FINAL EXAM, PHYSICS 1408, August 7, 2008, Dr. Charles W. Myles
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INSTRUCTIONS: Please read ALL of these before doing anything else!!!
PLEASE put your name on every sheet of paper you use & write on one side of the paper only!!
PLEASE DO NOT write on the exam sheets, there isn’t room! Yes, this wastes paper, but it makes my
grading easier!
PLEASE show all work, writing the essential steps in the solutions. Write formulas first, then put in
numbers. Partial credit will be LIBERAL, provided that essential work is shown. Organized, logical, easy to
follow work will receive more credit than disorganized work.
The setup (PHYSICS) of a problem will count more heavily than the math of working it out.
PLEASE write neatly. Before handing in your solutions, PLEASE: a) number the pages & put them in
numerical order, b) put the problem solutions in numerical order, & c) clearly mark your final answers. If I
can’t read or find your answer, you can't expect me to give it the credit it deserves.
NOTE: I HAVE 35 EXAMS TO GRADE!!! PLEASE HELP ME GRADE
THEM EFFICIENTLY BY FOLLOWING THE ABOVE SIMPLE
INSTRUCTIONS!!! FAILURE TO FOLLOW THEM MAY RESULT IN
A LOWER GRADE!! THANK YOU!!
An 8.5’’ x 11’’ piece of paper with anything written on it & a calculator are allowed. Problem 1 (Conceptual)
AND Problem 2 (Momentum/Collisions) ARE REQUIRED! Work EITHER Problem 3 OR Problem 4
(Rotations). Choose TWO (2) of the other problems for five (5) problems total. Each problem is equally
weighted & worth 20 points, for a total of 100 points on this exam.
NOTE: Some answers to the following problems are very large or very small numbers! PLEASE express
such answers in scientific (powers of 10) notation! Thanks!
1. MANDATORY Conceptual Questions!!! Answer briefly. Most answers should be complete,
grammatically correct English sentences. Keep formulas to a minimum. Use WORDS instead! If you use a
formula, YOU MUST DEFINE EVERY SYMBOL you use. (Note: Answers giving ONLY symbols, with no
explanation about what they mean, will receive NO credit!)
a. EITHER state Newton’s 1st Law of Motion (for translations) & tell me how many objects at a time it
applies to OR state Newton’s 3rd Law of Motion (for translations) & tell me how many objects at a time
b.
c.
d.
e.
2.
it applies to.
State Newton’s Universal Law of Gravitation.
State the Principle of Conservation of Mechanical Energy. Which kinds of forces are required to be
present in order for this principle to hold?
State the Principle of Conservation of Momentum. Under what conditions is momentum conserved?
State Newton’s 2nd Law for Rotations. (∑F = ma will get ZERO credit!).
MANDATORY Collision Problem!!! See figure. A bullet, mass m = 0.05 kg, traveling at
V = 7.3 m/s
velocity v strikes & becomes embedded in a block of wood, mass M = 3.5 kg, initially at
rest on a horizontal surface. The block-bullet combination then to moves to
v=?
the right. Just after the collision, their velocity is V = 7.3 m/s.
M
a. Calculate the momentum & kinetic energy of the bullet-block combination
just after the collision.
b. Calculate the momentum of the bullet just before the collision. Calculate its velocity v just before the
collision. What Physical Principle did you use to answer this?
c. Calculate the kinetic energy of the bullet just before the collision. Was kinetic energy conserved in the
collision? Explain (using brief, complete, grammatically correct English sentences! Hint: Please THINK
before answering this! Compare the kinetic energy found here with that found in part a! It’s Physically Impossible
to GAIN kinetic energy in a collision!)
d.
Calculate the impulse Δp delivered to the block by the bullet. Stated another way, calculate the
momentum change of the block in the collision. If the collision time was Δt = 2.5  10-3 s, calculate the
average force exerted by the bullet on the block. What Physical Principle did you use to answer this
question?
NOTE: EITHER PROBLEM 3 OR PROBLEM 4 IS REQUIRED!!!!!
3.
The figure is the free body diagram for a falling yo-yo of mass M = 0.3 kg & radius R =
0.2 m. It’s moment of inertia is I = (0.4)MR2. (Note: This means that it is NOT a uniform
disk, so the moment of inertia for a disk, Idisk = (½)MR2 should NOT be used!!) The yo-yo
string is wrapped around the yo-yo. The upward tension in the string is FT. The downward
acceleration of the yo-yo is a. The two unknowns are the acceleration a & the tension FT.
In order to solve this problem, two simultaneous linear equations in two unknowns must be
used & algebra must be done to solve for a & FT. (Note: In part a, when I ask you to write
M = 0.3 kg
R = 0.2 m
_ ___
a 

Newton’s 2nd Law, I don’t mean to just write it abstractly as ∑F = ma. I mean to write the equations
which result when Newton’s 2nd Law is APPLIED to this problem! In part b, when I ask you to
write Newton’s 2nd Law for rotations, I don’t mean to just write it abstractly as ∑τ = Iα. I mean to write the equations
which result when Newton’s 2nd Law is APPLIED to this problem!)
a.
b.
c.
d.
4.
By applying Newton’s 2nd Law for translational motion to the yo-yo as it falls, derive one of the
equations needed to solve for a & FT. (It might be convenient to take down as positive). More credit will be
given if you leave this equation in terms of symbols with no numbers substituted than if you substitute
numbers into it.
By applying Newton’s 2nd Law for rotational motion to the yo-yo as it rotates about it’s axis, derive a
second equation needed to solve for a & FT. More credit will be given if you leave this equation in
terms of symbols with no numbers substituted than if you substitute numbers into it.
Using the equations derived in parts a & b, do the algebra required to solve for a & FT & calculate
numerical values for them.
Using the results of part c, calculate the angular acceleration α experienced by the yo-yo in it’s rotation
about it’s axis & the torque produced by the tension force FT about the yo-yo axis.
See figure. A hollow SPHERE is on a track. It has radius R = 0.3 m & mass M = 15 kg. The moment of
inertia of a hollow sphere is I = (⅔)MR2. It starts from rest at point A. It rolls without slipping to the right &
down the track, past point B & moves to point C. It continues to the right past C, but that isn’t part of this
problem! The height difference between A & B, y1 in the figure, is unknown. The height difference
between B & C is y2 = 15 m. When it reaches B, it’s angular velocity (about an axis through it’s center of mass)
is ω = 34 rad/s.
A
a. Calculate the sphere’s rotational kinetic energy when it reaches B.

b. Calculate linear velocity V of the sphere’s center of mass & it’s
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translational kinetic energy when it reaches B. Use these results &
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y1
those of part a to calculate the sphere’s total kinetic energy when it
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reaches B.
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c. Calculate the sphere’s initial gravitational potential energy when it was

at A & it’s initial height y1 at A. What physical principle did you use
B
to do this calculation?
d. Calculate the sphere’s potential energy & it’s total kinetic energy when it has reached C.
C
NOTE: WORK TWO (2) OF PROBLEMS 5., 6., or 7!!!!!
5.
See figure. Use energy methods to solve this!!! NO credit
C
will be given for force methods! You don’t need force
components or the incline angle θ to solve this! A block, mass
x = 0.35 m
m = 4 kg, is on a horizontal, frictionless surface. It is pressed
against an ideal spring, of constant k = 1000 N/m, & is
initially at rest, as at point A. At point A, the spring is
compressed a distance x = 0.35 m from its equilibrium
A
B
position. The block is released & it moves to point B, at the bottom of
a frictionless incline. It then moves up the incline & stops at point C, at height h above the original position.
a. Calculate the elastic (spring) potential energy of the block at point A. How much work is done by the
spring on the block as it shoves the block from point A to point B?
b. Calculate the kinetic energy the block at point B & it’s speed there. What Physical Principle did you use?
c. Calculate the gravitational potential energy of the block at point C & the height h at which it stops.
What Physical Principle did you use? How much work is done by gravity on the block the block moves from
point B to point C?
d. Calculate the kinetic energy & velocity of the block when it is at height y = 0.7 m above the horizontal
surface (not shown in the figure: above point B & below point C).
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y2
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NOTE: WORK TWO (2) OF PROBLEMS 5., 6., or 7!!!!!
FP
6.
See figure. A box, mass m = 23 kg, is placed on a flat, horizontal surface. The coefficient
of kinetic friction between the box & the surface is μk = 0.18. The box is pulled a by a force
FP = 62 N using a cord making angle θ = 33º with the horizontal. There is no vertical motion.
a. Sketch the free body diagram for the box, properly labeling all forces. Calculate the
horizontal & vertical components of the force FP.
b. Calculate the weight of the box & the normal force FN between it & the surface. Is FN equal (&
oppositely directed) to the weight? Why or why not? Justify your answer using Newton’s 2nd Law in
the vertical direction. Calculate the friction force Ffr on the box as it moves to the right.
c. Use Newton’s 2nd Law to find the acceleration of the box. What forces cause this acceleration?
d. Calculate the work done by the constant FP & the work done by the friction force Ffr as the box moves
to the right through a horizontal displacement x = 10 m.
7.
See figure. Two masses (mI = 14 kg & mII = 26 kg) are connected by a massless cord
over a massless, frictionless pulley as in the figure. mI sits on a frictionless table. The
masses are released, & mI moves to the right with acceleration a & mII moves down
with the same acceleration.
a. Sketch the free body diagrams for the two masses, properly labeling all forces (call
a 
mI
the tension in the cord FT).
mII a 
The two unknowns are the acceleration a & the tension FT. In order to solve this, two
simultaneous linear equations in two unknowns must be used & algebra must be done to solve for a & FT.
(Note: In part b, when I ask you to write Newton’s 2nd Law, I don’t mean to just write it abstractly as ∑F = ma. I mean
to write the equations which result when Newton’s 2nd Law is APPLIED to this problem!)
b.
c.
d.
8.
By applying Newton’s 2nd Law to the two masses, find the two equations needed to solve for a & FT.
More credit will be given if you leave these equations in terms of symbols with no numbers substituted
than if you substitute numbers into them.
Using the equations from part b, calculate a & FT (in any order).
Calculate the work done by the force FT & the work done by gravity as mII falls a distance y = 3 m.
BONUS QUESTIONS! (10 bonus points total!) Answer briefly, in a few complete, grammatically correct
English sentences. You may supplement these sentences with equations, but keep these to a minimum and
EXPLAIN what the symbols mean! I want most of the answer to be in WORDS! (Note: Answers with
ONLY symbols, with no explanation about what they mean, will receive NO credit!)
a. (2 points) See figure. The round objects roll without slipping down an inclined
plane. The box slides without friction down the slope. The round objects all
have radius R & mass M (also box mass). Moments of inertia: Hoop: I = MR2,
Cylinder: I = (½)MR2, Sphere: I = (2/5)MR2. The objects are released, one at a
time, from the same height H. Which object arrives at the bottom with the
greatest (translational) speed V? Why? Which object arrives with the smallest V? Why? What Physical
Principle did you use to arrive at these conclusions? (Note: I want most of the answer in WORDS!)
b. (2 points) Yesterday (Wed., Aug. 6), I did a demonstration which tried to illustrate some of the physics
of the situation in part a. Briefly describe that demonstration. (Note: Here, I don’t mean the “Rotating
Professor” demonstration!)
c. (2 points) See figure. A box of mass m is sliding at constant velocity v across a flat,
horizontal, frictionless surface. Sketch the free body diagram for the box. Is there a
v
force in the direction of the motion (parallel to the velocity)? WHY or WHY NOT?
Explain (in English!) your answer using Newton’s Laws!
d. (2 points) See figure. A child sits in a wagon, which is moving to the right (xdirection) at constant velocity v0x. She throws an apple straight up (from her
viewpoint) with an initial velocity v0y while she continues to travel forward at v0x.
Neglect air resistance. Will the apple land behind the wagon, in front of the
wagon, or in the wagon? WHY? Explain (briefly!) your answer. (Use what you
know about projectiles!). Make a sketch of the situation to illustrate your explanation.
e. (2 points) Yesterday (Wed., Aug. 6), I did the “Rotating Professor” demonstration. Briefly describe that
demonstration & tell me what Physical Principle I was trying to illustrate by doing it.