Final Exam, PHYSICS 1403, August 9, 2012, Dr. Charles W. Myles
INSTRUCTIONS: Please read ALL of these before doing anything else!!!
1. PLEASE put your name on every sheet of paper you use and write on one side of the
paper only!! PLEASE DO NOT write on the exam sheets, there will not be room! This
wastes paper, but it makes my grading easier!
2. 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.
3. The setup (PHYSICS) of a problem will count more heavily than the math of working it out.
4. PLEASE write neatly. Before handing in your solutions, PLEASE: a) number the pages
& put the pages 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.
5. NOTE!! The words “EXPLAIN”, “DISCUSS” & “DEFINE” below mean to answer
mostly in ENGLISH, NOT math symbols!
I HAVE 32 EXAMS TO GRADE!! PLEASE HELP ME GRADE
THEM EFFICIENTLY BY FOLLOWING THESE SIMPLE
INSTRUCTIONS!!! FAILURE TO FOLLOW THEM MAY
RESULT IN A LOWER GRADE!!
Up to two (2) 8.5’’ x 11’’ pieces of paper with anything written on them & a calculator are
allowed. BOTH Problem 1 (Conceptual) and Problem 2 (Rotations) are REQUIRED! ALSO
You MUST work EITHER Problem 3 (Momentum) OR Problem 4 (Momentum). Choose
TWO (2) of the others for five (5) problems total. Each is equally weighted & worth 20 points,
for a total of 100 points on this exam. NOTE: Some answers to the problems are very large or
very small numbers! PLEASE express such answers in scientific (power of 10) notation! Thanks! Note
that there are BONUS questions on the last page!
1. MANDATORY CONCEPTUAL QUESTIONS!!! Answer briefly all parts in a few
complete, grammatically correct English sentences. Give answers using mainly ENGLISH
WORDS, NOT symbols or equations! If you insist on using symbols, DEFINE all symbols!
NO credit will be given for answers with ONLY symbols! If a part contains more than one
question, please answer each one!
a. (2 points) State Newton’s 1st Law of Motion. How many masses at a time does it apply to?
b. (2 points) State Newton’s 2nd Law of Motion. How many masses at a time does it apply to?
c. (2 points) State Newton’s 3rd Law of Motion. How many masses at a time does it apply to?
d. (2 points) State Newton’s Universal Law of Gravitation.
e. (2 points) State the Work-Energy Principle. (Note: This is NOT the same as the
definition of the work done by a constant force!)
f. (2 points) State the Principle of Conservation of Mechanical Energy. Which kinds of
g.
h.
i.
forces are required to be present in order for this principle to hold? Note: Answers which quote
the “Law of Conservation of Total Energy” are NOT correct and will get ZERO CREDIT!)
(3 points) State Newton’s 2nd Law in terms of Momentum. (Hint: This was Newton’s
original form for his 2nd Law. It is also the most general form for his 2nd Law! It is NOT the
definition of momentum, p = mv. Stating either p = mv or ∑F = ma will get ZERO CREDIT!).
(2 points) State the Principle of Conservation of Momentum. Under what conditions is
momentum conserved?
(3 points) State Newton’s 2nd Law for Rotational Motion. (∑F = ma will get ZERO credit!).
NOTE: Don’t forget to look at the BONUS questions (# 8 on the last page)!
2.
MANDATORY ROTATIONS PROBLEM!!! The figure shows a rigid,
SPHERICAL SHELL of radius R = 2.1 m. (A spherical shell is a sphere
with mass on its surface only, but empty inside.) The sphere’s mass is M
R
= 5.1 kg. It’s moment of inertia is I = (⅔)MR2. (Note: So, it is ISN’T a
2
uniform disk, & the disk moment of inertia, Idisk = (½)MR obviously
P
should NOT be used!!) At time t = 0, it starts from rest (initial angular
velocity ω0 = 0) & begins to rotate counterclockwise about an axis passing through center of
the sphere & perpendicular to the page. The figure looks down at the rotation plane, with
rotation in the counter-clockwise direction, as shown. It has a constant angular acceleration α
= 0.5 rad/s2. Parts a & b are about the sphere at time t = 18.0 s after it starts rotating.
Calculate the following:
a. The sphere’s angular velocity ω and its angular displacement θ at that time.
b. The sphere’s rotational kinetic energy and angular momentum at that time.
Parts c & d are about a point P on the sphere’s equator, a distance R = 2.1 m from the
rotation axis, (as shown) also at time t = 18 s after it starts rotating. Calculate the following:
c. The velocity v (m/s) of P at that time. The vector direction of v is tangent to the sphere.
The centripetal acceleration aR (m/s2) of P at that time. What is the vector direction of aR?
d. The tangential acceleration atan (m/s2) of P at that time. atan is a vector tangent to the equator.
The sphere’s angular acceleration α = 0.5 rad/s2 must be caused by a net torque τ applied to it.
e. Use Newton’s 2nd Law for Rotational Motion along with the angular acceleration α =
0.5 rad/s2 and the moment of inertia I = (⅔)MR2 to calculate the net torque τ causing the
sphere to rotate.
f. Assume that the force F which causes the torque calculated in part eis a vector applied
tangent to the sphere’s surface, at its equator at R = 2.1 m, as in the figure. Calculate the
force F responsible for giving the sphere the torque τ.
ω
F
NOTE: EITHER PROBLEM 3 (Momentum) OR PROBLEM 4 (Momentum) IS REQUIRED!!
Don’t forget to look at the BONUS questions (# 8 on the last page)!
3.
See figure. A bullet, mass m = 0.07 kg, traveling at an unknown velocity v strikes &
becomes embedded in a block of wood, mass M = 5.1 kg, initially at rest on a horizontal
surface. The block-bullet combination then moves to the
V = 7.7 m/s
m = 0.07 kg
right. After the collision, their velocity is V = 7.7 m/s.
↓
Calculate the following:
a. The momentum and the kinetic energy of the bullet-block
v=?
combination just after the collision.
↑
b. The momentum of the bullet and it’s velocity v just before the
M = 5.1 kg
collision. What Physical Principle did you use to answer this?
c. The bullet kinetic energy just before the collision. Was kinetic energy conserved in the
collision? Explain (with brief, complete, grammatically correct English sentences!)
Hint: Please THINK before answering! Compare the kinetic energy found here with that
in part a! It is Physically Impossible to GAIN kinetic energy in a collision!
d. The impulse Δp delivered to the block by the bullet. Stated another way, calculate the
momentum change of the block in the collision.
e. The average force exerted by the bullet on the block if the collision time was
Δt = 1.8  10-3 s. What Physical Principle did you use to answer this question?
NOTE: EITHER PROBLEM 3 (Momentum) OR PROBLEM 4 (Momentum) IS REQUIRED!!
Don’t forget to look at the BONUS questions (# 8 on the last page)!
4. See figure. Two bumper cars in an amusement park have an elastic
collision as one approaches the other from the rear. Their masses
are m1 = 410 kg and m2 = 530 kg. The initial velocities are both in
the same direction (Fig. a) & are (for m1) v1 = 5.2 m/s & (for m2)
v2 = 4.5 m/s. After the collision, the velocities v1´ & v2´ are still in
the same direction (Fig. b). Calculate the following:
a. The total momentum p1 + p2 and the total kinetic energy KE1 + KE2 of the two cars
before the collision.
b. The total momentum p1´+ p2´ and the total kinetic energy KE1´ + KE2´of the two cars
after the collision. (Hint: You can do this using only the results of part a, along with
physical principles! You DON’T need to know the answers to part c before answering
this!) What physical principles did you use to answer this? Is kinetic energy conserved
in this collision?
c. The velocities v1´ & v2´ of the cars after the collision. (Note: To solve this you MUST
solve two algebraic equations in two unknowns! Attempts to find the answers without
doing this algebra will not be successful and will be given ZERO credit!)
d. The impulse that was delivered to m1 by m2. Stated another way, calculate the
momentum change Δp1 of m1 due its collision with m2.
e. The average force exerted by m2 on m1 if the collision time was Δt = 3.9  10-3 s. What
Physical Principle did you use to answer this question?
h
NOTE: WORK ANY TWO (2) OF PROBLEMS 5, 6, or 7!!!!!
Don’t forget to look at the BONUS questions (# 8 on the last page)!
5.
See figure. Use energy methods to solve this!!! NO credit will be given for force methods!
You don’t need to know force components or the incline angle θ to solve this! A mass m = 5
kg, is initially at rest (at point C on the right of the figure) at the top of a frictionless inclined
plane a height h above a horizontal, frictionless floor. It is released and moves down the
v = 0, h = ??
incline to the floor below (at point B near the middle of the figure), where it’s velocity is

v = 8 m/s. It continues to move to the left until it
 v = 9 m/s
k = 890 N/m
encounters an ideal spring, of constant k = 890 N/m,


attached to a vertical wall. After it makes contact with
the spring, it continues to the left, compressing the
spring and slowing down. It eventually comes

v = 0, x = ??
instantaneously to rest (at point A on the left of the figure)
after it compresses the spring a distance x.
Calculate:
a. The block’s kinetic energy at point B.
b. The block’s gravitational potential energy at the height h (point C) at which it started &
the height h. What Physical Principle did you use to do this calculation?
c. The block’s velocity when it is at height y = 2.1 m above the horizontal surface (not
shown in the figure; above point B & below point C.) Note: Answers obtained by setting
the KE equal to the PE at this point will get ZERO credit!
d. The spring (elastic) potential energy of the mass-spring system when the block comes
instantaneously to rest at point A.
e. The distance x that the block has compressed the spring at point A. (Hint: The
gravitational acceleration g is totally irrelevant to this question and to the question in part
d because the gravitational potential energy doesn’t change as the block compresses the spring!)
m = 5 kg
NOTE: WORK ANY TWO (2) OF PROBLEMS 5, 6, or 7!!!!!
Don’t forget to look at the BONUS questions (# 8 on the last page)!
6.
The figure is the free body diagram for a crate, mass
m = 25 kg, which is pulled a distance x = 40 m across
a flat, horizontal floor. It is being pulled by a constant
force FP = 100 N, making an angle θ = 37° with the
horizontal as shown. There is NO vertical motion.
There is a friction force Ffr = 45 N between the crate
& the floor. Use the x-y coordinate system shown.
Calculate the following:
a. The horizontal and vertical components, FPx and FPy of the pulling force FP.
b. The normal force FN between the box and the floor. (Note: Answers stating that FN = mg
for the crate will get ZERO credit! Why is this not true for this problem?)
c. The coefficient of static friction, μk between the crate and the floor.
d. The acceleration a of the crate across the floor.
e. The work done by the pulling force FP and by the friction force Ffr in this process.
f. The work done by the normal force FN and by the weight mg in this process.
g. The net work done by all forces in the process. If the crate starts from rest, USE
ENERGY METHODS to calculate it’s kinetic energy & speed after it has gone x = 40 m.
NOTE: WORK ANY TWO (2) OF PROBLEMS 5, 6 or 7!!!!!
Don’t forget to look at the BONUS questions (# 8 on the next page!!)
7.
a 
FT
See figure. Two masses (m1 = 15 kg & m2 = 27 kg) are connected by a

m1
massless cord over a massless, frictionless pulley as in the figure. m1 sits
on a frictionless table. The masses are released, & m1 moves to the right
 FT
with acceleration a & m2 moves down with the same acceleration. The
tension in the cord is FT.
m2 a 
a. Sketch the free body diagrams for the 2 masses, properly labeling all forces.
b. The two unknowns are the acceleration a & the tension FT. By
applying Newton’s 2nd Law to the two masses, find the two equations needed to solve
for a & FT. (Note: Here, 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!)
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.
c. Using the equations from part b, calculate a & FT (in any order). (Note: To solve this you
MUST solve two algebraic equations in two unknowns! Attempts to find the answers
without doing this algebra will not be successful and will be given ZERO credit!)
d. Calculate the work done by FT, the work done by gravity, and the total work done on m2
as it falls a distance y = 3m.
e. If m2 starts falling from rest, use the Work-Energy Principle and the results of part d to
calculate its kinetic energy of after it falls the distance y = 3 m.
NOTE! There are BONUS QUESTIONS on the next page!!!
8.
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. 8), 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
v
across a flat, horizontal, frictionless surface. Sketch the free body diagram
for the box. Is there a 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 (x-direction) 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. 8), I did the “Rotating Professor” demonstration.
Briefly describe that demonstration & tell me what Physical Principle I was trying to
illustrate by doing it.