Part 1
A 100 g rubber ball is thrown horizontally with a speed of 5 m/s toward a wall. It is
initially traveling to the left. It rebounds with no loss of speed. The collision
force is shown in the top graph below.
a.) What is the value of the maximum force Fmax? (4 pts)
b.)Draw an acceleration-versus-time graph for the collision on the middle set of
axes below. Make your graph align vertically with the force graph, and provide
an appropriate numerical scale on the vertical axis. (4 pts)
c.) Draw a velocity-versus-time graph for the collision on the bottom set of axes
below. Make your graph align vertically with the acceleration graph, and provide
an appropriate numerical scale on the vertical axis. (4 pts)
A 0.5 kg cart and a 2.0 kg cart are attached and are rolling forward with a speed of 2.0
m/s. Suddenly a spring-loaded plunger pops out and blows the two carts apart from each
other. The smaller mass cart shoots backward at 2.0 m/s.
d. What are the speed and direction of the 2 kg cart? (4 pts)
e. If the spring constant of the plunger is 25,000 N/m, by how much was the spring
initially compressed? Assume there is no friction. (4 pts)
Part 2
a.) A 12-cm-diameter, 2.0 kg uniform circular disk, which is initially at rest,
experiences the net torque shown in the figure below. What is the disk’s angular
velocity at t = 12 s? The disk rotates about an axis perpendicular to the plane of the
disk and through its center. (Note: : IDisk = MR2
/2 ) (10 pts)
b.) A U-shaped tube is open to the air at both ends and is partially filled with Mercury
(density = 13,600 kg/m3). Water (density = 1000 kg/m3) is poured into the left arm until
the water is 10.0 cm deep. How far upward from its initial position does the mercury rise
on the right side? (10 pts)
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Part 3
Consider the situation depicted below.
There is no friction between the mass m1 and the inclined plane. The coefficient of
kinetic friction between the inclined plane (with mass m2) and the ground is µk.
a) What is the magnitude of the force F necessary to have the mass m1 stationary with
respect to the moving inclined plane? (10 pt)
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b.) A skier, whose mass is 70 kg, stands at the top of a 10° slope on her new frictionless
skis. A strong horizontal wind blows against her with a force of 50 N. Using the concepts
of energy conservation, find the skier’s speed after traveling 100 meters down (along) the
slope. (10 pts)
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Part 4
Consider the frictionless piston system below where gravity is pointing downwards and
outside of the piston-gas system is vacuum.
The piston mass is Mp and its cross sectional area is A. The gas is ideal.
a) Suppose the piston is initially held by hand at a certain initial height, and the initial pressure of
the gas at that point is P1. Subsequently, the piston is released and allowed to fall. Write down
an inequality expression involving Mp , A, P1 , and g which is necessary for the piston to fall.
Express your answer in the form “P1< ….”. (3 pts)
b) Suppose during the fall depicted in part a), heat is drawn out of the gas such that the gas
maintains a constant temperature as the piston falls. If the initial height of the piston is h, what
is the final height of the piston? [Express your final answer in terms of Mp , A, P1 , g, and h.]
(7 pts)
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Here’s a new problem:
c.) A tube, open at both ends, is filled with an unknown gas. The tube is 190 cm in length
and 3.0 cm in diameter. By using different tuning forks, it is found that resonances
can be excited at frequencies of 315 Hz, 420 Hz, and 525 Hz, and at no frequencies
in between these.
What is the speed of sound in this gas? (10 pts)
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Part 5
i) A window washer of mass M is sitting on a negligible mass platform suspended by a
system of cables and pulleys with negligible mass as shown (only object that has
appreciable mass is the washer):
What is the approximate magnitude of the force F that the washer must exert to pull
himself (including the platform system) up at constant speed? (4 pts)
a) (3/2)Mg b) (2/3)Mg c) 3Mg d) Mg/3 e) Mg your answer:
ii) A 2 kg mass is hung at the end of a 1 m long string to form a pendulum. Suppose the
pendulum is released from rest with an initial angle of the string with respect to the vertical
being 0.1 radian. How long does the pendulum take to reach -0.05 radians? (4 pts)
a) 0.7 s b) 0.9 s c) 0.4 s d) 0.1 s e) 0.2 s your answer:
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iii) Consider the roller coaster ride segment shown below where the radius of the circle is
20.0 m:
What is the minimum speed of the roller coaster car at point A which would guarantee that
the roller coaster car will not leave the track assuming that the roller coaster car is upside
down at point A (neglect wind resistance and other similar complications)? (4 pts)
a) 7 m/s b) 14 m/s c) 20 m/s d) 100 m/s e) 200 m/s your answer:
iv.) A 0.20 kg plastic cart and a 2.0 kg lead cart can both slide without friction along a
horizontal track. Equal forces (same direction and magnitude) are used to push each
cart forward for 1 second, starting from rest. After the force is removed at t = 1 s,
which of the following statements is true? (4 pts)
a. The momentum of the plastic cart is less than the momentum of the lead cart.
b. The momentum of the plastic cart is equal to the momentum of the lead cart.
c. The momentum of the plastic cart is greater than the momentum of the lead cart.
d. There is not enough information to compare the momenta of the two carts.
your answer:
v.) A 0.20 kg plastic cart and a 2.0 kg lead cart can both glide without friction along a
horizontal track. Equal forces (same direction and magnitude) are used to push each
cart forward for 1 m, starting from rest. After the force is removed at x = 1 m, which
of the following statements is true? (4 pts)
a. The kinetic energy of the plastic cart is less than the kinetic energy of the lead
cart.
b. The kinetic energy of the plastic cart is equal to the kinetic energy of the lead
cart.
c. The kinetic energy of the plastic cart is greater than the kinetic energy of the lead
cart.
d. There is not enough information to compare the kinetic energies of the two carts.
your answer: