Physics 221.
Exam 2 (Midterm)
Spring 2003
The situation below refers to the next two questions:
Two particles A and B move along the x-axis according to the graph shown below.
x (m)
A
0
1
B
2
3
4
5
t (s)
52. Which of the following statements about the x-component of their accelerations
between t = 0 and t = 5 s is true?
a.
b.
c.
d.
e.
ax,A > 0 , ax,B > 0
ax,A > 0 , ax,B = 0
ax,A = 0 , ax,B > 0
ax,A < 0 , ax,B > 0
ax,A < 0 , ax,B = 0
53. When is their relative velocity equal to zero?
a.
b.
c.
d.
e.
At some point between t = 0 and t = 1 s.
At some point between t = 1 and t = 2 s.
At some point between t = 2 and t = 3 s.
At some point between t = 3 and t = 4 s.
At some point between t = 4 and t = 5 s.
Page 1 of 15
Physics 221.
Exam 2 (Midterm)
Spring 2003
54. Two vectors A and B have the same magnitude. Vector A is in the positive xdirection. Vector B is in the negative y-direction. Which of these figures correctly depicts
the angle between vectors A and (A-B)? (Ignore length of vectors in the figure).
A−B
a.
A−B
b.
90°
A
c.
45°
A
A
45°
A−B
A−B
d.
60°
A
e.
60°
A
A−B
55. Force vector FA has the magnitude of 5.0 N and an angle of 300° with respect to the
positive x-axis (counter-clockwise). Force vector FB has a magnitude of 5.0 N and an
angle of 60° with respect to the positive x-axis (counter-clockwise). What is the
magnitude of the third force vector, which must be added to FA and FB in order to make
the net force equal to zero? (All forces act on the same object).
a.
b.
c.
d.
e.
2.5 N
5.0 N
7.5 N
10.0 N
None of the above
56. Let A = i + 2 j + α k and B = 3 i − j + β k. Find the values of α and β that will make
A×B = 0.
a.
b.
c.
d.
e.
α = −2, β = 0
α = 0, β = 2
α = −2, β = −2
α = 3, β = −2
There are no values of α and β that will make A×B = 0.
57. If you go from the origin to x = 10.0 m in 5.0 s, stay there for 2.0 s, and then go to
x = −2.0 m in 3.0 s, what will be the x-component of your average velocity during this
trip?
a.
b
c.
d.
e.
vx,average = –2.0 m/s
vx,average = –1.2 m/s
vx,average = –0.2 m/s
vx,average = 0.2 m/s
vx,average = 1.2 m/s
Page 2 of 15
Physics 221.
Exam 2 (Midterm)
Spring 2003
58. Three blocks A, B and C rest on a frictionless, horizontal surface. A force F = 18 N
is applied on block A. What is the force exerted on block C by block B?
a.
b.
c.
d.
e.
FC,B = 5 N
FC,B = 8 N
FC,B = 12 N
FC,B = 14 N
FC,B = 18 N
F
A
B
C
mA = 2 kg
mB = 3 kg
mC = 4 kg
The situation below refers to the next two questions:
A particle of mass m = 1.0 kg travels in a circle of radius R = 3.0 m at a constant speed of
2.0 m/s.
59. Find the work done by the net force acting on it during half a revolution.
a.
b.
c.
d.
e.
W=0
W = 4π J
W = 8π J
W = 16π J
None of these.
60. Find the angular displacement of the particle in 5.0 s.
a.
b.
c.
d.
e.
∆θ =
∆θ =
∆θ =
∆θ =
∆θ =
35°
78°
120°
150°
190°
Page 3 of 15
Physics 221.
Exam 2 (Midterm)
Spring 2003
61. For a particle in circular motion at constant speed v, which of the five plots best
shows the magnitude of the acceleration a as a function of radius r?
a
a
a
r
a.
a
r
a
r
b.
r
c.
d.
r
e.
The situation below refers to the next two questions:
A block of mass m = 9.0 kg is released from rest at the top of a frictionless ramp of length
d = 1.5 m. The speed of the block at the bottom is 2.5 m/s.
d
θ
62. What is the angle θ between the ramp and the horizontal?
a.
b.
c.
d.
e.
θ = 5°
θ = 8°
θ = 12°
θ = 30°
θ = 40°
63. A force F is applied on the box, perpendicularly to the box top surface, as shown in
the figure below. How does this affect N, the magnitude of the normal force exerted by
the ramp on the box, and a, the magnitude of the acceleration of the box? The incline is
still frictionless.
a.
b.
c.
d.
e.
F
N increases, a stays the same.
N increases, a decreases.
N stays the same, a stays the same.
N stays the same, a decreases.
N stays the same, a increases.
θ
Page 4 of 15
Physics 221.
Exam 2 (Midterm)
Spring 2003
The situation below refers to the next two questions:
The figure below shows the overhead view of two identical stones that travel in circles
over a frictionless horizontal surface. Each stone is tied to a massless string whose
opposite end is anchored at the center of the circle. Both stones have the same period.
64. Compare TL and TS, the tensions on the long and the short string, respectively.
a. TL < TS
b. TL = TS
c. TL > TS
d. You cannot tell without knowing the magnitude of the centripetal acceleration in each
case.
e. You cannot tell without knowing the mass of the stone.
65. Let ωL and ωS be the angular velocity vectors of the stone with the long and the short
string, respectively.. Which of the following is true?
a.
b.
c.
d.
e.
ωL points into the page, ωS points out of the page, and ωL= ωS
ωL points out of the page, ωS points into the page, and ωL= ωS
They both point out of the page, and ωL< ωS
They both point into the page, and ωL> ωS
They both point into the page, and ωL= ωS
Page 5 of 15
Physics 221.
Exam 2 (Midterm)
Spring 2003
66. A frictionless roller coaster cart of mass m tops the hill at point A with speed v0. Find
the work done on the cart by the gravitational force as it moves from point A to point B.
v0
B
A
h
h
h/3
a. Wg = mgh
1
b. Wg = mgh
3
c. Wg = 2mgh
2
d. Wg = mgh
3
e. Wg = 0
67. A small 0.20-kg rock is released from rest at point A, which is at the top edge of a
large hemispherical bowl with radius R = 0.50 m. Assume that the size of the rock is
small compared to the R, so the rock can be treated as a particle, and assume that the rock
slides rather than rolls. The work done by friction on the rock when it moves from point
A to point B at the bottom of the bowl is –0.08 J. What is the speed of the rock when it
reaches point B?
A
a.
b.
c.
d.
e.
vB =
vB =
vB =
vB =
vB =
2.00 m/s
2.26 m/s
3.00 m/s
3.13 m/s
3.26 m/s
B
Page 6 of 15
Physics 221.
Exam 2 (Midterm)
Spring 2003
The situation below refers to the next four questions:
Three velocities from a collision of objects A and B are drawn to scale in the figure
below. The initial velocity of object B, vB,i, is not shown, but it is known to have no
component in the y-direction. Note that | vA,i | = | vA,f |. There are no external forces acting
on the system.
vA,f
y
vA,i
vB,f
x
68. The ratio between the masses of the objects is:
a.
mA 2
=
mB 5
b.
mA 2
=
mB 3
c.
mA
=1
mB
d.
mA 4
=
mB 3
e.
mA
=2
mB
69. Which of the following is true about vB,i, the initial velocity of object B?
a. It points in the +i direction.
b. It points in the −i direction.
c. It is zero.
d. Its direction cannot be determined without knowing whether the collision is elastic or
inelastic.
e. Its direction cannot be determined without the actual value of each mass.
70. Which of these arrows best represents
the direction of the impulse on ball A?
a. A
b. B
c. C
d. D
B
e. E
C
D
E
A
71. Which of the following correctly describes the motion of the center of mass of this
system during this process?
a.
b.
c.
d.
e.
Always in the +i direction, at constant speed.
Always in the −i direction, at constant speed.
Always in the +i direction, but the speed is different before and after the collision.
At constant speed but in different directions before and after the collision.
It is at rest all the time.
Page 7 of 15
Physics 221.
Exam 2 (Midterm)
Spring 2003
The situation below refers to the next two questions:
Two blocks are connected through an ideal, massless string that goes over an ideal,
massless pulley, as shown in the figure below. The mass of block A is mA = 10.0 kg and
the coefficient of kinetic friction between block A and the incline is µk = 0.2. The angle
between the incline and the horizontal is θ = 30°.
A
B
θ
72. Block A slides down the incline at constant speed. What is the mass of block B?
a.
b.
c.
d.
e.
2.0 kg
3.3 kg
5.0 kg
6.7 kg
10.0 kg
73. If friction was not there but the masses and the angle of the incline remained the
same, the tension on the string would be:
a.
b.
c.
d.
e.
Larger.
Larger on the side of block A only.
The same.
Smaller
Smaller on the side of block A only.
Page 8 of 15
Physics 221.
Exam 2 (Midterm)
Spring 2003
The situation below refers to the next three questions:
A box stands in an elevator that travels a distance of 20m. During the displacement,
work done on the box by the normal force exerted by the elevator floor is WN = 12 kJ,
and the work done on the box by gravity is Wg = –10kJ. Use g = 10 m/s2 for simplicity.
74. What is the mass of the box?
a.
b.
c.
d.
e.
mbox = 20 kg
mbox = 40 kg
mbox = 50 kg
mbox = 80 kg
mbox = 100 kg
75. What is the magnitude of the normal force that the elevator exerts on the box?
a.
b.
c.
d.
e.
N = 100N
N = 200N
N = 300N
N = 400N
N = 600N
76. The elevator is:
a.
b.
c.
d.
e.
Moving up and slowing down.
Moving up at constant speed.
Moving up and speeding up.
Moving down and slowing down.
Moving down and speeding up.
Page 9 of 15
Physics 221.
Exam 2 (Midterm)
Spring 2003
77. A motorist drives south at 20.0 m/s for 3.00 minutes, then turns west and travels at
25.0 m/s for 2.00 minutes, and finally travels northwest at 30.0 m/s for 1.00 minute.
Determine the magnitude of total displacement.
a.
b.
c.
d.
e.
6.25 km
5.53 km
2.50 km
4.87 km
3.75 km
N
W
E
S
78. A car, initially at rest, accelerates at a constant rate a1 for ∆t1 = 5.0 s and then
accelerates at a2 = −5.0 m/s2 for ∆t2 = 10.0 s after which the car is going with speed
vf = 5.0 m/s. Find a1, the acceleration of the car for the first 5 seconds.
a.
b.
c.
d.
e.
a1 = 5.0 m/s2
a1 = 11 m/s2
a1 = 14 m/s2
a1 = 18 m/s2
a1 = 20 m/s2
79. A car is initially moving at a speed of 25 km/h when the brakes are applied, resulting
in a constant deceleration that brings the car to rest in 15 m. Assuming the same
deceleration, what would the stopping distance ∆x be if the initial speed were 50 km/h?
a.
b.
c.
d.
e.
∆x = 30 m
∆x = 45 m
∆x = 60 m
∆x = 75 m
∆x = 90 m
Page 10 of 15
Physics 221.
Exam 2 (Midterm)
Spring 2003
80. You can keep a book immobile against a vertical wall by applying a force
perpendicular to the book. If you press twice as hard, the magnitude of the static friction
between the book and the wall changes by a factor of:
a.
b.
c.
d.
e.
1 (It does not change).
2
1/2
4
1/4
The situation below refers to the next two questions:
Two billiard balls (same mass) collide head-on on a billiard table. The collision can be
considered elastic. The initial velocity of ball A is vA,i = 1.3 m/s i and the initial velocity
of ball B is vB,i = −0.85 m/s i.
81. What is vB,f, the final speed of ball B?
a.
b.
c.
d.
e.
vB,f = 0.58 m/s
vB,f = 0.69 m/s
vB,f = 0.85 m/s
vB,f = 1.3 m/s
vB,f = 1.9 m/s
82. If someone put gum (of negligible mass) on one of the balls and they stick together
after they collide, what is their final momentum pf? Each ball has a mass m = 0.34 kg.
a.
b.
c.
d.
e.
pf = −(0.31 kg m/s) i
pf = −(0.25 kg m/s) i
pf = 0.15 kg m/s i
pf = 0.45 kg m/s i
pf = 0.60 kg m/s i
Page 11 of 15
Physics 221.
Exam 2 (Midterm)
Spring 2003
The situation below refers to the next two questions:
The graph below shows the potential energy U as a function of position x for a particle of
mass m = 0.5 kg. The only force acting on this particle is the force associated to this
potential energy.
U (J)
50
10
−8
−6
−4
−2
2
4
6
8
x (m)
83. Determine the force on the particle at x = 0 m.
a.
b.
c.
d.
e.
F (x = 0 m) = − 40 N i
F (x = 0 m) = − 6 N i
F (x = 0 m) = 0
F (x = 0 m) = 6 N i
F (x = 0 m) = 40 N i
84. If the mechanical energy of the particle is E = 30 J when its position is x = 4 m,
determine at which position will the particle achieve its maximum speed.
a.
b.
c.
d.
e.
x = −6 m
x = −3 m
x = 1.5 m
x=5m
x=6m
Page 12 of 15
Physics 221.
Exam 2 (Midterm)
Spring 2003
85. Two balls are thrown simultaneously from point P and follow the trajectories shown
in the figure below. Which ball hits the ground first?
Ball A
Ball B
P
a.
b.
c.
d.
e.
Ball A
Ball B
They hit the ground simultaneously.
You cannot tell without knowing the initial velocities.
You cannot tell without knowing the angles at which they are thrown.
86. A pilot must fly due north, to reach the destination. The speed of the airplane is
300 km/h (relative to the air) and wind blows from the northeast at a speed of
90 km/h relative to the ground. Find the speed of the airplane relative to the ground.
a.
b.
c.
d.
e.
vplane, ground = 230 km/h
vplane, ground = 260 km/h
vplane, ground = 290 km/h
vplane, ground = 300 km/h
vplane, ground = 310 km/h
N
E
W
vwind
45°
S
Page 13 of 15
Physics 221.
Exam 2 (Midterm)
Spring 2003
87. Determine the center of mass of the following surface, made with 5 identical, uniform
squares of side a.
y
a
a
x
a.
b.
c.
d.
e.
( xCM , yCM ) = 
3 9 
a, a 
 2 10 
3
( xCM , yCM ) =  a, a 
2

2
( xCM , yCM ) =  a, a 
3

9
( xCM , yCM ) =  a, a 
 10 
2
( xCM , yCM ) =  a, a 
 3 
Page 14 of 15
Physics 221.
Exam 2 (Midterm)
Spring 2003
88. A bullet of mass m = 20 g is shot against a wooden block of mass M = 4 kg that is
attached on the opposite side to a strong spring of constant k = 4 ×104 N/m, which is itself
fixed to a rigid, immovable support (see figure below). The bullet strikes the block and
embeds itself in it. The spring is compressed a maximum distance x = 0.1 m. Before the
shot, the spring is perfectly relaxed. Friction is negligible.
k
vi
M
m
Find vi, the initial speed of the bullet.
a.
b.
c.
d.
e.
vi = 120 m/s
vi = 750 m/s
vi = 900 m/s
vi = 1500 m/s
vi = 2000 m/s
89. A 320 N bag hangs from three ropes as shown. The ropes make angles θ1 = 60° and
θ2 = 30° with the ceiling. The system is in equilibrium. Find T2, the tension on the righthand rope.
θ1
θ2
T1
T2
T3
a.
b.
c.
d.
e.
T2 = 130 N
T2 = 150 N
T2 = 160 N
T2 = 210 N
T2 = 280 N
Did you bubble in your exam version?
Page 15 of 15