the tree stands. The
snowball hits the tree 0.60s after it is released.
a. What was the snowball’s initial horizontal velocity? (25m/s)
b. How far above the base of the tree does the snowball hit the tree? (2.2m)
73. Spiderman has a mass of 80.0kg. He swings in a vertical circular arc on a web 4.00m long.
a. If his speed is 3.20m/s at the bottom of his swing, what is the tension in the web? (989N)
b. If the maximum tension the web can withstand is 1800N, at what speed would it break?
(7.13m/s)
74. A ball is released from the top of a track and rolls down
hill, where it enters a loop the loop of radius 15.0cm.
From what minimum height must the ball be released in
order to make it around the loop, assuming the track is
frictionless? (37.5cm)