FINAL EXAM, PHYSICS 1403
August 5, 2005
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 and 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, and 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 50+ 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!!
Problem 1 (Conceptual Questions) IS REQUIRED! Work any one (1) of Problems 2 (vibrations), 3, or 4
(fluids). 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. THIS QUESTION (conceptual) IS MANDATORY!!! Answer briefly, in complete,
grammatically correct English sentences. Supplement answers with equations, but keep these
to a minimum and EXPLAIN WHAT THE SYMBOLS MEAN!!
a. State Newton’s 1st Law of Motion (for Translation).
b. State Newton’s 3rd Law of Motion (for Translation).
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? (Note: You may write an equation, but explain the meaning of the symbols.
I want most of the answer in WORDS!)
g. 5 Point Bonus!! During our discussion on rotational motion, I did a demonstration to try
to illustrate the answer to part h. 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, as several of you have habitually done this session, you probably won’t be able to
answer it!)
NOTE!!! Work any one (1) of Problems 2 (vibrations), 3 (fluids), or 4 (fluids).
2. (Vibrations) See figure. A mass m = 10 kg is attached to a spring of constant k = 120 N/m. The mass
is pulled a distance 1.6 m from its equilibrium position & released from rest. It undergoes simple
harmonic motion. Neglect friction. (Note: Answers to this problem which attempt to use the constant
acceleration kinematic equations from Ch. 2 will get ZERO credit!) Compute:
a. The amplitude, the period and the frequency of the motion.
b. The total mechanical energy and the maximum speed.
c. The maximum force on the mass and the maximum
acceleration it experiences.
d. The force on the mass, the potential energy, & the kinetic
energy when x = 1.0 m.
e. Use the results of part d to compute the speed of the mass
when x = 1.0 m.
f. Write an expression for x as a function of time (x(t)).
3. (Static fluid) See figures. A crown is hung by a masseless hook attached to a scale &
weighed twice. At the left, it is weighed in air & the scale reads w = mg = 125 N. At
the right, it is submerged in alcohol & weighed & the scale reads w′ = m′g = 105 N.
Alcohol density: ρa = 800 kg/m3. Neglect atmospheric pressure & assume that the
crown doesn’t move (that’s what “static” means!).
a. At the right, the vertical distance from the top alcohol surface to the point
where the crown is attached to the hook is h = 0.25 m. Compute the pressure in
the alcohol at that point.
b. Suppose a sheet of thin plastic of cross sectional area A = 0.02 m2 is
submerged in the alcohol at the right to the same depth, h = 0.25 m, as in part a.
If its surface is parallel to the top alcohol surface, compute the force on this sheet
produced by the fluid pressure. (Hint: Use the definition of pressure in terms of force.)
c. State Archimedes’ Principle (for the buoyant force on an object partially or completely
submerged in a fluid).
[Hint: To answer parts c, d, & e, you MUST use some 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. Compute the buoyant force FB, that the alcohol exerts on the crown.
e. Compute the crown volume V.
f. Compute the crown density ρc.
g. In the weighing experiments discussed above, the scale reading is equal & opposite to
the tension FT in the wire in both cases. What Physical Principle causes the preceding
sentence to be a true statement?
4. (Flowing fluid)
a. State Bernoulli’s Principle (for a flowing fluid).
For parts b to f, see figure. A horizontal hypodermic syringe contains a
v1 
fluid medicine with density ρ = 3.0  103 kg/m3. A horizontal force F is
exerted to the right on the plunger (left of the figure), causing a pressure
P1 = 5.0  103 N/m2 in the syringe. This moves the fluid to the right with velocity v1 = 0.75 m/s, making it
squirt from the needle (right of the figure) with velocity v2. The plunger & syringe barrel have cross
sectional area A1 = 4.0  10-4 m2. The needle has cross section A2 = 1.6  10-4 m2. Neglect atmospheric
pressure effects & friction between the plunger & the syringe. (Hint: “Horizontal” here means that in this
problem height differences in the syringe can be neglected!). Compute:
b. The force F applied to the right on the plunger. (Hint: Use the definition of pressure
in terms of force.)
c. The volume flow rate in the syringe.
PROBLEM 4 IS CONTINUED ON THE NEXT PAGE!!
PROBLEM 4, CONTINUED!!
d. The velocity v2 of the medicine at the end of the needle.
e. The fluid pressure P2 in the needle just before the fluid squirts out.
f. What Physical Principle did you use to compute the pressure in part e?
NOTE: Work any three (3) of Problems 5, 6, 7, & 8!!
5. The figure is an end view of a flat, uniform cylindrical satellite, of radius R = 3.0 m
F
and mass M = 2,500 kg, which engineers are testing in a lab. It’s moment of inertia is
I = (½)MR2. There are four rocket engines, arranged 90° apart, which are at radius R
& which, when fired simultaneously, exert four equal forces F = 1000 N tangent to
the circle as shown. They give the satellite an angular acceleration α. Assume that
F
the four forces F are only forces producing torques about the axis of rotation.

Compute:
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 = 10 rad/s after the rockets have been firing for a
time t. Compute:
e. Compute the time t.
f. Compute the velocity v & the centripetal (radial) acceleration aR of a point on the rim at
the time t found in part e.
6. A hollow sphere of radius R = 0.4 m & mass M = 7.0 kg starts from rest at the top of an inclined
plane. Initially, it is at height H above the bottom of the plane. The sphere’s moment of inertia is I =
(⅔)MR2. When it reaches the bottom, the translational velocity of its center of mass is V = 8 m/s.
y=H=?
V=0
ω=0
y=0
V = 8 m/s
ω=?
Before
After
Compute:
a. The angular velocity ω (about an axis through its center of mass) when it reaches the bottom.
b. The sphere’s rotational kinetic energy & the angular momentum (both about an axis through
its center of mass) when it reaches the bottom.
c. The translational kinetic energy of the sphere’s center of mass and the total kinetic
energy of sphere the when it reaches the bottom.
d. The gravitational potential energy of the sphere at its initial position and its initial height H at
the top of the incline. What Physical Principle did you use to do this last calculation?
Consider the a point when the sphere is partway between the top & the bottom of the
incline. At that point, it is at a height y = 3.5 m (less than H!) above the bottom.
e. Compute the gravitational potential energy & the 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!)
Suppose that the constant angular acceleration on the sphere as it moves from its
highest point to its lowest point is α = 8.0 rad/s2.
f. Compute the net torque on the sphere during its motion. What Physical Principle did you use
to do this last calculation?

F
NOTE: Work any three (3) of Problems 5, 6, 7, & 8!!
7. See figure. A block of mass m = 11 kg is pulled across a table by a massless cord, to
which is applied a force FP = 40 N. The cord makes an angle 30º with the horizontal.
The mass stays on the horizontal surface; there is no vertical motion. There is friction;
the coefficient of kinetic friction between the mass & the table is μk = 0.2.
a. Sketch the free body diagram for the mass, properly labeling all forces.
Compute:
b. The horizontal & vertical components of the applied force FP.
c. The normal force between the mass & the horizontal surface. (NOTE: ZERO credit will be given
if you say that the normal force is equal in size & opposite in direction to the weight!)
d. The frictional force between the mass & the table.
e. The acceleration of the mass. What Physical Principle did you use to do this last calculation?
f. If the mass starts from rest, compute the distance it has moved after 7 s.
8. See figure. A block, mass m = 10 kg, is on a horizontal, frictionless surface. It is pressed against an
ideal spring, of constant k = 700 N/m, and is initially at rest, on the left of the figure at point A. At A,
the spring is compressed an unknown distance xA from its equilibrium position. It is released and it
moves without friction to point B, where it has velocity vB = 8 m/s. Parts a, b, and c deal with m at
points A, B and a point in between. (Hint: In the following, PLEASE remember to take square roots
properly!)
m = 10 kg
vB = 8 m/s 
A
B
M = 15 kg
v=0
C
stick together!
V=?
D
a. Compute the kinetic energy and the momentum of m at point B.
b. Compute the elastic (spring) potential energy of m at point A and 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 and B, when m is a
distance x = 0.4 m (less than xA!) from the spring’s equilibrium position. The spring is still
touching m at that point! Compute the elastic potential energy and the kinetic energy of
m at that point. (NOTE: ZERO credit will be given if you set the KE = the PE at that point!)
Parts d and e deal with m as it moves to the right of point B. It continues to move without
friction until it collides with a second block, mass M = 15 kg, at point C near the middle of the
figure. The collision is inelastic, so that the two masses stick together, as at point D at the
right of the figure. At D, the velocity V of the masses is unknown.
d. Compute the momentum of the two stuck together masses and their velocity V at point D.
What Physical Principle did you use to find these?
e. Compute the kinetic energy of the two stuck together masses at point D. Is kinetic energy
conserved in the collision? Why or why not?
9. BONUS!! During the session, I did some demonstrations. If you were present at any one of those,
please 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 and you will (probably)
not be able to answer this. Have a good rest of the summer and good luck in the future!