Physics 221.
Exam III
Spring 2003
The situation below refers to the next three questions:
A solid cylinder of radius R and mass M with initial velocity v0 rolls without slipping up
the inclined plane.
R
M
102. While the cylinder is rolling up, the frictional force is _________________
the cylinder is rotating ___________________
and
a. directed uphill , clockwise.
b. directed downhill, with constant angular speed
c. directed uphill , counterclockwise
d. zero, clockwise
e. directed downhill, with constant angular acceleration.
103. If the cylinder moves up a vertical height H before it starts rolling back down the
inclined plane, its initial speed v0 must be:
a. v0 = gH
b.
c.
v0 =
10
gH
7
v0 =
10
gH
3
d. v0 = gH
e.
v0 =
4
gH
3
104. If the mass and the radius of the cylinder moving uphill are doubled, the magnitude
of the acceleration of the center of mass changes by a factor of:
a.
b.
c.
d.
e.
1/2
1 (does not change)
2
4
8
Page 1 of 14
Physics 221.
Exam III
Spring 2003
105. A solid wood door a = 1 m wide and b = 2 m high is hinged on one of the long sides
(as a regular door) and has a total mass M = 40 kg. Initially the door is at rest. It is struck
with a handful of sticky mud of mass m = 0.5 kg traveling perpendicular to the door at 12
m/s before impact. The mud hits the door at its geometrical center. What is ωf, the final
angular speed of the door? (Idoor with respect to hinges = Ma2/3)
a. ωf = 0.10 rad/s
b. ωf = 0.22 rad/s
c. ωf = 0.43 rad/s
d. ωf = 0.56 rad/s
e. ωf = 0.80 rad/s
106. Four small identical balls are arranged in a square using four massless rods. The
system can rotate about three different axis, as shown in the figures below. Rank the
moments of inertia of the system in each case.
1
a.
b.
c.
d.
e.
2
3
I1 > I2 > I3
I1 > I3 > I2
I1 = I3 > I2
I1 = I2 = I3
I1 > I2 = I3
Page 2 of 14
Physics 221.
Exam III
Spring 2003
107. All the forces applied to the objects (three rods, one disk) in the figure below have
magnitude F or 2F. Each object is free to rotate in the plane of the figure about the axis
indicated with a dot ●. Compare the magnitude of the net torque about the corresponding
axis on each system.
1
2
F
L
L
L
3
L
4
2F
2F
F
F
L/2
a.
b.
c.
d.
e.
F
L
L
τ1 < τ3 < τ2 = τ4
τ2 < τ1 < τ4 < τ3
τ4 < τ3 < τ 1 = τ 2
τ2 < τ1 < τ3 = τ4
τ1 = τ2 < τ4 < τ3
Page 3 of 14
Physics 221.
Exam III
Spring 2003
The situation below refers to the next two questions:
A ladder of mass M = 15 kg and length L = 3 m is put against a frictionless wall as shown
in the figure. The floor has a static friction constant µs = 0.25.
θ
108. If the angle θ = 10°, the magnitude of the force exerted on the ladder by the wall is:
a.
b.
c.
d.
e.
10 N
13 N
17 N
21 N
26 N
109. The largest angle θ MAX before the ladder slides down is: (Choose the closest
answer)
a.
b.
c.
d.
e.
θ MAX = 14°
θ MAX = 19°
θ MAX = 27°
θ MAX = 30°
θ MAX = 34°
Page 4 of 14
Physics 221.
Exam III
Spring 2003
The situation below refers to the next two questions:
A mass m = 3.0 kg sits on a plank. The plank has length L = 2.0 m and mass M = 2.5 kg.
The plank is positioned atop two scales fixed to the ground. Scale 1 is at one end of the
plank, scale 2 is a distance D = 1.25 m from scale 1. The 3-kg mass is d = 0.50 m from
the end of the plank, as shown in the figure.
L
d
m
M
Scale 2
Scale 1
D
110. What does scale 2 read (in kg)?
a.
b.
c.
d.
e.
1.1 kg
2.3 kg
2.7 kg
3.2 kg
4.3 kg
111. If the 3-kg mass is moved to the right to a distance 2d from the end of the plank, the
reading on scale 1 _________ and the reading on scale 2 _________.
a. decreases, increases by the same amount that the reading on scale 1 decreases.
b. decreases, increases by twice the amount that the reading on scale 1 decreases.
c. decreases, increases by one half the amount that the reading on scale 1 decreases.
d. increases, decreases by the same amount that the reading on scale 1 increases.
e. increases, decreases by twice the amount that the reading on scale 1 increases.
Page 5 of 14
Physics 221.
Exam III
Spring 2003
The situation below refers to the next two questions:
A thin rod of mass M = 2 kg and length d = 1 m rests on frictionless ice. A ball of putty
of equal mass M with an initial velocity v = 5 m/s hits one end of the rod as shown in the
figure. After the collision, the putty sticks to the rod.
M
d
v
M
112. Which of the following physical quantities is conserved in this process?
a.
b.
c.
d.
e.
Kinetic energy only.
Linear momentum only.
Angular momentum only.
Both linear momentum and angular momentum.
All three (kinetic energy, linear momentum and angular momentum)
113. Find the magnitude of the angular momentum of the system with respect to the
center of mass of the system after the collision.
a.
b.
c.
d.
e.
1.0 kg m2/s
2.5 kg m2/s
5.0 kg m2/s
10 kg m2/s
25 kg m2/s
Page 6 of 14
Physics 221.
Exam III
Spring 2003
114. The motion of three different particles 1, 2 and 3 is studied and it is found that the
relation between the displacement x and the acceleration a for each of them is:
Particle 1: a = 2 x
Particle 2: a = −5 x
2
Particle 3: a = 4 x
Which of these particles has simple harmonic motion?
a.
b.
c.
d.
e.
Particle 1 only
Particle 2 only
Particle 3 only
Particles 1 and 2 only
Particles 1 and 3 only
The situation below refers to the next two questions:
A block of mass m = 250 g is suspended from a spring with constant k = 85 N/m. The
damping constant b = 70 g/s. We assume that the damping force is F =−bv, where v is
velocity.
115. How long does it take for the amplitude of the damped oscillations to drop to half
its initial value?
a.
b.
c.
d.
e.
5.0s
6.0s
7.0s
8.0s
9.0s
116. During this same time, the mechanical energy of the system changes by a factor of:
a.
b.
c.
d.
e.
1/8
1/4
1/2
1
None of the above.
Page 7 of 14
Physics 221.
Exam III
Spring 2003
The situation below refers to the next two questions:
Two identical springs of spring constant k are attached to a block of mass m and to a
fixed support. Friction can be neglected.
x=0
x
117. What is the frequency of oscillations?
a.
b.
c.
d.
e.
f =
1
2π
2k
m
f =
1
2π
4k
m
f =
1
2π
k
2m
f =
1
2π
k
4m
f =
1
2π
k
m
118. The block is pulled a distance A to the right of the equilibrium position and released
from there at t = 0. The position of the block as a function of time can be written as:
x = A sin(ωt + φ)
with A > 0
Set the origin x = 0 at the equilibrium position of the block and take x > 0 to the right (as
shown in the figure). Determine the phase angle φ.
a. ϕ = −π rad
π
ϕ =−
2 rad
b.
c. ϕ = 0
ϕ=
π
2 rad
d.
ϕ
=
π
e.
rad
Page 8 of 14
Physics 221.
Exam III
Spring 2003
Page 9 of 14
Physics 221.
Exam III
Spring 2003
119. In the figure, two tiny conducting balls of identical mass m and identical charge q
hang from non-conducting threads of length L. If θ = 1.2°, m = 10 g, and x = 5 cm, what
is q?
L
q
a.
b.
c.
d.
e.
θ
L
x
q
q = ± 4.2 × 10−9 C
q = ± 1.0 × 10−8 C
q = ± 2.4 × 10−8 C
q = ± 5.4 × 10−8 C
q = ± 9.7 × 10−8 C
120. A proton and an electron are placed at two corners of an equilateral triangle of side
length a = 2 × 10−6 m. What is the magnitude of their net electric field at the third
corner?
a.
b.
c.
d.
e.
45 N/C
90 N/C
180 N/C
360 N/C
480 N/C
121. A surface has area vector A = (2i + 3j + 4k) m2. What is the magnitude of the flux
of an electric field E = 5i N/C through this surface?
a.
b.
c.
d.
e.
10 Nm2/C
15 Nm2/C
20 Nm2/C
25 Nm2/C
0
Page 10 of 14
Physics 221.
Exam III
Spring 2003
122. Two long, charged, concentric cylinders have radii a = 3 cm and b = 6 cm. The
charge per unit length is λin = 2×10−6 C/m on the inner cylinder, and λout = −8×10−6 C/m
on the outer cylinder. Find the magnitude of the electric field at r = 4 cm, where r is the
radial distance from the common central axis.
a.
b.
c.
d.
e.
E(r) = 2.7×106 N/C
E(r) = 3.6×106 N/C
E(r) = 4.5×105 N/C
E(r) = 5.4×105 N/C
E(r) = 9.0×105 N/C
The situation below refers to the next two questions:
A charge Q is placed near an uncharged metal slab as shown in the figure.
Q
metal
123. Which of the following statements is true?
a. Both the charge and the metal slab are pulled toward each other.
b. Both the charge and the metal slab are pushed away from each other.
c. The charge is pulled toward the metal slab, but no force is exerted on the metal slab.
d. The charge is pushed away from the metal slab, but no force is exerted on the metal
slab.
e. There is no net electric force on either of the two objects.
124. The metal slab is grounded. The charge is taken away (to infinity) and then the
grounding is cut. After this process, the net charge on the slab is:
a.
b.
c.
d.
e.
2Q
Q
0
−Q
−2Q
Page 11 of 14
Physics 221.
Exam III
Spring 2003
125. The figure below depicts a uniformly charged sphere with net charge Q > 0 and a
concentric Gaussian sphere of radius r around it. The net electric flux through this surface
is Φ. If a positive point-charge is brought to point P, the net electric flux through the
Gaussian surface _________ and the magnitude of the net electric field at point R (on the
Gaussian surface) __________.
r
Q>0
R
P
Gaussian
sphere
a.
b.
c.
d.
e.
decreases, decreases
increases, stays the same
increases, increases
stays the same, decreases
stays the same, stays the same
126. The potential energies associated with four orientations of an electric dipole in an
electric field are (1) 3U, (2) 4U, (3) 5U, (4) −3U, (5) −5U, where U is positive. Rank the
orientations according to the angle between the electric dipole moment p and the electric
field E, smallest first.
a.
b.
c.
d.
e.
1, 2, 3, 4, 5
5, 4, 3, 2, 1
5, 4, 1, 2, 3
1, 2, 3, 5, 4
3, 2, 1, 4, 5
Page 12 of 14
Physics 221.
Exam III
Spring 2003
127. The figure below shows the electric field lines in a region of space. The direction of
one of the lines is given.
Q
q
Which of the following statements about the two charges, Q and q, is true?
a.
b.
c.
d.
e.
|Q| < |q|, Q>0
|Q| < |q|, Q<0
|Q| = |q|, Q>0
|Q| > |q|, Q>0
|Q| > |q|, Q<0
Page 13 of 14
Physics 221.
Exam III
Spring 2003
128. The figure below shows three arrangements of a charge q (in gray) and several
charges Q and 2Q (in white). Rank the arrangements according to the magnitude of the
net electrostatic force on charge q due to the other charges.
q
d
q
Q
Q
d
d
Q
Q
Fig 1
d
Fig 2
d
q
2Q
Fig 3
a.
b.
c.
d.
e.
F2 < F3 = F1
F3 = F2 < F1
F2 = F1 < F3
F2 < F1 < F3
F1 = F3 < F2
Page 14 of 14