PSI AP Physics B
Dynamics
Multiple-Choice questions
1. After firing a cannon ball a cannon moves in opposite direction from the ball. This an example of
A. Newton’s First law
B. Newton’s Second Law
C. Newton’s Third Law
D. Newton’s Law of Gravitation
E. None of the above
2. In the absence of an external force a moving object will
A. slow down and come to a stop
B. speed up
C. move with a constant speed in a long a straight line
D. turn to the right
E. turn to the left
3. A passenger standing in a moving bus, facing forward suddenly falls forward. This can be an indication which of
the following?
A. The bus speeds
B. The bus slows down
C. The bus doesn’t change its velocity
D. The bus turns to the right
E. The bus turns to the left
4. A heavy box sits on a floor. Which of the following about the net force on the box is true?
A. Non-zero vector pointing up
B. Non-zero vector pointing down
C. Non-zero vector pointing left
D. Non-zero vector pointing right
E. It is zero
5.
A loaded truck collides with a car causing a huge damage to the car. Which of the following is true about the
collision?
A. The force on the truck is greater than the force
B. The force on the car is greater than the force on the truck
C. The force on the truck is the same in magnitude as the force on the car
D. During the collision the truck makes greater displacement than the car
E. During the collision the truck has greater acceleration than the car
6. The Earth pulls down on a railroad wagon with a force of 200 kN.
Which of the following is the “reaction force”?
A. The wagon pulls up the Earth with 200 kN
B. The wagon pushes down the railroad with 200 kN
C. The railroad pushes up the wagon with 200 kN
D. The buoyant force pushes up the wagon with 200 kN
E. The wagon pushes down the Earth with 200 kN
7. A railroad wagon pushes down on a railroad with a force of 200
kN. Which of the following is the “reaction force”?
A. The wagon pulls up the Earth with 200 kN
B. The wagon pushes down the railroad with 200 kN
C. The railroad pushes up the wagon with 200 kN
D. The buoyant force pushes up the wagon with 200 kN
E. The wagon pushes down the Earth with 200 kN
8. Which of the following is true about an astronaut’s weight on the surface of Moon compared to Earth?
A. Weight is the same, mass is less
B. Weight is less, mass is the same
C. Weight is less, mass is less
D. Weight is less, mass is greater
E. Weight is greater, mass is the same
9. An object is thrown straight up. How do we compare the net force on the object to its weight when it is at the
highest point the path?
A. It is greater than the weight
B. It is slightly less than the weight
C. It is zero
D. It is equal to the weight
E. It can’t be determine
In the diagram below, a block of mass m slides down an inclined plane with a constant speed at an angle θ with
respect to the horizontal. Use this diagram for questions 10 through 14.
10. What is the x-component of the gravitational force?
A. mg cosθ
B. mg sinθ
C. mg tanθ
D. mg
E. Zero
11. What is the y-component of the gravitational force?
A. mg cosθ
B. mg sinθ
C. mg tanθ
D. mg
E. Zero
12. What is the normal force applied to the block?
A. mg cosθ
B. mg sinθ
C. mg tanθ
D. mg
E. Zero
13. What is the kinetic friction force applied to the block?
A. µmg cosθ
B. µmg sinθ
C. µmg tanθ
D. µmg
E. Zero
14. Which of the following is true about the coefficient on kinetic friction?
A. µ = cosθ
B. µ = sinθ
C. µ = tanθ
D. µ = mg
E. Zero
In the diagram to the right, a block with a mass m = 5 kg slides
down an inclined plane with an angle θ = 37°. The block
maintains a constant acceleration a = 5.6 m/s2. (sin37° = 0.6,
cos37° = 0.8). The coefficient of kinetic friction between the
block and the inclined surface is 0.05. Use this diagram to
answer questions 15 through 17.
15. Which of the following diagrams best represents the
gravitational force W, the frictional force f, and the normal
force N that act on the block?
A.
B.
C.
16. What is the normal force on the block?
A. 50 N
B. 40 N
C. 30 N
D.
E.
D. 20 N
E. 10 N
17. What is the friction force between the block and inclined plane?
A. 2 N B. 5 N C. 6 N D. 30 N E. 40 N
18. A system of two blocks is accelerated by an applied force of magnitude F on the frictionless horizontal surface.
The tension in the string between the blocks is:
A. 3F
B. 5F
C. 3/8 F
D. 1/3 F
E. 1/5 F
19. A student pulls a wooden box along a rough horizontal floor at
constant speed by means of a force P as shown to the right.
Which of the following must be true?
A. P > f and N < W.
B. P > f and N = W.
C. P = f and N > W.
D. P = f and N = W.
E. P < f and N = W.
20. A boy pushes a sled of mass m across a rough
horizontal surface by applying a force of magnitude F
directed at angle . The coefficient of kinetic friction
between the sled and the surface is . The normal
force on the sled is:
A. mg
B. mg sin
C. mg cos
D. mg + F sin
E. mg –F sin
21. A boy pushes a sled of mass m across a rough horizontal
surface by applying a force of magnitude F directed at
angle . The coefficient of kinetic friction between the sled
and the surface is .The frictional force on the sled is:
(A) (mg + Fsin)
(B) (mg-Fsin) (C) (mg+ Fcos)
(D) (mg-Fcos) (E) mg
22. A block of mass m is pulled along a horizontal surface at
constant speed v by a force Fapp , which acts at an angle of 
with the horizontal. The coefficient of kinetic friction
between the block and the surface is .The normal force
exerted on the block by the surface is:
A. mg - Fapp cos B. mg- Fapp sin C. mg
D. mg + Fapp sin E. mg + Fapp cos
23. A block of mass m is pulled along a horizontal surface at
constant speed v by a force Fapp , which acts at an angle of 
with the horizontal. The coefficient of kinetic friction
between the block and the surface is .The friction force on the
block is:
A. (mg - Fapp cos)
B. (mg- Fapp sin)
D. (mg + Fapp sin)
E. (mg + Fapp cos)
C. mg
24. An ideal spring obeys Hooke's law, F = -kx. A mass of 0.30 kg hung vertically from this spring stretches the
spring 0.015 meter. The value of the spring constant is nearly
A. 150 N/m
B. 200 N/m
C. 300 N/m
D. 250 N/m
E. 350 N/m
25. Two blocks are attached by a compressed spring and are
initially held at rest on a frictionless surface. The blocks are
then released simultaneously. If block I has four times the
mass of block II, which of the following quantities is the same
for both blocks as the spring pushes the two blocks away from each other?
(A) Speed (B) Velocity (C) Acceleration (D) Displacement (E) Force on each block
26. The two spheres have equal densities and are subject only to their
mutual gravitational attraction. Which of the following quantities must
have the same magnitude for both spheres?
A. Acceleration
B. Velocity
C. Kinetic Energy
D. Displacement from the center of mass
E. Gravitational force
27. A block of mass 4m can move without friction on a horizontal table.
This block is attached to another block of mass m by a string that
passes over a frictionless pulley. If the masses of the string and the
pulley are negligible, what is the magnitude of the acceleration of
the descending block?
A. g/5
B. g/4
C. g/3
D. 2g/3
E. g
28. Three forces act on an object. Which of the following is true in order to keep the object in translational
equilibrium?
I. The vector sum of the three forces must equal zero.
II. The magnitudes of the three forces must be equal.
III. All three forces must be parallel.
(A) I only
(B) II only
(C) I and III only
(D) II and III only
29. Three objects can only move along a straight, level path.
The graphs below show the position d of each of the
objects plotted as a function of time t. The net force on the
object is zero in which of the cases?
A. II only
D. I and III only
B. III only
C. I and II only
E. I, II, and III
(E) I, II, and III
30. A locomotive is pulling an empty freight car with a constant acceleration on a horizontal surface. The mass of the
locomotive is five times the mass of the car. Which statement is true about the force applied by the car on the
locomotive?
A. 5 times greater than the force of the locomotive on the car
B. 5 times less than the force of the locomotive on the car
C. Zero since they move with a constant acceleration
D. Equal to the force of the locomotive on the car
E. More information is required
31. A block with initial velocity of 3 m/s slides 9 m across a rough horizontal surface before coming to rest. What is
the coefficient of kinetic friction?
A. 0.10 B. 0.50 C. 0.30 D. 0.05 E. 0.01
32. A student performs an experiment on measuring friction forces in different trials. The first time he pulls
a wooden block across a horizontal surface with a constant speed – trial A. The second time he makes
the same surface incline at angle Θ with respect to the horizontal line – trial B. Which of the following
is true about friction force between the block and the surface?
A. The inclined case B has greater friction force
B. The inclined case B has less friction force
C. The friction force the same in both cases A and B
D. The friction force is not dependent from the incline angle
E. The friction force increases with angle
33. A bus driver makes an emergency stop by slamming the bus’s breaks. How far will the bus skid if its speed is
doubled?
A. The stopping distance stays the same
B. The stopping distance is doubled
C. The stopping distance is quadrupled
D. The stopping distance is tripled
E. The mass of the bus is required
In the diagram to the right, two blocks A and B with masses m
and 2m are in contact on a horizontal frictionless surface. A
force F is applied to block A. Us this diagram to answer
questions 34 and 35.
34. What is the acceleration of the system two blocks?
A. F/m
B. F/2m C. F/3m
D. F/4m
E. F/5m
35. What is the force exerted by block A on block B?
A. F/2
B. F/3
C. 3F/2 D. 2F/3 E. F/5
36. A block with a mass m is placed on the top of identical block m and the
system of two blocks is at rest on a rough horizontal surface. The top
block is tied to the wall. The coefficient of static friction between all
surfaces is µ. What maximum value does force F reach before the lower
block starts sliding to the left?
A. 3 µmg
B. 2 µmg
C. 4 µmg
D. ½ µmg E. ¼ µmg
37. Three blocks connected with each other by two light strings. The blocks have different masses m2 > m3 >m1. The
heaviest of three blocks is placed on a frictionless table. The system of three blocks is released from rest. What is
the acceleration of block m2?
A. (m2 - m3 - m1)g/(m1 + m2 + m3)
B. (m1 - m3 - m2)g/(m1 + m2 + m3)
C. (m3 - m1)g/(m1 + m2 + m3)
D. (m3 - m2- m1)g/(m1 + m2 + m3)
E. (m1 - m3 )g/(m1 + m2 + m3)
38. A lamp of mass m is suspended from two cables of unequal length
as shown above. Which of the following is true about the tensions T1
and T2 in the cables?
A. Tl > T2
B. T1 = T2
D. Tl - T2 = mg
39.
C. T1 < T2
E. T1+T2 = mg
A heavy ball of mass m is suspended from two massless strings of an equal
length as shown above. The tension force in each string is:
A. ½ mgcos
B. 2mgcos
C. mgcos
D. mg/(cos)
E. mg/(2cos)
40. A wooden rod on a horizontal tabletop is pivoted at one
end and is free to rotate without friction about a vertical
axis, as shown above. A force F is applied at the other
end, at an angle  to the rod. If a new force is applied
perpendicular to the rod, at what distance from the axis
should it be applied in order to produce the same torque?
A. d sin 
D. d tan 
B. d cos 
E.
2 d
C. d
41. A uniform rope of weight 30 N hangs from a hook as shown above. A box of mass
40 kg is suspended from the rope. What is the tension in the rope?
A. 30 N throughout the rope
B. 400 N throughout the rope
C. 100 N throughout the rope
D. 340 N throughout the rope
E. It varies from 400 N at the bottom of the rope to 430 N at the top.
42. Two blocks of masses 2 and 3 kg are hung from the ends of a lever with negligible mass. At which of the points
should the lever be placed on the fulcrum in order to stay in horizontal equilibrium?
A. A
B. B
C. C
D. D
E. E
Free-response Problems
1. A 2 kg block slides down a frictionless incline at an angle of 25 ̊.
a. Draw a free body diagram.
b. Find its acceleration.
2. A 2 kg block slides down a rough incline at an angle of 25 ̊ with a constant speed.
a. Draw a free body diagram.
b. Find the coefficient of kinetic friction between the block and the incline.
3. A 2 kg block remains stationary on an incline. The coefficients of static and kinetic friction are 0.15 and
0.1.
a. Draw a free body diagram.
b. Determine the angle that the block will start to move.
4. A 2 kg block is pulled up an incline at an angle of 25 ̊ at a constant velocity. The coefficient of kinetic
friction between the block and the incline is 0.15.
a. Draw a free body diagram.
b. Find the applied force.
5. A 2 kg block accelerates up an incline at an angle 0f 25 ̊ at a rate of 0.5 m/s2. The coefficient of kinetic
friction between the block and the incline is 0.15.
a. Draw a free body diagram.
b. Find the applied force.
6. A 0.3 kg block slides down a rough incline at an angle of 12 ̊ with a constant speed.
a. Draw a free body diagram.
b. Find the coefficient of kinetic friction between the block and the incline.
7. Two blocks with masses m1 and m2, respectively, are connected by a light string. Block 1 is placed on an
inclined plane which makes an angle θ with the horizontal. Block 2 is suspended from a pulley that is
attached to the top on the inclined plane. The coefficient of kinetic friction between block 1 and the
incline is µ.
a. Block 1 moves up the inclined plane with a constant velocity v. On the diagram below show all
the applied force on each block.
b. Determine the mass of block 2 that allows block 1 to move up the incline with a constant
speed.
c. Determine the mass of block 2 that will cause block 1 to accelerate up the incline at a constant
rate a.
d. The string between the blocks is cut. Determine the acceleration of block 1.
8. Two masses m1 = 400 g and m2 = 600 g are connected with a light string which goes over a frictionless
pulley of negligible mass. The system of two masses is released from rest.
i) Calculate the acceleration of each mass
ii) Calculate the tension force in the string
iii) Calculate the support force in the pivot of the pulley.
9. In the system presented on the diagram, block 2m and block 3m are connected by a light string passing
over a frictionless pulley. Block 2m is placed on the surface of a horizontal table with negligible friction.
Present all answers in terms of m, l, and fundamental constants.
a. Determine the acceleration of the system after it is released from rest.
b. Determine the velocity of 3m block just before it hits the floor.
c. Determine the velocity of 2m block at the edge of the table.
d. Determine the distance between the blocks after they landed on the floor.
10. Block M1 is connected to block M2 by a light string that passes over a frictionless pulley. Block M1 is
placed on a rough horizontal table. The coefficients of static and kinetic friction between the surface and
block M1 are µs and µk respectively.
a. On the diagram below show all the applied force on each block.
b. Determine the minimum value of coefficient of static friction, which will prevent the blocks from
moving.
An extra mass Δm is placed on the top of block M2, the extra mass causes the system of two blocks to
accelerate.
c. Determine the acceleration of the system.
D. Determine the tension force in the string.
11. A railroad wagon accelerates
from rest. A small metallic
sphere of mass m is suspended
at the end of a light string
which attached to the wagon’s
ceiling and makes an angle θ
with the vertical.
a. On the diagram to the right, draw a free-body diagram of the sphere.
The wagon accelerates for a total 30 s and reaches a velocity of 15 m/s.
b. Determine the acceleration of the wagon.
c. Determine the angle θ between the string and the vertical during the acceleration of the wagon.
12. An 80 kg passenger stands on a measuring scale in an elevator. The scale reading for the first 20 s are
presented by the graph below. Use g = 10 m/s2 in the following calculations.
a. Calculate the acceleration of the elevator for the following time intervals:
0 – 5 s;
5 – 10 s;
10 – 15 s;
15 – 20 s.
b. Calculate the velocity of the elevator at the end of the following time intervals:
0 – 5 s;
5 – 10 s;
10 – 15 s;
15 – 20 s.
c. Calculate the displacement of the elevator from the starting point to the end of the following time
intervals: 0 – 5 s;
5 – 10 s;
10 – 15 s;
15 – 20 s.
d. Draw the following graphs: a(t), v(t), x(t).
Answers
Multiple Choice
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
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24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
C
C
B
E
C
A
C
B
D
B
A
A
A
C
C
B
A
C
A
D
A
B
B
B
E
E
A
A
C
D
D
B
C
C
D
A
C
C
E
A
E
D
Free Response
1.
FN
mg cosθ
mg
mg sinθ
a)
b) a = 4.23 m/s2
2.
f
FN
mg cosθ
mg
mg sinθ
a)
b) μ = 0.47
3.
fs
FN
mg cosθ
mg
mg sinθ
a)
b) θ = 8.5O
4.
FAPP
FN
mg cosθ
FK
mg
mg sinθ
a)
b) FAPP = 11.2 N
5.
FAPP
FN
mg cosθ
FK
mg
mg sinθ
a)
b) FAPP = 12.2 N
6.
f
FN
mg cosθ
mg
mg sinθ
a)
b) μ = 0.21
7.
FN
FT
FT
mg cosθ
m2g
FK
m1g
mg sinθ
a)
b) m2 = m1 (sin θ + μ m1 cos θ)
c) m2 =
m1 (g sin 𝛉+ μg cos𝛉+a)
(g−a)
d) a = g sin θ – μg cos θ
or
a = g (sin θ – μ cos θ)
8.
a) a = 2 m/s2
b) T = 4.8 N
c) FSUPP = 9.6 N
9.
a)
b)
c)
d)
a = 3/5 g
v = √(6gL/5)
v = √(6gL/5)
x = 2L√(6/5)
10.
FN
FT
Fs
FT
M2g
M1g
a)
b) μs = M2/M1
c)
𝑎=
𝑔 ( 𝑀2 + ∆𝑚− 𝜇𝑀1 )
𝑀1 + 𝑀2 + ∆𝑚
d) FT = M1g (M +
𝑔 ( 𝑀2 + ∆𝑚− 𝜇𝑀1 )
𝑀1 + 𝑀2 + ∆𝑚
)
11.
T
T cos θ
mg
a)
b) a = .5 m/s2
c) θ = 2.9O
T sin θ
12.
a) a(0-5s) = 0 m/s2, a(5-10s) = 5 m/s2, a(10-15s) = 0 m/s2, a(15-20s) =-5 m/s2
b) v(0-5s) = 0 m/s, v(5-10s) = 25 m/s, v(10-15s) = 25 m/s, v(15-20s) =0 m/s
c) x(0-5s) = 0 m, x(5-10s) = 62.5 m, x(10-15s) = 187.5 m, x(15-20s) =250 m
d)