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FINAL EXAM, PHYSICS 1403
August 9, 2007, Dr. Charles W. Myles
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 will not be room! Yes, this wastes paper, but it
makes my grading easier!
PLEASE show all work, writing the essential steps in the solutions. Write appropriate 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.
For answers which are very small or very large numbers PLEASE use scientific (power of 10) notation!
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 and put the
pages in numerical order, b) put the problem solutions in numerical order, 7 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 65 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!! THANKS!!
Problem 1 (Conceptual Questions) AND Problem 2 (fluid statics) ARE REQUIRED!! Work any three (3) 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.
1. MANDATORY QUESTIONS!!! Answer briefly, in complete, grammatically correct English
sentences. Supplement answers with equations, but keep these to a minimum & EXPLAIN WHAT
THE SYMBOLS MEAN!! Answers which have only equations & no explanation will receive very
little (if any) credit!
a. State Newton’s 1st Law of Motion (for translational motion).
b. State Newton’s 3rd Law of Motion (for translational motion).
c. State the Principle of Conservation of Mechanical Energy.
d. State the Law of Conservation of Linear Momentum.
e. State Newton’s 2nd Law for Rotational Motion. (∑F = ma will get ZERO credit!).
f. 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 the box mass). Moments of inertia:
Hoop: I = MR2, Cylinder: I = (½)MR2, Sphere: I =
(2MR2)/5. 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?
g.
(Note: I want most of the answer in WORDS!)
5 Point Bonus!! During our rotational motion discussion, I did a demonstration to try to illustrate the
answer to part f. Briefly describe this demonstration. (If you were in class the day I did this demonstration,
likely will be able to answer this. If you “cut” class that day, you probably won’t be able to answer it!)
NOTE: I did other rotational motion demonstrations that day. The one I’m referring to was specifically about
objects rolling down an incline. This was NOT the “rotating professor” demonstration!
2. (Fluid Statics) MANDATORY PROBLEM!!!
a. State Archimedes’ Principle (for the buoyant force on an object partially or completely submerged in a fluid).
Answer using mostly English words, with equations kept to a minimum!
See figure on NEXT PAGE. A crown is hung by a masseless hook attached to a scale & weighed
twice. At left, it is weighed in air & the scale reads w = mg = 132 N. At right, it is put in oil, weighed
& the scale reads w′ = m′g = 115 N. Oil density: ρo = 900 kg/m3. Neglect atmospheric pressure. Assume
that the crown doesn’t move (that’s what “static” means!).
b. At right, the vertical distance from the oil surface to the point where the crown is attached to the
hook is h = 0.15 m. Calculate the oil pressure at that point.
PROBLEM 2 CONTINUES ON NEXT PAGE!
PROBLEM 2, CONTINUED!
c. A sheet of thin plastic of cross sectional area A = 0.018 m2 is submerged
in the oil at the right to the same depth, h = 0.15 m, as in part b. If its
surface is parallel to the oil surface, calculate the force on this sheet
produced by the oil. (Hint: Use the definition of pressure in terms of force.)
[Hint: To answer parts d, e, & f you MUST use a combination of 1) Archimedes’
Principle, 2) Newton’s 2nd Law in the vertical direction with a = 0, AND the
definition of density in terms of mass & volume!. Answers attempting to use ONLY
the definition of density in terms of mass & volume will get ZERO credit!].
d. Calculate the buoyant force FB that the oil exerts on the crown.
e. Calculate the crown volume V
f. Calculate the crown density ρc.
NOTE: Work any three (3) of Problems 3, 4, 5, & 6!!
3. A hollow sphere of radius R = 0.62 m & mass M = 8.3 kg starts rolling at the bottom of an inclined
plane (left figure). The initial velocity of it’s center of mass is V = 10 m/s. It’s moment of inertia is I =
(⅔)MR2. (That is, it ISN’T a uniform disk & the moment of inertia for a uniform disk, (½)MR2 is ISN’T valid
here!). It rolls without slipping up the plane & stops at a height H above the bottom (right figure).
y = 0, ω = ?
 V = 10 m/s
Before
y=H=?
V = 0, ω = 0
After
a. Calculate the sphere’s initial angular velocity ω (about an axis through the center of mass) at the
bottom of the plane.
b. Calculate the sphere’s initial rotational kinetic energy & angular momentum (about an axis through
the center of mass).
c. Calculate the initial translational kinetic energy of the sphere’s center of mass and it’s initial
total kinetic energy at the bottom of the plane.
d. Calculate the sphere’s final gravitational potential energy at the top of the plane and it’s final
height H above the bottom. What Physical Principle did you use to do this calculation?
e. Consider a point when the sphere is partway between the top & the bottom of the incline. At that
point, it is at a height y = 4.5 m above the bottom. Calculate the sphere’s gravitational potential
energy and total kinetic energy of the sphere at that point. (NOTE: ZERO credit will be given if you set the
KE = the PE at that point!!)
NOTE: Work any three (3) of Problems 3, 4, 5, & 6!!
4. See figure. A block, mass m = 12 kg, is on a horizontal, frictionless surface. It is pressed against an
ideal spring, of constant k = 679 N/m, & is initially at rest, on the left at point A. There, the spring is
compressed an unknown distance xA from its equilibrium position. It is released & moves without
friction to point B, where it has velocity vB = 9.2 m/s. Parts a, b, & c are about m at points A, B & a
point in between. (Hint: In the following, PLEASE be sure to take square roots properly!)
m = 12 kg
xA = ??
vB = 9.2 m/s 
M = 17 kg
v=0
Stick together!
V=?
A
B
C
D
a. Calculate the kinetic energy & the momentum of m at point B.
PROBLEM 4 CONTINUES ON NEXT PAGE!
PROBLEM 4, CONTINUED!
b. Calculate the elastic (spring) potential energy of m at point A & the initial distance xA that the
spring is compressed at point A. What Physical Principle did you use to find these?
c. Consider the mass-spring combination at a point between points A & B, when m is at x = 0.5 m
(less than xA!) from the spring’s equilibrium position. The spring still touches m there! Calculate
the elastic potential energy & the kinetic energy of m at that point. (NOTE: ZERO credit will be given if
you set the KE = the PE there!!)
Parts d & e deal with m as it moves to the right of point B. It moves without friction until it collides
with a second block, mass M = 17 kg, at point C near the middle of the figure. The collision is inelastic,
so that the masses stick together, as at point D at the right of the figure. At D, the velocity V of the
masses is unknown.
d. Calculate the momentum of the two stuck together masses & their velocity V at point D. What
Physical Principle did you use to find these?
e. Calculate the kinetic energy of the two stuck together masses at point D. Is kinetic energy
conserved in the collision? Why or why not?
5.
NOTE: Work any three (3) of Problems 3, 4, 5 & 6!!
See figure. Two masses (m1 = 23 kg, m2 = 34 kg) are connected by a massless cord & placed on a
horizontal, frictionless surface. The mass system is accelerated to the right by a force FP = 48 N using
a cord attached to m1 that makes an angle  = 35º with the horizontal. There is no vertical motion.
a. Let the tension in the cord connecting the two masses be FT, & sketch the free body diagrams for
the two masses, properly labeling all forces.
b. Calculate the horizontal & vertical components of FP.
c. Write the equations resulting from applying Newton’s 2nd
Law to both m1 & m2 in both the horizontal (x) & the
vertical (y) directions. You will receive more credit by writing these in terms of symbols, without
numbers substituted in, than you will by writing them with numbers substituted in!
d. Calculate the normal force between mass m1 & the horizontal surface. Is this normal force equal
(and oppositely directed) to the weight m1g? If so, why? If not why not? Justify your answer using
the appropriate Newton’s 2nd Law equation from part c.
e. Using the appropriate Newton’s 2nd Law equations from part c., calculate the acceleration a of the
system & the tension FT in the cord connecting the two masses. (Hint: If part c has been done
correctly, getting the answers to this part will require you to simultaneously solve two linear algebraic
equations with two unknowns: FT & a.)
NOTE: Work any three (3) of Problems 3, 4, 5 & 6!!
F
The figure is an end view of a flat, cylindrical satellite, radius R = 3.5 m & mass M =
2
2,750 kg, which engineers are testing. It’s moment of inertia is I = (0.57)MR . (Note:
This means it isn’t perfect, so it’s moment of inertia IS NOT (½)MR2!!) There are four
rocket engines, arranged 90° apart, at radius R. When fired simultaneously, they exert
four equal forces F = 1150 N tangent to the circle as shown. They give the
F
satellite an angular acceleration α. Assume that the 4 forces F are only ones

producing torques about the axis of rotation. Calculate:
a. The total (net) torque τnet exerted by the four rocket engines.
b. The angular acceleration α of the satellite.
c. The tangential acceleration atan of a point on the rim.
F
d. What Physical Principle did you use to find the angular acceleration in part b?
The satellite starts from rest & has an angular velocity ω = 12 rad/s after the rockets have been firing for a
time t. Calculate:
e. Calculate the time t & the velocity v of a point on the rim at that time.
6.
5. BONUS!! During the session, I did some demonstrations. If you were present at any one of them, write a few short, complete,
grammatically correct English sentences telling about ONE of them. (You cannot discuss the same demonstration as you did in
Problem 1, part g!) Tell me what demonstration I did AND what physical principle I was trying to illustrate. If you do this, I will
add five (5) points to your Final Exam grade as a small reward for attending class. If you missed class on demonstration days,
you will (probably) not know what demonstrations I did & you will (probably) not be able to answer this. Have a good rest of
the summer and good luck in the future!

F