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 106.
The mean score was 81.3; the median was 83.
The exam period was 90 minutes. 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 resistance.
Two objects of mass M (= 1 kg) each travel with identical
speed (|v1| = |v2| = 3 m/s) making
an angle of θ relative to the x-axis. After they
collide with each other, they travel as one object of mass 2M and
with a velocity v3 (|v3| = 2 m/s) in
the horizontal direction.
Is the collision elastic or inelastic?
(a) 2.5 J
(b) 5 J
(c) 10 J
(d) 15 J
(e) 20 J
(a) 0.50 radians
(b) 0.84 radians
(c) 1.37 radians
(d) 1.51 radians
(e) 1.60 radians
You have two balls of identical mass (m = 0.1 kg) but made of
different materials. Let's call one the happy ball and the other the
sad ball. When the happy ball is dropped and hits the floor at a speed
of 2 m/s, it bounces back with the same speed. In contrast, the sad
ball, when it is dropped and hits the floor at a speed of 2 m/s, it
sticks to the floor without bouncing.
What is the magnitude of the impulse delivered to the floor by the
(a) 0 kg m/s
(b) 0.05 kg m/s
(c) 0.1 kg m/s
(d) 0.2 g m/s
(e) 0.4 kg m/s
(a) the happy ball
(b) the sad ball
A student is pushing a box of mass M (= 5 kg) by applying a
force F (= 100 N) on a horizontal floor. The kinetic coefficient
of friction between the box and the floor is 0.2. The box starts from
rest and moves to the right over a distance of 2 m.
How much work is done by the student to the box?
(a) 0 J
(b) -141 J
(c) 141 J
(d) -94 J
(e) 94 J
(a) It is zero.
(b) It is positive.
(c) It is negative.
Kaushiki throws a ball straight up from an initial height of 1 m. The
initial speed of the ball is 5 m/s. Ignore friction due to air for this
problem. The mass of the ball is 0.3 kg.
What is the maximum height reached by the ball?
(a) 2.28 m
(b) 3.56 m
(c) 4.73 m
(d) 5.88 m
(e) 6.97 m
(a) 0 m/s
(b) 10 m/s
(c) 5 m/s
(a) 3.5 J
(b) 6.7 J
(c) 9.3 J
(d) 11.1 J
(e) 12.9 J
Fred (75 kg) and Jane (50 kg) are at rest on skates facing each
other. Jane then pushes Fred with a constant force F = 45 N for
a time Δt. Jane then moves at a speed of 1.35 m/s.
What can you say about Fred's motion after the push?
(a) He moves at the same speed as Jane's and in the opposite direction.
(b) He moves at a speed higher than Jane's and in the opposite direction.
(c) He moves at a speed lower than Jane's and in the opposite direction.
(a) 0.5 s
(b) 1 s
(c) 1.5 s
(d) 2 s
(e) 3 s
At one end of a light bar of length L is fixed a small ball of
mass M. The other end of the bar is fixed to the ground at point
P but can rotate freely around the point. A person supports the end of
the bar where the ball is fixed with a force F that is perpendicular to
the bar as noted in the figure. Initially, the bar makes an angle of
60° with the horizontal ground as illustrated below. You can ignore
the mass of the bar.
To keep the bar stationary as shown in the figure, what force must
the person exert? Give its magnitude. Here g is the
acceleration of gravity.
(a) Mg / 4
(b) Mg / 2
(a) nonzero and clockwise around Q (seen from you)
(c) nonzero and counterclockwise around Q (seen from you)
What is the magnitude of the angular acceleration α of
the bar around point P immediately after the force F is gone?
(a) α = g / 2
(b) α = 3g / 4
(c) α = g / 4
(d) α = g / 2L
(e) α = 3g / 4L
What can you say about the relation between the rotation kinetic
energy Kpulley of the pulley and the translational
energy Kblock of the block after the block has
dropped by a distance of L?
(a) Kpulley = Kblock / 4
(b) Kpulley = Kblock / 2
(c) Kpulley = Kblock
(d) Kpulley = 2Kblock
(e) Kpulley = 4Kblock
You have invented a new recording device that uses a disk of radius
4.1 mm, similar to a DVD or CD (see figure). The outermost track is
with radius 4 mm and the innermost track is with radius 1 mm. The
reading speed (linear speed) is kept constant irrespective of the
position on the disk by adjusting the angular velocity depending on
which track is being read. The angular velocity of the disk when the
outermost track is being read is 241 rad/s.
For the outermost track, what is the linear reading speed? (The
linear reading speed is the constant tangential speed which is
maintained while playing the disk.)
(a) 0.96 m/s
(b) 1.08 m/s
(c) 1.15 m/s
(d) 1.52 m/s
(e) 1.97 m/s
(a) 52 rad/s
(b) 109 rad/s
(c) 243 rad/s
(d) 823 rad/s
(e) 961 rad/s
(a) α = 246 rad/s
(b) α = 246 rad/s2
(c) α = 385 rad/s
(d) α = 385 rad/s2
(e) α = 454 rad/s
(a) solid cylinder
(b) hollow cylinder
(c) They arrive at the same time.
A puck of mass 0.2 kg slides in a circular path on a horizontal
frictionless table at an angular speed ω of 10 rad/s. It
is held at a constant radius of 1 meter by a string threaded through a
frictionless hole at the center of the table. Then, you pull on the
string such that the radius decreases by a factor of 3. What happens to
the angular speed of rotation?
(a) It decreases by a factor of nine.
(b) It decreases by a factor of three.
(c) It does not change.
(d) It increases by a factor of three.
(e) It increases by a factor of nine.