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PHYS218 Spring15
MidtermExam3
Physics 218: Midterm Exam3
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): 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)
The static friction force creates a clockwise torque around the center of the ball.
The static friction force creates a counterclockwise torque around the center of the ball.
There is a kinetic friction force slowing down the motion of the ball.
The normal reaction force creates a clockwise torque around the center of the ball.
The normal reaction force creates a counterclockwise torque around the center of the ball.
1.2 (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) Both the translational and the rotational kinetic energy are nonzero and equal to each other.
b) Its rotational kinetic energy is larger than its translational kinetic energy.
c) Both forms of energy are zero since there is no slipping during the rolling process.
d) Its translational kinetic energy is larger than its rotational kinetic energy.
e) You need to know the speed of the sphere to know which energy is larger.
1.3 (5 points): A lawn-mower blade rotates with angular velocity ω(t) = (0.50 rad/s + [1.40 rad/s3]t2). What is
the angular acceleration, in rad/s2, of the blade at t = 1.5 s?
a) -3.15
b) 3.90
c) 4.20
d) -6.30
e) 10.6
1.4 (5 points): A 100N-weight is placed on a massless board at the distance L1 from a frictionless pin. A force F
is applied vertically to the end of the board, at a distance L2 from the pin. Which of the following changes
have no effect on the magnitude of the support force F needed to keep the system in equilibrium?
a) The 100-N weight is moved to a position closer to the
support force F at the right end of the board.
b) The 100-N weight is moved to a position closer to the
frictionless pin at the left end of the board.
c) The distance L2 to the support force is increased (the board
is made longer) but the distance L1 is unchanged.
d) The distances L1 and L2 are doubled (the board is made
longer), no other change.
e) The weight is increased to 150N but the distances L1 and L2
are not changed.
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Problem 2 (20 points)
A target in a shooting gallery consist of a vertical square wooden board of side H 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 an unknown speed. The bullet remains embedded in the board. If the board
swings up to a horizontal position after the impact then falls back, calculate:
a) The angular speed of the board immediately after bullet’s impact only in terms of H, g, and mb/M.
b) The initial value of the bullet speed v only in terms of H, g, and mb/M.
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Problem 3 (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 altitude of this satellite above Earth’s surface only in terms of the known symbolic data.
Support your derivation with an annotated diagram.
b) Calculate the total energy of this geosynchronous satellite. 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 4 (20 points)
Your amazing and beautiful S2000 convertible blew a tire. The
car has a width of x=1.75m and a height y=1.30m; 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=13kN 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) What is the minimum coefficient of friction the tire must have with the road to prevent it from sliding?
b) If the applied force is just enough to start to lift the car, what is its mass?
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Problem 5 (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 0.0650 kg·m2, and the radius is 15 cm. She then holds a carbide bar steadily
against the wheel, causing it to slow down at constant acceleration. If it takes 200 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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