Test A - Physics 218

PHYS218 Spring15
Exam#2
Physics 218: Midterm#2
March 25th, 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_______________________
Instructor’s Name:________________________
Section Number: ______________________
Your Signature: _______________________
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Short Problems (20)
__________
Problem 2 (20)
__________
Problem 3 (20)
__________
Problem 4 (20)
__________
Problem 5 (20)
__________
Total Score (100)
__________
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Problem 1 (20 points): Circle the correct option. No partial credit.
1.1 (5 points): A string is attached to the rear-view mirror of a car. A ball is hanging at the other end of the
string. The car is driving around in a circle, at constant speed. From the point of an observer at rest outside the
car, which of the following choices, with no extras, gives all of the forces directly acting on the ball?
a)
b)
c)
d)
e)
f)
g)
gravity
tension
tension and gravity
tension, gravity, and normal
tension, gravity, and centripetal force
tension, gravity, centripetal force, and friction
tension, gravity, centripetal force, and normal
1.2 (5 points): A 4.00-kg block rests between the floor and a 3.00-kg block as shown in the figure. The 3.00-kg
block is tied to a wall by a horizontal rope. If the coefficient of static friction is 0.800 between each pair of
surfaces in contact, what minimum horizontal force must be applied to the 4.00-kg block to make it move?
a)
b)
c)
d)
e)
f)
g)
23.5 N
29.4 N
31.4 N
39.2 N
54.9 N
68.6 N
78.4 N
1.3 (5 points): The potential energy of a particle constrained to move on the x-axis is U(x)=Ax2-Bx, where A=1.0
N/m and B=6.0 N. The particle starts from the point x=2.0m and has a negative total energy E=-5.0J. What are
the positions (in meters) where the particle changes the direction of motion? (Hint: The kinetic energy is zero
at those positions).
a)
b)
c)
d)
e)
f)
g)
0.0 and 3.0
0.0 and 5.0
0.0 and 6.0
1.0 and 3.0
1.0 and 5.0
1.0 and 6.0
3.0 and 5.0
1.4 (5 points): An object at rest on a horizontal surface suddenly explodes in three equal mass fragments.
Immediately after explosion, two of the fragments move in the horizontal plane with equal speeds v at a right
angle to each other. What is the speed of the third fragment immediately after explosion?
a)
b)
c)
d)
e)
f)
v/2
v/√2
v
√2 ∙ v
2∙v
None of the above
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Problem 2 (20 points)
Two blocks, connected together by a thin but strong cord, are placed on a ramp as shown in the figure. The
angle of the ramp is θ=30o, the masses of the blocks are mA = 1.00kg and mB = 2.00kg, and the coefficient of
static and kinetic friction between boxes and ramp are µs = 0.500 and µk = 0.200. The gravitational acceleration
is 9.8m/s2. The mass of the cord is negligible. The cord does not stretch and does not break.
a) Force F is applied to the upper block as shown in the figure. Draw free body diagrams for the two
blocks.
b) Calculate the value of the constant force F necessary for the two blocks to start sliding up the ramp at
constant speed.
c) Once the boxes are in motion up the ramp with constant speed, what is the tension in the cord?
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Problem 3 (20 points)
The figure below shows a box of mass m=2.0 kg on a ramp of angle θ=30o tied to a light rope passing over a
light pulley and attached to an ideal spring with constant k=70 N/m. The rope does not stretch or break. The
box is released from rest when the spring is unstretched. Once released, the box travels downward a
distance x=20 cm, where it stops and stays at rest. The coefficient of static friction between the ramp and the
block is µs and the coefficient of kinetic friction is µk . These coefficients are not given.
a) Use the work-energy theorem and the information provided to calculate the coefficient of kinetic friction µk.
b) What is the magnitude and direction of the force of friction at the farthest point x=20 cm?
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Problem 4 (20 points)
A roller coaster car has the mass m when is fully loaded with passengers. The car moves along the frictionless
path shown in the figure. The radii of the circular segments are R1 and R2. The coaster starts from rest at the
initial height h. In terms of m, g, h, and R1, calculate:
a) The magnitude and direction of the force exerted by the track on the coaster at the point A? Justify
your answer with a free body diagram.
b) What should be the minimum value of the radius R2 such that the coaster would reach point B without
flying from the track? Justify your answer with a free body diagram.
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Problem 5 (20 points)
Two spheres with masses m1 and m2 hang at rest at the ends of equal length strings. These two strings are
attached to the same point in the ceiling. The sphere of mass m1 is released from a height h1, as shown in the
figure, and it collides with the sphere of mass m2. The two spheres stick together after collision and rise to the
height h2, moving strictly in the plane of the figure. Neglecting air resistance, express your answers in terms of
m1, m2, h1, and g as needed.
a) The magnitude and direction of the velocity of the two spheres (stuck together) immediately after
collision.
b) The height h2 reached by the two spheres moving together after their collision.
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