True-false questions are worth 2 points each, three-choice multiple
choice questions are worth 3 points each, five-choice multiple choice
questions are worth 6 points each. The maximum possible score is 120.
The exam period was 90 minutes. The mean score was 101.1; the median
was 106. Click here to see page1
page2 of the formula sheet that came
with the exam.
Unless told otherwise, you should assume that the
acceleration of gravity near the surface of the earth is 9.8
m/s2 downward and ignore any effects due to air
A solid sphere and a solid cylinder, both with mass M and radius R,
are released from rest simultaneously at the top of a ramp.
Which reaches the bottom of the ramp first?
(c) They arrive at the same time.
(c) They have the same kinetic energy.
A box of mass m = 2.2 kg is suspended from a thin wire which
is wound around a solid, cylindrical frictionless pulley with mass
M = 5.6 kg and radius R = 0.2 m. The box is released from
rest at a height h = 0.8 m off the ground.
What is the acceleration of the box?
(a) 1.27 m/s2
(b) 2.66 m/s2
(c) 3.05 m/s2
(d) 4.31 m/s2
(e) 5.07 m/s2
(a) 6.77 J
(b) 9.66 J
(c) 12.8 J
(d) 15.02 J
(e) 17.25 J
Two masses are suspended from a massless rod, which is supported at a
pivot point, as shown. In this figure LA = 3 m,
L1 = 1 m, L2 = 2.5 m,
m1 = 1 kg, and m2 = 5 kg. Note
that the figure is not drawn to scale.
What mass would have to be placed at the point A to balance the
(a) 0.22 kg
(b) 1.91 kg
(c) 2.86 kg
(d) 3.83 kg
(e) 4.07 kg
(a) 5.5 kg
(b) 8.6 kg
(c) 12.5 kg
(d) 13.7 kg
(e) 14.2 kg
(a) 1.57 N
(b) 2.08 N
(c) 3.36 N
(d) 4.78 N
(e) 5.12 N
(a) 4.32 J
(b) 6.00 J
(c) 17.28 J
A hoop of radius R = 0.4 m and mass M = 0.4 kg is
released from rest at the top of an inclined plane with height h
= 0.8 m. The angle between the plane and the horizontal is 20°. The
hoop rolls without slipping.
What is the ratio of the hoop's rotational kinetic energy to its
translational kinetic energy?
(a) Krot / Ktrans = 1/3
(b) Krot / Ktrans = 1/2
(c) Krot / Ktrans = 1
(d) Krot / Ktrans = 3/2
(e) Krot / Ktrans = 2
(a) 2.8 m/s
(b) 3.6 m/s
(c) 4.2 m/s
(d) 5.7 m/s
(e) 6.6 m/s
Two solid disks with mass m1 = 3.5 kg and
m2 = 0.8 kg and radius R1 =
R2 = 0.2 m both slide and rotate without friction on a
vertical axis. Initially, the upper disk m1 is
rotating with angular velocity ω1 and the lower
disk is at rest. The upper then disk falls, sticks to the lower disk,
after which they are observed rotate together at angular velocity
ω2 = 23 rad/s.
What was the initial angular velocity of the upper disk,
(a) 4.71 rad/s
(b) 28.26 rad/s
(c) 51.80 rad/s
(d) 75.35 rad/s
(e) 98.90 rad/s
(a) 0.064 kg m2
(b) 0.075 kg m2
(c) 0.086 kg m2
A girl on a sled slides from the top of a hill of height
h0 (point A) starting from rest. The girl and the sled have
a combined mass of 30 kg. The sled (with the girl) slides down on a
frictionless hill to point B. Then it slides up another hill to point C
and down again to point D which is at the same height as point B. The
sled's speed at point B at the bottom of the hill is
v0 = 19.8 m/s.
What is the height of point A, h0, that the sled started
(a) 16 m
(b) 18 m
(c) 20 m
(a) 5 m/s
(b) 8 m/s
(c) 12 m/s
(d) 14 m/s
(e) 16 m/s
(a) -5240 J
(b) -5520 J
(c) -5880 J
(a) 7 m
(b) 10 m
(c) 20 m
A block of mass M1= 3 kg slides without friction
down a ramp, starting from rest at height h1. At the
bottom, it runs into another block of mass M2 = 8 kg
which is at rest before the collision. The two blocks stick together
and slide up the second ramp (see the drawing below). They reach a
maximum height h2 before sliding back down. (Note:
the drawing is not to scale.) Immediately after sticking together, the two blocks move with the
velocity v = 6 m/s.
What was the velocity of the 3 kg block
immediately before the collision?
(a) 5 m/s
(b) 13 m/s
(c) 19 m/s
(d) 22 m/s
(e) 33 m/s
(a) 1.66 m
(b) 1.84 m
(c) 2.10 m
(d) 2.45 m
(e) 2.75 m
An object of mass 8 kg moves horizontally in a straight line at speed
v0 on a frictionless surface. A force F = 100
N slows it down to 11 m/s in 2 seconds.
What was the starting speed v0?
(a) 12 m/s
(b) 16 m/s
(c) 31 m/s
(d) 36 m/s
(e) 38 m/s
(a) -2100 J
(b) -3500 J
(c) -4700 J
(d) -5100 J
(e) -5900 J
Three objects collide. Two of them have equal mass
m1 = m2 = 5 kg and equal and
opposite velocities in the x-direction, v1 =
-v2 = 5 m/s. The third object, whose mass
m3 = 2 kg, has velocity 10 m/s in the +y
direction (see the figure below.) After the objects collide, they stick
together and move with a final velocity vtotal .
What is the magnitude of the momentum after the collision?
(a) 20 kg m/s
(b) 70 kg m/s
(c) 120 kg m/s
(a) 1.15 m/s
(b) 1.30 m/s
(c) 1.67 m/s
(d) 1.90 m/s
(e) 2.00 m/s
(a) along the +x direction
(b) along the -x direction
(c) along the +y direction
(d) along the -y direction
(e) vtotal has components in both the x and y directions.