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PHYS218 Spring15
Exam#3
Physics 218: Midterm#3
April 22nd, 2015
Please read the instructions below, but do not open the exam until told to do so.
Rules of the Exam:
1. You have 75 minutes to complete the exam.
2. Formulae are provided on a separate sheet. You may not use any other formula sheet,
handwritten, or printed materials.
3. You may use any SAT approved handheld calculator. However, you must show your
work to get credit.
4. The use of any communication devices like phone, radio, or iPod is strictly prohibited
during the exam.
5. Be sure to put a box around your final answers and clearly indicate your work.
6. Partial credit can be given only if your work is clearly explained and labeled. No credit
will be given unless we can determine which answer you are choosing, or which
answer you wish us to consider. If the answer marked does not follow from the work
shown, even if the answer is correct, you will not get credit for the answer.
7. You do not need to show work for the multiple choice questions.
8. If you need extra space, indicate/ mark on the main page of the problem that you are
continuing on another page.
9. Do not remove any pages from this booklet.
10. Have your TAMU ID ready when submitting your exam to the proctor.
Sign below to indicate your understanding of the above rules.
Full name (in CAPS): _____________________________________________________
UIN_______________________
Section Number: ______________________
Instructor’s Name:________________________
Your Signature: _______________________
Row/seat Number_____________
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Short Problems (20)
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Problem 2 (20)
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Problem 3 (20)
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Problem 4 (20)
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Problem 5 (20)
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Total Score (100)
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Problem 1 (20 points): Circle the correct option. No partial credit.
1.1 (5 points): Consider a uniform solid sphere of radius R and mass M, which is in the process of rolling
without slipping on a horizontal surface. Which statement about the kinetic energy of the sphere is correct?
a) Its translational kinetic energy is larger than its rotational kinetic energy.
b) Its rotational kinetic energy is larger than its translational kinetic energy.
c) Both the translational and the rotational kinetic energy are nonzero and equal to each other.
d) You need to know the speed of the sphere to know which energy is larger.
e) Both forms of energy are zero since there is no slipping during the rolling process.
1.2 (5 points): Two masses are tied to a rope that is passed over a pulley. The pulley has mass. The mass on
the right has more weight than the one on the left and when the masses are released from rest the heavier
one falls. There is no slipping of the rope. Which of the following statements is true?
a) The tension in the rope is the same on both sides of the pulley because
there is only one rope.
b) The tension is constant along any simple rope as long as the mass of the
rope can be ignored.
c) The tension in the rope must be larger on the left side of the pulley in
order to cause the left mass to move up.
d) The tension in the rope must be larger on the right side of the pulley in
order to turn the pulley towards the right.
e) The tensions in the rope on the two sides are equal to the weights of
the masses on the corresponding sides.
1.3
(5 points): A ball is slowing down as it rolls up
a ramp without slipping. Which of the following
statements is true?
a)
b)
c)
d)
e)
There is a normal force from the ramp equal in magnitude to the weight of the ball.
There is a kinetic friction force, pointing down the ramp and slowing down the ball.
There is a static friction force, pointing down the ramp and slowing down the ball.
Since the ball is rolling without slipping, there is no friction force in this case.
Since the ball is slowing down, the friction force points up the ramp in this case.
1.4 (5 points): A turbine blade rotates with angular velocity ω(t) = (5.00 rad/s – [1.80 rad/s3]t2). What is the
angular acceleration, in rad/s2, of the blade at t = 1.2 s?
a) 2.59
b) 3.46
c) -4.32
d) -5.18
e) 6.05
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Problem 2 (20 points)
In a student machine shop, a student sets a grinding wheel freely rotating at 35.0 rpm. The moment of inertia
of the wheel is known to be 0.0850 kg·m2, and the radius is 12 cm. She then holds a carbide bar steadily
against the wheel, causing it to slow down at constant acceleration. If it takes 220 revolutions for the wheel to
come to a complete stop,
a) What time is required to for the wheel to stop?
b) What frictional force is exerted by the carbide bar on the wheel during this process?
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Problem 3(20 points)
Your amazing and beautiful S2000 convertible blew a tire. The
car has a width of x=1.60m and a height y=1.20m; you may
assume the center-of-mass is in the middle of the car. You lift
the right side using a simple jack, and for simplicity let’s assume
the car is a rectangle with its axis of rotation at the bottom left
as shown. The jack is set up so it makes an angle of =35°
above the horizontal and provides a normal force of F=15.5kN
to the bottom-right of the car. The center of mass, the jack,
and the pivot point are in the same plane, shown as a rectangle
in the figure. Hint: This is a two-dimensional problem; you
should ignore the length of the car.
a)
b)
If the applied force is just enough to start to lift the car, what is its mass?
What is the minimum coefficient of friction the tire must have with the road to prevent it from
sliding?
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Problem 4 (20 points)
A satellite navigating in the Earth’s equatorial plane is observed permanently above the same point on Earth’s
surface. The known data are: T (time taken by Earth for a complete spin around its axis), RE (Earth’s radius at
equator), ME (Earth’s mass), and G (the universal constant of gravitation).
a) Calculate the linear speed of this satellite in terms of the given symbolic data. Support your derivation
with an annotated diagram.
b) Calculate the net energy that must be supplied to this geosynchronous satellite to move to another
circular orbit at a double distance from Earth’s surface. Take the potential gravitational energy of the
system to be zero at an infinite distance between the satellite and Earth.
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Problem 5(20 points)
A target in a shooting gallery consist of a vertical square wooden board of side D and mass M that pivots freely
on a horizontal axis along its top edge, as shown in the figure. The board is struck face-on at its center by a
bullet of mass mb traveling at a speed v. If the bullet remains embedded in the board, calculate:
a) The angular speed of the board immediately after bullet’s impact only in terms of D, v and mb /M.
b) The minimum value of the bullet speed vmin needed for the board to swing all the way over after
impact only in terms of D, g, and mb /M.
c)
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