Homework Review
AP1
Q9
Suppose a yo-yo has a center shaft that has a 0.250 cm radius and that its string is
being pulled.
(a) If the string is stationary and the yo-yo accelerates away from it at a rate of 1.50
m/s2 , what is the angular acceleration of the yo-yo?
(b) What is the angular velocity after 0.750s if it starts from rest?
(c) The outside radius of the yo-yo is 3.50 cm. What is the tangential acceleration
of a point on its edge?
Q15
Consider the 12.0 kg motorcycle wheel. Assume it to be approximately an annular ring
with an inner radius of 0.280 m and an outer radius of 0.330 m. The motorcycle is on
its center stand, so that the wheel can spin freely.
(a) If the drive chain exerts a force of 2200 N at a radius of 5.00 cm, what is the angular
acceleration of the wheel?
(b) What is the tangential acceleration of a point on the outer edge of the tire?
(c) How long, starting from rest, does it take to reach an angular velocity of 80.0 rad/s?
Q17
An automobile engine can produce 200 N · m of torque. Calculate the angular
acceleration produced if 95.0% of this torque is applied to the drive shaft, axle, and rear
wheels of a car, given the following information. The car is suspended so that the
wheels can turn freely. Each wheel acts like a 15.0 kg disk that has a 0.180 m radius.
The walls of each tire act like a 2.00 kg annular ring that has inside radius of 0.180 m
and outside radius of 0.320 m. The tread of each tire acts like a 10.0-kg hoop of radius
0.330 m. The 14.0 kg axle acts like a rod that has a 2.00 cm radius. The 30.0 kg drive
shaft acts like a rod that has a 3.20 cm radius.
388 Q2
Five forces of equal magnitude, labeled A–E, are applied to the object shown below. If
the object is anchored at point P, which force will provide the greatest torque?
724 Q7
7. What is the period of 60.0 Hz electrical power?
10. A stroboscope is set to flash every 8.00×10−5 s . What is the frequency of the flashes?
14. If the spring constant of a simple harmonic oscillator is doubled, by what factor will
the mass of the system need to change in order for the frequency of the motion to remain
the same?
15. A 0.500-kg mass suspended from a spring oscillates with a period of 1.50 s. How much
mass must be added to the object to change the period to 2.00 s?
29. A pendulum with a period of 2.0000s in one location g = 9.80 m/s2 is moved to a new
location where the period is now 1.99796s. What is the acceleration due to gravity at its
new location?
31. Find the ratio of the new/old periods of a pendulum if the pendulum were transported
from Earth to the Moon, where the acceleration due to gravity is 1.63 m/s2 .
358 Q27
27. A rubber ball is dropped from rest at a fixed height. It bounces off a hard floor and
rebounds upward, but it only reaches 90% of its original fixed height. What is the best way
to explain the loss of kinetic energy of the ball during the collision?
a. Energy was required to deform the ball’s shape during the collision with the floor.
b. Energy was lost due to work done by the ball pushing on the floor during the collision.
c. Energy was lost due to friction between the ball and the floor.
d. Energy was lost due to the work done by gravity during the motion.
358 Q29
29. Two objects, A and B, have equal mass. Prior to the collision, mass A is moving 10 m/s
in the +x-direction, and mass B is moving 4 m/s in the +x-direction. Which of the
following results represents an inelastic collision between A and B?
a. After the collision, mass A is at rest, and mass B moves 14 m/s in the +x-direction.
b. After the collision, mass A moves 4 m/s in the –x-direction, and mass B moves 18 m/s in
the +x-direction.
c. After the collision, the two masses stick together and move 7 m/s in the +x-direction.
d. After the collision, mass A moves 4 m/s in the +x-direction, and mass B moves 10 m/s
in the +x-direction.
358 Q41
41. Mass A (2.0 kg) has an initial velocity of 4 m/s in the +x-direction. Mass B (2.0 kg) has
an initial velocity of 5 m/s in the –x-direction. If the two masses have an elastic collision,
what will be the final velocities of the masses after the collision?
a. Both will move 0.5 m/s in the –x-direction.
b. Mass A will stop; mass B will move 9 m/s in the +x-direction.
c. Mass B will stop; mass A will move 9 m/s in the –x-direction.
d. Mass A will move 5 m/s in the –x-direction; mass B will move 4 m/s in the +x-direction.
358 Q43
43. Mass A (2.0 kg) is moving with an initial velocity of 15 m/s in the +xdirection, and it collides with mass B (5.0 kg), initially at rest. After the
collision, the two objects stick together and move as one. What is the change
in kinetic energy of the system as a result of the collision?
a. no change
b. decrease by 225 J
c. decrease by 161 J
d. decrease by 64 J
358 Q51
Two cars of equal mass approach an intersection. Car A is moving east at a speed of 45
m/s. Car B is moving south at a speed of 35 m/s. They collide inelastically and stick
together after the collision, moving as one object. Which of the following statements is
true about the center-of-mass velocity of this system?
a. The center-of-mass velocity will decrease after the collision as a result of lost energy
(but not drop to zero).
b. The center-of-mass velocity will remain the same after the collision since momentum is
conserved.
c. The center-of-mass velocity will drop to zero since the two objects stick together.
d. The magnitude of the center-of-mass velocity will remain the same, but the direction of
the velocity will change.
310 Q20
20. A 100-g toy car is propelled by a compressed spring that starts it moving. The car
follows the curved track. Show that the final speed of the toy car is 0.687 m/s if its initial
speed is 2.00 m/s and it coasts up the frictionless slope, gaining 0.180 m in altitude.
1
2
𝐾𝐸2 = 𝑚𝑣 2 = 0.0236𝐽
𝐾𝐸1 =
1
0.1
2
22 = 0.2𝐽
𝑃𝐸 = 𝑚𝑔ℎ = 0.1764𝐽
𝐽
310 Q21
21. In a downhill ski race, surprisingly, little advantage is gained by getting a running start.
(This is because the initial kinetic energy is small compared with the gain in gravitational
potential energy on even small hills.) To demonstrate this, find the final speed and the time
taken for a skier who skies 70.0m along a 30º slope neglecting friction:
(a) Starting from rest.
(b) Starting with an initial speed of 2.50 m/s.
(c) Does the answer surprise you? Discuss why it is still advantageous to get a running
start in very competitive events.
𝑃𝐸 = 𝑚𝑔ℎ = 𝑚𝑔35 = 343𝑚 𝑣𝑓 =
2𝑃𝐸
𝑚
1
2
= 26.2𝑚/𝑠
1
2𝑃𝐸 + 𝐾𝐸0
2
𝐾𝐸0 = 𝑚𝑣 = 3.125𝑚 𝑣𝑓 =
2
𝑚
1
2
= 26.25𝑚/𝑠
310 Q24
24. A 60.0-kg skier with an initial speed of 12.0 m/s coasts up a 2.50-m-high rise as shown
in the following Figure. Find her final speed at the top, given that the coefficient of
friction between her skis and the snow is 0.0800. (Hint: Find the distance traveled up the
incline assuming a straight-line path as shown in the figure.)
Q32
32. A person in good physical condition can put out 100 W of useful power for several
hours at a stretch, perhaps by pedaling a mechanism that drives an electric generator.
Neglecting any problems of generator efficiency and practical considerations such as
resting time:
(a) How many people would it take to run a 4.00-kW electric clothes dryer?
(b) How many people would it take to replace a large electric power plant that generates
800 MW?
311 Q33
33. What is the cost of operating a 3.00-W electric clock for a year if the cost of electricity
is $0.0900 per kW ⋅ h ?
34. A large household air conditioner may consume 15.0 kW of power. What is the cost of
operating this air conditioner 3.00 h per day for 30.0 d if the cost of electricity is $0.110
per kW ⋅ h ?
217 Q2
2. (a) When rebuilding her car's engine, a physics major must exert 300 N of
force to insert a dry steel piston into a steel cylinder. What is the magnitude of
the normal force between the piston and cylinder?
(b) What is the magnitude of the force would she have to exert if the steel parts
were oiled?
217 Q4
4. Suppose you have a 120-kg wooden crate resting on a wood floor.
(a) What maximum force can you exert horizontally on the crate without
moving it?
(b) If you continue to exert this force once the crate starts to slip, what will the
magnitude of its acceleration then be?
217 Q9
9. Show that the acceleration of any object down an incline where friction
behaves simply (that is, where fk = μkN ) is a = g( sin θ − μkcos θ). Note that the
acceleration is independent of mass and reduces to the expression found in the
previous problem when friction becomes negligibly small (μk = 0).
217 Q11
11. (a) Calculate the acceleration of a skier heading down a 10.0º slope,
assuming the coefficient of friction for waxed wood on wet snow.
(b) Find the angle of the slope down which this skier could coast at a constant
velocity. You can neglect air resistance in both parts.
217 Q12
12. If an object is to rest on an incline without slipping, then friction must equal
the component of the weight of the object parallel to the incline. This requires
greater and greater friction for steeper slopes. Show that the maximum angle of
an incline above the horizontal for which an object will not slide down is θ =
tan–1 μs . You may use the result of the previous problem.
186 Q15
15. What net external force is exerted on a 1100-kg artillery shell fired from a
battleship if the shell is accelerated at 2.40×104 m/s2 ? What is the magnitude of
the force exerted on the ship by the artillery shell?
186 Q16
16. A brave but inadequate rugby player is being pushed backward by an
opposing player who is exerting a force of 800 N on him. The mass of the losing
player plus equipment is 90.0 kg, and he is accelerating at 1.20 m/s2 backward.
(a) What is the force of friction between the losing player’s feet and the grass?
(b) What force does the winning player exert on the ground to move forward if
his mass plus equipment is 110 kg?
(c) Draw a sketch of the situation showing the system of interest used to solve
each part. For this situation, draw a free-body diagram and write the net force
equation.
186 Q23
23. A 5.00×105-kg rocket is accelerating straight up. Its engines produce
1.250×107 N of thrust, and air resistance is 4.50×106 N . What is the rocket’s
acceleration? Explicitly show how you follow the steps in the Problem-Solving
Strategy for Newton’s laws of motion.
186 Q24
24. The wheels of a midsize car exert a force of 2100 N backward on the road to
accelerate the car in the forward direction. If the force of friction including air
resistance is 250 N and the acceleration of the car is 1.80 m/s2 , what is the mass
of the car plus its occupants? Explicitly show how you follow the steps in the
Problem-Solving Strategy for Newton’s laws of motion. For this situation, draw
a free-body diagram and write the net force equation.
138 Q26
26. A ball is kicked with an initial velocity of 16 m/s in the horizontal direction
and 12 m/s in the vertical direction.
(a) At what speed does the ball hit the ground?
(b) For how long does the ball remain in the air?
(c) What maximum height is attained by the ball?
138 Q27
27. A ball is thrown horizontally from the top of a 60.0-m building and lands
100.0 m from the base of the building. Ignore air resistance.
(a) How long is the ball in the air?
(b) What must have been the initial horizontal component of the velocity?
(c) What is the vertical component of the velocity just before the ball hits the
ground?
(d) What is the velocity (including both the horizontal and vertical components)
of the ball just before it hits the ground?
133 Q9
9. Suppose you add two vectors A and B .
a) What relative direction between them produces the resultant with the greatest
magnitude?
b) What is the maximum magnitude?
c) What relative direction between them produces the resultant with the
smallest magnitude?
d) What is the minimum magnitude?
10. Give an example of a nonzero vector that has a component of zero.
11. Explain why a vector cannot have a component greater than its own
magnitude