Dynamics
v2
1.
2.
v1
A ball moves horizontally with an initial velocity v1, as shown above. It is then struck by a tennis racket. After
leaving the racket, the ball moves vertically with a velocity v2, which is smaller in magnitude than v1. Which of
the following vectors best represents the direction of the average force that the stick exerts on the ball?
A satellite is orbiting the Earth. If FE is the magnitude of the force exerted by the Earth on the satellite and FS
is the magnitude of the force exerted by the satellite on the Earth, then which of the following is true?
(A) FE is much greater than FS. (B) FE is slightly greater than FS.
(C) FE is equal to FS.
(D) FE is slightly greater than FS
(E) FE is much greater than FS
3. An object released from rest at time t = 0 slides down a frictionless incline 2 meters during the first 2 seconds.
The distance traveled by the object during the time interval from t = 2 second to t = 3 seconds is
approximately,
(A) 2.5 m
4.
(D) 11 m
(E) 13 m
(B) 3mbt1 + 2c
(C) mbt1
(D) mbt1 + c
(E) 2mbt1
A force F is exerted by a broom handle on the head of the broom, which has a mass m. The handle is
at an angle  to the horizontal, as shown above. The work done by the force on the head of the
broom as it moves a distance d across a horizontal floor is
(A) Fd sin 
6.
(C) 9 m
A marble of mass m moves along a path with a speed defined by the function v = bt2 + c, where t is time and b
and c are constants. What is the magnitude F of the net force on the particle at time t = t1?
(A) bt1 2 + c
5.
(B) 4.5 m
(B) Fd cos
(C) Fm cos
(D) Fm tan
(E) Fmd sin
A body’s position as it moves on a straight path is given by the equation x = 2t3 - 3t2 + 4t, where x is in meters
and t is in seconds. The net force on the body is equal to zero when t is equal to
(A) zero
(B) 1/2 s
(C) 3 s
(D) 4/5 s
(E) 5 s
V
t
7.
The parabola above is a graph of speed v as a function of time t for an object. Which of the following graphs
best represents the magnitude F of the net force exerted on the object as a function of time t?
(A) F
8.
(B) F
A descending box of mass 500 kg is uniformly decelerated to rest over a distance of 4 m by a rope in which the
tension is 6000 N. The speed vi of the elevator at the beginning of the 4 m descent is most nearly
(A) 4 m/s
(B) 10 m/s
(C) 12 m/s
(D) 16 m/s
(E) 22 m/s
9.
When the frictionless system shown above is accelerated by an applied force of magnitude F a, the tension in
the string between the blocks is
(A) 2 Fa
(B) Fa
(C) (3/5) Fa
(D) (2/5) Fa
(E) 3 Fa
10. Two 0.5-kilogram blocks are connected by a string that passes over a frictionless pulley, as shown above. The
blocks are initially held at rest. If a third block with a mass of 0.25 kilograms is added on top of one of the
0.5-kilogram blocks as shown and the objects are released, the magnitude of the acceleration of the
0.25-kilogram object is most nearly
(A) 10.0 m/s2
(B) 6.0 m/s2
(C) 4.0 m/s2
(D) 2.0 m/s2
(E) 1.0 m/s2
11. A 50-newton weight is suspended by two strings as shown above. The tension T in the slanted string is
(A) 50 N
(B) 100 N
(C) 150 N
(D) 200 N
(E) 250 N
12. A rubber band ball of mass m is attached to a string of length R as shown above. The ball is released from rest
from position X where the string is horizontal, swings through position Y where the string is vertical, and
reaches position Z where the string is again horizontal. What are the directions of the acceleration vectors of
the ball at positions Y and Z?
Position Y
Position Z
(A) Downward
Downward
(B) Downward
To the right
(C) Upward
Downward
(D) Upward
To the left
(E) To the right
To the left
13. As shown above, two blocks are pushed along a horizontal frictionless surface by a 30 newton force to the
right. The force that the 4-kilogram block exerts on the 6-kilogram block is
(A) 8 newtons to the left
(B) 8 newtons to the right
(D) 12 newtons to the left
(C) 10 newtons to the left
(E) 12 newtons to the right
14. A mass m moves on a curved path from point X to point Y. Which of the following diagrams indicates a
possible combination of the net force F on the mass, and the velocity v and acceleration a of the mass at the
location shown?
(A)
F
X
(B)
X
(C)
m
m
(D) X
X
v
Y
a
a
m
F
a
v
Y
Y
X
F
F
F
(E)
m
m
v
a
v
v
Y
a
Y
15. Two identical massless springs are hung from the ceiling. The springs suspend a block of mass 2.4 kg, as shown
above. When the block is in equilibrium, each spring is stretched an additional 0.3 meters. The force constant
of each spring is most nearly:
(A) 40 N/m
(B) 48 N/m
(C) 60 N/m
(D) 80 N/m
(E) 96 N/m
16. A 10 kilogram block lies on an inclined plane, as shown above. The incline is 8 meters wide and 6 meters tall.
The coefficient of friction between the plane and the block is 0.3. The magnitude of the force F necessary to
move the block up the plane with constant speed is most nearly
(A) 64 N
(B) 76 N
(C) 82 N
(D) 90 N
(E) 108 N
W
Z
X
Y
17. A figure of a dancer on a music box moves counterclockwise at constant speed around the path shown above.
The path is such that the lengths of its segments, WX, XY, YZ, and ZW, are equal. Arcs WX and YZ are
semicircles. Which of the following best represents the magnitude of the dancer's acceleration as a function of
time t during one trip around the path, beginning at point W ?
(C)
(B)
(A)
a
a
a
tW
tX
tY
tZ
t
tW
tW
tX
tY
tZ
tW
t
tW
tX
tY
tZ
tW
t
(E)
(D)
a
a
tW
tX
tY
tZ
tW
t
tW
tX
tY
tZ
tW
t
18. A ball is released from rest at time t = 0 and falls in the presence of air, which exerts a resistant force. The
acceleration a of the ball is given by a = g - bv, where v is the object's velocity and b is a constant. If limiting cases
for large and small values of t are considered, which of the following is a possible expression for the speed of the
object as an explicit function of time?
(A) v = g(1 - e-bt)/b
(B) V = (geht)/b
(C) v = gt - bt2
(D) v = (g + a)t/b
(E) v = v0+ gt, v0  0
Questions 19-20
F
Θ
f
As shown above, a block of mass m is pulled across a rough surface by a force F exerted at an angle Θ with the
horizontal. The frictional force on the block exerted by the surface has magnitude f.
19. What is the acceleration of the block?
(A) F/m
(B) FcosΘ /m
(C) (F-f)/m (D) (FcosΘ-f)/m
(E) (FsinΘ-mg)/m
20. What is the coefficient of friction between the block and the surface?
(A) f/mg
(B) mg/f
(C) (mg-FcosΘ)/f
(D) f/(mg-FcosΘ)
(E) f/(mg-FsinΘ)
21. A 10 kg object moves according to the function: x=3t2-4t+7. Which of the following represents the net force
that acts on the object?
(A) 52 N
(B) 60N
(C) 67 N
(D) 78 N
(E) 84 N
Questions 22-25
m3
m1
m2
The system above consists of three blocks, m1, m2 and m3 where m1 and m2 are attached to a virtually massless
cord and m3 sits on top of m1. The system is attached to a massless pulley and accelerates downward. There is no
friction between the surface and m1 however there is friction between the m1 and m3. The coefficient of kinetic
friction is µ however the coefficient of static friction is not given. Block m3 does not slide off of block m1.
22. Find the acceleration of m2
(A) m1g/(m2+m3)
(B) (m1+m2+m3)/m2g
(C) m2g/(m1+m2+m3)
(D) (m1+m3)g/m2
(E) (m1+m3)/m2g
23. What coefficient of static friction must there be in order for m3 not to slide off of block m1?
(A) m2/(m1+m2+m3)
(B) m1/(m2+m3)
(C) (m1+m3)/m2
(D) (m1+m2+m3)/m2
(E) m3/(m1+m2+m3)
Now block m3 begins to slide off block m1.
24. Find the acceleration of block m3.
(A) µg(m1+m2+m3)/m3
(B) µm3g/m1
(C) µg
(D) µg(m1+m3)/m2
(E) µgm3/(m1+m2+m3)
25. What is the acceleration of block m2?
(A) (m2-µm3)g/(m1+m2) (B) m2g/µ(m1+m3) (C) (m1+m2+m3)µ/3m1g (D) (m1+m3) µg (E)(m1+m3)g/µ(m1+m2+m3)
26. A ball of mass m falls in the presence of air resistance. The resistive force is represented by F=bv 2 where b is a
constant and v represents the ball’s velocity. The acceleration of the ball is most nearly
(A) mg/v
(B) b-g
T1
(C) g-bv2/m
(D) bv+g/m
(E) bvg
T2
27. A rubber band ball is suspended by two strings of unequal lengths. Which of the following is true about T 1 and
T2 in the strings?
(A) T1< T2
(B) T1> T2
(C) T1= T2
(D) T1- T2=mg
(E) (T1+T2)sinѲ=mg
Fa
53°
Questions 28-30
A 60 newton force is pushing a 5 kg box is being pushed up an incline at a 53° angle (cos53°=0.6, sin53°=0.8). The
coefficient of kinetic friction is 0.5.
28. Which diagram best represents the block’s weight W, normal force F n and the friction force Fr on the block?
(A)
Fa
(B)
Fn
W
Ffr
(C)
Fn
Fa
W
Ffr
(D)
Fn
Fa
W
Fn
Fa
(E)
W
Fa
Ffr
Ffr
W
Ffr
Fn
29. The normal force on the block is
(A) 10 N
(B) 20 N
(C) 30 N
(D) 40 N
(E) 50 N
30. Calculate the block’s acceleration as it moves up the incline
(A) 0.5 m/s2
(B) 1.0 m/s2
(C) 2.9 m/s2
(D) 3.5 m/s2
(E) 4.2 m/s2
31. A truck of mass 5m collides head on with a car of mass 3m. FT represents the force the truck applies to the car.
FC represents the force the car applies to the truck. Which of the following is true?
(A) FT> FC
(B) FT<FC
(C) FT=FC
(D) 3FT=5FC
(E) 5FT=3Fc
32. A car is traveling with velocity v and sees a kid playing with a ball in the street. The driver slams on the brakes
with a force F and stops in time for the kid to move away safely. If the car was traveling twice as fast how much
force would be required to stop at the same spot?
(A) F/4
(B) F/2
(C) F
(D) 2F
(E) 4F
Questions 33-34
A 30 kg block and 10 kg block are set up on an incline plane using a pulley system (Friction is not negligible). The 30
kg block accelerates downward while the 10 kg block is accelerating up the incline. The acceleration is equal to
2m/s2.
33. Determine the tension in the string.
(A) 200 N
(B) 210 N
(C) 220 N
(D) 230 N
(E) 240 N
34. Determine the friction force acting on the 10 kg block.
(A) 75 N
Question
Number
(B) 100 N
Answer
(C) 140 N
Question
Number
(D) 160 N
Answer
1
b
18
a
2
c
19
d
3
a
20
e
4
e
21
b
5
b
22
c
6
b
23
a
7
e
24
c
8
a
25
a
9
d
26
c
10
d
27
a
11
b
28
b
12
d
29
c
13
d
30
b
14
b
31
c
15
a
32
e
16
c
33
e
17
a
34
c
(E) 175 N