Download PSI AP Physics C – Work and Energy

PSI AP Physics C – Work and Energy
(Algebra Based)
Multiple Choice Questions (use g = 10 m/s2)
1. A student throws a ball upwards from the ground level where gravitational potential
energy is zero. At a height of 15 m, the ball has a potential energy of 60 J, and is moving
upwards with a kinetic energy of 40 J. Ignoring air resistance, the maximum height
achieved by the ball is most nearly:
(A) 10 m
(B) 20 m
(C) 25 m
(D) 30 m
(E) 40 m
2. A box of mass m is lifted a vertical distance h in time t with a constant velocity. The
power supplied by the lifting force is approximately:
(A) mght
(B)
𝑚𝑔ℎ
𝑡
(C) zero
(D)
𝑚𝑔𝑡
ℎ
(E)
𝑚𝑔
ℎ𝑡
3. A crate is lifted by a force F which is greater in magnitude than the crate’s weight W.
The change in kinetic energy of the crate during this time is equal to the
(A) work done by the net force (F - W). (B) work done by F. (C) work done by W.
(D) the change in momentum of the rock before and after this time.
(E) the change in the potential energy of the rock before and after this time.
4. A constant force supplies an average power of 8 W to a box during a certain time
interval. If the box has an average speed of 4 m/s and the force acts in the same
direction as motion of the object, the magnitude of the force is
(A) 8 N
(B) 6 N
(C) 4 N
(D) 2N
(E) 1N
5. A pencil is moved from point A to point B along a curved path. The work done by the
gravitational force on the pencil depends on which of the following:
(A) the velocity of the object as it moves between A and B
(B) the positions of points A and B
(C) the path taken between A and B
(D) both the positions of A and B and the path taken between them
(E) the nature of the external force that moves the object from A to B
6. A student lifts a mass m at constant speed to a height h in time t. How much work is
done by the student?
(A) mgt
(B) zero
(C) mgh
(D)
𝑚𝑔ℎ
𝑡
(E)
𝑚𝑔𝑡
ℎ
7. A 3 m long frictionless pendulum swings with a maximum angular displacement of
10°from the vertical. At its lowest position, the kinetic energy of the pendulum is 20 J.
What is the potential energy of the pendulum when the kinetic energy is 5 J?
(A) 3.3 J
(B) 5 J
(C) 6.7 J
(D) 10 J
(E) 15 J
8. On top of a 300 m skyscraper, a 2 kg ball is thrown directly downwards with an initial
speed of 20 m/s. If the ball reaches the ground with a speed of 60 m/s, the energy lost
to friction is approximately:
(A) 0J
(B) 1800 J
(C) 2300 J
( D) 2800 J
(E) 3300 J
9. A student pushes a box across a rough, flat surface at a constant speed of 1 m/s. The
box has a mass of 50 kilograms, and the coefficient of sliding friction is 0.2. The power
supplied by the student to the box is:
(A) zero
(B) 5 W
(C) 50 W
(D) 100 W
(E) 200 W
45°
L
10. A ball of mass m is suspended at the end of a massless string of length L as shown
above. This pendulum is lifted to a 45° angle with the vertical and released. At the low
point of its swing, the speed of the ball is:
(A) gL
(B) 2 gL
(C)
(D) gL
(2 - 2 )gL
(E) 1/2gL
11. A 5 kilogram block is pushed horizontally, at a constant speed of 3 m/s, across a rough
surface with a coefficient of kinetic friction of 0.2 by a force F. The work that is done by
the force in 20 s is:
(A) 200 J
(B) 400 J
(C) 600 J
(D) 800 J
(E) 1000 J
12. A spring gun with a spring constant k launches a ball of mass m off a cliff of height h. If
the velocity of the ball right before it hits the ground is v, how much was the spring
compressed?
(A) 0
(B) mgh
1
(C) 2mv
2𝑚𝑔ℎ
(D) √
𝑘
𝑚(𝑣 2 −2𝑔ℎ)
(E) √
𝑘
13. A 10 kg block is lifted 5 m upward at a constant speed of 2 m/s. What is the average
power supplied?
(A) 200 W
(B) 120 W
(C) 20 W
(D) 25 W
(E) 50 W
14. A 2-kg mass accelerates for 10 m across a frictionless surface by a 40 N force as shown
in the figure above. The work done over this interval is:
(A) 120 J
(B) 200√3 J
(C) 120√3 J
(D) 400 J
(E) 200 J
Problems 15-16
15. The graph represents the force exerted on a particle, where F is in N and x is in m. What
is the work done by F on the object from x = 0 to x = 4 m?
(A) 8 J
(B) 10 J
(C) 15 J
(D) 16 J
(E) 20 J
16. What is the work done by F on the object from x=0 to x=6 m?
(A) 4 J
(B) 6 J
(C) 10 J
(D) 12.5 J
(E) 25 J
17. Which of the following is an accurate statement?
(A) Potential energy is always negative.
(B) Total energy is always positive.
(C) During simple harmonic motion, the kinetic energy is always equal to the potential
energy.
(D) Kinetic energy is never negative.
(E) None of these is true.
18. A stone is dropped from the edge of a cliff. Which of the following graphs best represents
the stone's kinetic energy KE as a function of time t?
(A)
(B)
(D)
(C)
(E)
19. A 4 kg ball is attached to a 1.5 m long string and whirled in a horizontal circle at a
constant speed 5 m/s. How much work is done on the ball during one period?
(A) 9 J
(B) 4.5 J
(C) zero
(D) 2 J
(E) 8 J
Questions 20-21 A ball swings from point 1 to point 3.
Assuming that point 3 is 2 m above the lowest point 2.
Answer the following questions.
20. What happens to the kinetic energy of the ball when it moves from point 1 to point 2?
(A) increases (B) decreases (C) remains the same (D) zero
(E) more information is required
21. What is the velocity of the ball at the lowest point 2?
(A) 2.2 m/s
(B) 3.5 m/s
(C) 4.7 m/s
(D) 5.1 m/s
(E) 6.3 m/s
22. A block with a mass of m slides at a constant velocity V0 on a horizontal frictionless
surface. The block collides with a spring and comes to rest when the spring is
compressed to the maximum value. If the spring constant is k, what is the maximum
compression in the spring?
𝑚
(A) 𝑣𝑜 √ 𝑘
(B)
𝑚𝑣𝑜
𝑚𝑣𝑜
(C) √
𝑘
𝑘
𝑘
(D) 𝑣𝑜 √𝑚
(E)
𝑚𝑣𝑜2
𝑘
Questions 23-24 A 500 kg roller coaster car starts
from rest at point A and moves down the curved
track. Ignore any energy loss due to friction.
23. Find the speed of the car at the lowest point B.
(A) 10 m/s
(B) 20 m/s
(C) 30 m/s
(D) 40 m/s
(E) 50 m/s
24. Find the speed of the car when it reaches point C.
(A) 10 m/s
(B) 20 m/s
(C) 30 m/s
(D) 40 m/s
(E) 50 m/s
25. Two projectiles A and B are launched from the ground with velocities of 50 m/s at
60 ̊and 50 m/s at 30 ̊ with respect to the horizontal. Assuming there is no air resistance
involved, which projectile has greater kinetic energy when it reaches the highest point
of its trajectory?
(A) projectile A
(B) projectile B
(C)They both have the same none zero kinetic energy.
(D)They both have zero kinetic energy at the highest point.
(E)More information is required.
Questions 26-27 An object with a mass of 2 kg is
initially at rest at a position x = 0. A non-constant force
F is applied to the object over 6 m.
26. What is the total work done by F on the object at the end of 6 m?
(A) 200 J
(B) 150 J
(C) 170 J
(D) 190 J
(E) 180 J
27. What is the velocity of the object at 6 m?
(A) 150 m/s
(B) 25 m/s
(C) 300 m/s
(D) 12 m/s
(E) 35 m/s
28. An object has 150 J of kinetic energy after increasing its speed from 5 m/s t 15 m/s.
Which of the following choices best represents the mas of the object?
(A) 0.5 kg
(B) 1.5 kg
(C) 2.2 kg
(D) 3.4 kg
(E) 5.6 kg
29. A block of mass m is at rest on the frictionless
inclined plane with an incline angle of θ. The block is
just in a contact with the free end on an unstretched
spring with a spring constant k. If the block is slowly
moved down the incline (acceleration approximately
equal to 0 m/s2), what is the maximum compression
in the spring?
(A) kmg sinθ (B) kmg cosθ
(C) 2mg sinθ/k
(D) mg/k
(E) kmg
30. A box of mass M begins at rest with point 1 at a height of 6R, where 2R is the radius of
the circular part of the track. The box slides down the frictionless track and around the
loop. What is the ratio between the normal force on the box at point 2 to the box’s
weight?
(A) 1:1
(B) 2:1
(C) 3:1
(D) 4:1
(E) 5:1
31. A ball of mass m is fastened to a string. The ball swings in a vertical circle of radius r with
the other end of the string held fixed. Neglecting air resistance, the difference between
the string’s tension at the bottom of the circle and at the top of the circle is:
(A) mg
(B) 2mg
(C) 3mg
(D) 6 mg
(E) 9 mg
32. A system of two blocks is shown above. Block A is placed on the surface of a rough
horizontal table and on one side is connected to a vertical wall by an unstretched spring
on the other is connected to block B by a light string. The string passes over a frictionless
and massless pulley. Block B is slowly moved down until it reaches the equilibrium
position. Which of the following statements is true?
(A) The total mechanical energy of the system is increased.
(B) The loss in potential energy of block B is equal to the work done by the friction force
on block A.
(C) The gain in potential energy of block A is equal to the loss in potential energy of the
spring.
(D) The gain in potential energy of block A is greater than the loss in potential energy of
the spring.
(E) The gain in potential energy of block A is less than the loss in potential energy of the
spring.
33. A crane can develop a 2.5 kW power output when lifting a metal block up. How long will
it take for the crane to lift a 250 kg block at a constant speed to a height of 5 m above
the ground?
(A) 5 s
(B) 10 s
(C) 15 s
(D) 20 s
(E) 25 s
34. A small block is released from rest at the top of a frictionless inclined plane. When the
block reaches the bottom of the plane, it enters onto a rough horizontal surface. How
far does the block slide on the horizontal section before it comes to rest?
(A)
µ𝑔
ℎ
µ
(B) 𝑔ℎ
µ
(C) ℎ
ℎ
(D) µ
ℎ
(E) µ𝑔
35. Two blocks of masses 0.5 kg and 0.75 kg are connected with a light string that passes
over a frictionless and massless pulley. What is the change in gravitational potential
energy and change in kinetic energy of the system, 2 s after it released from rest?
Change in Potential Energy
Change in Kinetic Energy
(A) +10 J
+10 J
(B) -10 J
-10 J
(C) +10 J
-10 J
(D) -10 J
+10 J
(E) 0 J
0J
36. A 2500 kg car accelerates from rest at a constant rate of 2 m/s2. What power is required
to increase the car’s speed to 20 m/s?
(A) 10,000 W
(B) 25,000 W
(C) 30,000 W
(D) 35,000 W
(E) 50,000 W
37. A block of mass m is placed on the frictionless inclined plane with an incline angle of θ.
The block is just in a contact with the free end on an unstretched spring with a spring
constant k. If the block is released from rest, which of the following is true when it
moves down the incline?
Work done by gravity on block
Work done by spring on block
(A) Positive
Positive
(B) Negative
Negative
(C) Negative
Positive
(D) Positive
Negative
(E) Zero
Zero
38. A constant force F = 100 N pushes a 5 kg box 10 m upward along the inclined plane.
Which of the following choices best represents the work done by the force F on the
box?
(A) 250 J
(B) 866 J
(C) 500 J (D) 765 J (E) 966 J
39. An external force is applied to a system of two blocks. Which of the following is true if
the blocks do not move with respect to each other?
Work done by friction on block A
Work done by friction on block B
(A) Positive
Positive
(B) Negative
Negative
(C) Positive
Negative
(D) Negative
Positive
(E) Zero
Zero
40. A car is traveling on a level road with an initial velocity vo. If the coefficient of kinetic
friction between the road and the tires is µ, what is the shortest distance the car can
travel after the driver locks the breaks?
(A)
𝑣𝑜2
2µ𝑔
𝑣2
(B) µ𝑔𝑜
𝑣2
(C) 2µ𝑜
𝑣
𝑜
(D) 2µ𝑔
𝑣2
(E) 2𝑔𝑜
Answer Key
1.C
6.C
11.C
16.B
21.E
26.B
31. D
36.E
2.B
7.E
12.E
17.D
22.A
27.D
32.D
37.D
3.A
8.D
13.A
18.B
23.C
28.B
33.A
38.E
4.D
9.D
14.E
19.C
24.B
29.C
34.D
39.D
5.B
10.C
15.A
20.A
25.B
30.A
35.D
40. A