This exam consists of 25 questions; 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 87. The exam period was 90 minutes; the
average score was 68.4; the median score was 70. Click here to see
of the formula sheet that came with the exam.
A block of mass m1 = 3 kg is attached by a rope passed
over a pulley to another block of mass m3 = 8 kg, as shown in
the figure below. The first block slides on a frictionless table
surface. The pulley is a uniform cylinder of mass m2 and
radius 12 cm ( I = ½ M R2 ). The suspended block
accelerates downward with an acceleration a = 6.7 m/s2.
(a) T2 = 10.9 N
(b) T2 = 24.8 N
(c) T2 = 39.7 N
(d) T2 = 43.5 N
(e) T2 = 58.4 N
(a) 0.5 kg
(b) 0.8 kg
(c) 1.1 kg
(d) 1.4 kg
(e) 1.7 kg
(a) smaller than 6.7 m/s2.
(b) equal to 6.7 m/s2.
(c) larger than 6.7 m/s2.
(a) T1 > T2
(b) T1 = T2
(c) T1 < T2
A uniform disc of mass M = 20 kg and radius R = 60 cm is rotating
about an axis through the center as shown in the figure, with an angular
velocity ω = 120 rad/s. A block of mass m = 3 kg falls vertically
on the top surface of the disc at a distance r = 35 cm from the axis of
rotation and sticks to the surface.
What is the angular velocity of the disc and the block after the block
has fallen on the disc?
(a) 69 rad/s
(b) 83 rad/s
(c) 109 rad/s
(a) smaller than ωf.
(b) equal to ωf.
(c) larger than ωf.
A sphere of radius R = 30 cm is initially rotating at an angular
speed of 250 revolutions per minute (rpm). A tangential force is
applied to the sphere. As a result, the sphere slows down with a
constant angular acceleration of 3 rad/s2.
How long does it take for the sphere to stop?
(a) 8.7 s
(b) 12.1 s
(c) 15.9 s
(a) 10.3 revolutions
(b) 18.1 revolutions
(c) 23.4 revolutions
(a) less than n revolutions.
(b) n revolutions.
(c) more than n revolutions.
To lift a small sunken ship from the bottom of the ocean two ballasts
of equal volumes are attached to the ship. The ballast are filled with
air. The mass of the ship is 50,000 kg and the mass of each ballast is
50 kg. The density of ocean water is 1027 kg/m3. The
density of air is 1.25 kg/m3.
What is the minimum volume V each ballast should be in order to lift
the ship to the surface of the ocean?
(a) V = 13.3 m3
(b) V = 24.4 m3
(c) V = 36.6 m3
(d) V = 47.7 m3
(e) V = 51.1 m3
(a) FB would increase.
(b) FB would stay the same.
(c) FB would decrease.
A block of unknown mass M is attached to the ceiling by a spring
with force constant k = 130 N/m. A force of 200 N is applied to the
block compressing the spring from its equilibrium position. At time t =
0, the force is removed and the block starts to oscillate up and down
with angular frequency ω = 1.4 s-1.
What is the maximum compression of the spring during these
(a) 0.72 m
(b) 1.23 m
(c) 1.54 m
(a) M = 38 kg
(b) M = 66 kg
(c) M = 92 kg
(a) y(t) = -ymax sin(ωt)
(b) y(t) = -ymax cos(ωt)
(c) y(t) = +ymax cos(ωt)
(a) 154 J
(b) 189 J
(c) 237 J
(a) ω > 1.4 s-1
(b) ω = 1.4 s-1
(c) ω < 1.4 s-1
A large container with height 0.5 m is filled with water ( ρ =
1000 kg/m3 ). A pipe is attached to the reservoir and is
plugged at the far end as shown in the figure so the water is not
flowing. In regions a, and b the pipe has a diameter
0.04 m. Region c has a slight constriction reducing the diameter
to 0.03 m.
Calculate ΔP, the pressure difference between the top of the
container, and the bottom of the container.
(a) ΔP = 2300 N/m2
(b) ΔP = 3900 N/m2
(c) ΔP = 4900 N/m2
(a) Pa > Pb
(b) Pa = Pb
(c) Pa < Pb
(a) Pc > Pb
(b) Pc = Pb
(c) Pc < Pb
(a) vc = 1.5 m/s
(b) vc = 2 m/s
(c) vc = 3.6 m/s
A grandfather clock keeps time with a simple pendulum. Unfortunately
the clock is running fast, (e.g. the period of the motion is 0.9 sec).
Which of the following changes could improve the clock’s
(a) increase the length of the pendulum
(b) decrease the length of the pendulum
(c) increase the amplitude of the pendulum’s swing
(b) at the same rate.
A hydraulic lift consists of a narrow piston (diameter 0.25 m) connected
to a large piston (diameter 1.5 m). A 500 Kg mass is placed on the
large platform as shown in the diagram.
Calculate F the minimum force which must be applied to the
small piston necessary to lift the 500 Kg block.
(a) 85 N
(b) 136 N
(c) 269 N
(d) 490 N
(e) 770 N
(a) h = 2.8 cm
(b) h = 47.3 cm
(c) h = 100 cm