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Name_____________________________
Phys 121: Final Exam
Summer, 2005
"An expert is a man who has made all the mistakes
which can be made in a very narrow field."
-Niels Bohr
Welcome to the Final Exam!
Please feel free to ask questions.
I will grade these over the weekend and turn in your grades on Monday. If you’d like to
pick up your graded exam (and/or your final homework) please email me next week to
arrange something.
Enjoy the (possibly physics-free?) rest of your summer!
Here’s the rundown for this exam:
Part I: Multiple Choice Problems (1-7): 21 points total
Part II: Short Answer / Short Calculation Problems (8-12): 29 points total
Part III: Calculation Problems (13-18): Choose 5 of the 6 for 50 points total.
For Part III, you can do all the problems for extra credit.
Part I: Multiple Choice Problems: No Partial Credit Available
1. (3 points)
An 80 kg man on roller skates pushes a 40 kg boy on a skateboard with a force of 100 N.
The magnitude of the force exerted by the boy on the man is
a) 200 N
b) 100 N
c) 50 N
d) 40 N
2. (3 points)
An object is moving along with some speed, hence it has some kinetic energy K. Some
time later, the object is moving in the opposite direction with three times its initial speed.
What is the kinetic energy now?
some time
some time later
a) K
b) 3K
v
3v
c) -3K
d) 9K
e) -9K
1
3. (3 points) (partial credit is available for this one since you will choose two)
Two stones of the same mass are thrown with the same initial speed at the same instant
from the roof of a building. Stone number one is thrown at an angle of 30 degrees above
the horizontal, and stone number two is thrown horizontally. Neglecting air resistance,
choose the TWO correct statements.
a) Stone one strikes the ground first.
b) Stone two strikes the ground first.
c) The stones strike the ground at the same time.
d) Stone one lands with a higher speed than stone two.
e) Stone two lands with a higher speed than stone one.
f) The stones land with the same speed.
4. (3 points)
A solid cylinder and a solid sphere have equal masses. Both roll without slipping on a
horizontal surface. If their kinetic energies are the same, then what can be said about
their translational (linear) speeds?
a) The translational speed of the cylinder is greater than that of the sphere.
b) The translational speed of the cylinder is less than that of the sphere.
c) The translational speeds of the two objects are the same.
d) a, b, or c could be correct depending on the radii of the objects.
Note: Isphere = 2/5MR2
Icylinder = MR2
5. (3 points)
A block of mass m is at rest on a plane inclined at an angle of φ with the horizontal.
Which of the following statements about the force of static friction is necessarily true?
a) Ffs = μsmgcos(φ)
b) Ffs = mgsin(φ)
c) Ffs = μsmgsin(φ)
d) Ffs = mgcos(φ)
2
6. (3 points)
A 5 kg ball is suspended from a steel wire of length 5 m and radius 2 mm. By how much
does the wire stretch? (Esteel = 500 x 106 N/m2)
7. (3 points) Two forces F1 and F2 act on a "Rocky and Bullwinkle" lunch box as the
lunch box slides at constant velocity over a frictionless lunchroom floor. If the angle β is
decreased without changing the magnitude of F2 and we want to keep the lunch box
sliding at a constant velocity, should we increase, decrease, or maintain the magnitude of
F1?
F2
F1
β
3
Part II: Short Answer / Calculation : Partial Credit available
8. (6 points)
My sister (who has the same mass as I do) and I are sitting on the floor of a merry-goround. I am sitting close to the outer edge, and she is sitting close to the center. As the
merry-go-round rotates, who experiences the larger frictional force? Why?
9. (6 points)
Mirrors are made by a complicated process of melting and vaporizing aluminum (or other
metals) in a vacuumed chamber. When the aluminum vapor hits a plate of glass, it
condenses back into a solid, forming a thin sheet of reflective material on the glass. If I
wanted to melt (I’ll vaporize it later) 80 grams of aluminum that started at room
temperature (22°C), how much heat would I need to add? (Give your answer in calories.)
relevant information for aluminum:
Specific Heat, c:
0.22 kcal/(kg*C°) = 0.22 cal/(gm*C°)
Latent Heat of Fusion Lf:
94.5 kcal/kg = 94.5 cal/gm
Melting Temperature:
659 °C
4
10. (6 points)
a) What is the magnitude of the acceleration of an oscillator of amplitude A and angular
frequency ω when the speed is maximum?
b) How about when the displacement is maximum?
5
11. (5 points)
Dean reads in his physics book that when two people pull on the end of a rope in a tugof-war, the forces exterted by each on the other are equal and opposite, according to
Newton’s Third Law. Misunderstanding the law tragically, Dean runs out to challenge
Hugo the Large, convinced that the laws of physics guarantee a tie. Hugo lumbers over,
picks up the rope, pulls Dean off his feet, and then drags him through a puddle, across the
road, and up the steps of the physics building. Use 2 Free-Body Diagrams (one on Dean,
one on Hugo) (and another for the whole system consisting of Dean and Hugo, if you
want) and some explaining to show Dean that, in spite of Newton’s 3rd law, it is possible
for one side to win a tug-of-war.
6
Part III: Calculation Problems, Partial Credit Available (choose 5 of the next 6)
12. (10 points)
A string of length L=120 cm has a ball of mass m=1kg attached to one end, and is fixed
at its other end. The distance d to the fixed peg at point P is 75 cm. When the initially
stationary ball is released with the string horizontal as shown, it will swing along the
dashed arc.
a) What is the tension in the string immediately before it hits the peg?
b) What is the tension in the string immediately after it hits the peg?
L
d
P
7
13. (10 points)
Romeo takes a uniform 10 m ladder and leans it against the smooth (frictionless) wall of
the Capulet residence. The ladder’s mass is 19.0 kg, and the bottom rests on the ground
2.8 m from the wall. When Romeo (mass is 75 kg) gets 7 m up the ladder, it begins to
slip. What is the coefficient of static friction between the ground and the ladder?
7m
2.6 m
8
14. (10 points)
A block of mass m slides along a surface. It encounters an upward slope of height h and
then a patch of friction (coefficient of kinetic friction μk) of distance d. It then runs into a
spring of spring constant k, compressing it a distance x before stopping. What was the
initial velocity of the block?
k
m
h
μk
d
x
9
15. (10 points)
A policeman chases a master jewel thief across city rooftops. They are both running at 5
m/s when they come to a gap between buildings that is 4 m wide and has a drop of 3m.
The thief, having studied a little physics, leaves at 5 m/s at 45° from the horizontal and
clears the gap easily. The policeman did not study physics and thinks he should
maximize his horizontal velocity, so he leaves at 5 m/s horizontally.
a) Does the policeman clear the gap?
b) By how much does the thief clear the gap?
3m
4m
3m
4m
10
16. (10 points)
Two blocks with masses m1=22kg and m2=57 kg, shown in the figure, are free to move.
The coefficient of static friction between the blocks is μs =0.16, and the surface beneath
m2 is frictionless. What is the minimum force F required to hold m1 against m2?
μs
F
frictionless
m1
m2
11