FINAL EXAM, PHYSICS 1403-002 & 1403-003
May 6, 2005, Dr. Charles W. Myles
INSTRUCTIONS: Please read ALL of these before doing anything else!!!
1. PLEASE! Make the first page of your answers a “title page”! In LARGE
letters on that page, PLEASE write your name AND your section number
(002 is TT, 003 is MWF)!! PLEASE start your solutions on the second page!
2. PLEASE! a) Write your name on every sheet of paper you use, b)
number your pages, c) write on one side of the paper only, d) write large
enough that an “old guy” can read it (!), & e) 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. PLEASE DO NOT write on the exam sheets, there will not be room!
3. PLEASE! When you are finished, before handing in your solutions, put
your problems in numerical order and put your pages in numerical order!
PLEASE also put your solutions in the correct box for your section!
4. PLEASE! Do not hand in either the question sheets (I already know what they
say!) or your “cheat sheets”.
5. PLEASE! Show all work, writing the essential steps in the problem solution.
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.
NOTE: IN THE 2 SECTIONS, I HAVE
260 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!!
Three 8.5’’ x 11’’ pieces of paper with anything written on them and a
calculator are allowed. Problem 1 (Conceptual Questions) IS
REQUIRED! Work either Problem 2 or Problem 3 (on fluids). Work
any three (3) of the remaining problems for five (5) problems total on
the exam. Each problem is equally weighted and worth 20 points, for a
total of 100 points on this exam.
1. THIS QUESTION IS MANDATORY!!! Answer briefly, in complete, grammatically
correct English sentences. Supplement answers with equations, but keep these to a minimum
& use English words to EXPLAIN WHAT THE SYMBOLS MEAN!!!!
a. State Newton’s 1st, 2nd and 3rd Laws of Motion (for Translational Motion).
b. State the Principle of Conservation of Mechanical Energy.
c. State the Law of Conservation of Linear Momentum.
d. State Newton’s 2nd Law for Rotational Motion. (∑F = ma will get ZERO credit!)
e. State the 1st and 2nd conditions for static equilibrium.
f. State Archimedes’ Principle (for the buoyant force on an object partially or completely
submerged in a fluid).
g.
State Bernoulli’s Principle (for a flowing fluid).
NOTE!!! Work EITHER Problem 2 OR Problem 3!
2. See figures. A rectangular block, mass m = 10 kg, is suspended by a wire from a scale and
immersed in water (water density ρw = 1.0  103 kg/m3). It’s free body
diagram is at the far right. FB is the buoyant force on the block due to the
water and FT is the tension in the wire. The block’s horizontal faces have
area A = 0.01 m2 and it’s vertical dimension is L = 0.12 m, so it’s volume
is V = AL = 1.2  10-3 m3. It’s top face is a distance y = 0.15 m below the
water surface. The block and the water are static.
a. Compute the density ρB of the block.
Neglect the effect of atmospheric pressure when answering the following.
b. Compute water pressure P1 on the top face of the block and the water
pressure P2 on it’s bottom face. Use these results to compute the downward force F1
due to the water on the block’s top face and the upward force F2 on it’s bottom face.
(Hint: Use the definition of pressure in terms of force).
c. Compute the upward buoyant force FB exerted by the water on the block. What physical
principle did you use to compute this force?
d. Compute the tension FT in the wire. What physical principle did you use to compute this
force? The magnitude of FT is the same as the scale reading. This is true because of what
physical principle?
NOTE!!! Work EITHER Problem 2 OR Problem 3!
3. See figure. A horizontal hypodermic syringe contains a fluid
with density ρ = 2.0  103 kg/m3. A force F = 1.0 N is exerted
to the right on the plunger (left of the figure), causing the
v1 
medicine to move to the right with velocity v1 = 0.5 m/s. This
makes the fluid squirt from the needle (right of the figure) with velocity v2. The plunger and the
barrel of the syringe have cross sectional area A1 = 2.5  10-4 m2. The needle is narrower with
cross sectional area A2 = 1.0  10-4 m2. Neglect the effect of atmospheric pressure when
answering the following.
a. Compute the volume flow rate in the syringe.
b. Compute the velocity v2 of the medicine at the end of the needle.
c. Compute the fluid pressure P1 in the left part of the syringe. (Hint: Use the definition of
pressure in terms of force).
d. Compute the fluid pressure P2 in the right part of the syringe. What physical
principle did you use to compute this pressure?
 
FB FT
 

mg

NOTE: Work any three (3) of Problems 4, 5, 6 and 7!
4. See figure. A block, mass m = 5 kg, is on a horizontal, frictionless surface. It is pressed
against an ideal spring, of constant k = 800 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 = 5 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 = 5 kg
vB = 5 m/s 
A
B
M = 10 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 = 0.2 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 = 10 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?
NOTE: Work any three (3) of Problems 4, 5, 6 and 7!
5. The figure is an end view of a flat, uniform cylindrical satellite, of radius R =
F
5.0 m and mass M = 4,000 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 and which, when fired simultaneously, exert
F
four equal unknown forces F tangent to the circle as shown. They give the
2

satellite an angular acceleration α = 0.1 rad/s . Assume that the four
forces F are only forces producing torques about the axis of rotation.
a. Compute the tangential acceleration atan of a point on the rim.
b. Compute the total (net) torque exerted by the four rocket engines. What
F
Physical Principle did you use to find this torque?
c. Compute the value of the unknown force F.
The satellite starts from rest and has an angular velocity ω = 40 rad/s after the rockets have been
firing for a time t.
d. Compute the time t.
e. Compute the velocity v & the centripetal (radial) acceleration aR of a point on the rim at
the time t.

F
NOTE: Work any three (3) of Problems 4, 5, 6 and 7!
6. See Figure. A box, mass m = 32 kg, is shoved across a horizontal surface. It is released at
the origin with an initial velocity v0 in the +x direction. After it is released, the only
horizontal force on the box is friction between the box and the surface, which
 Ff
causes it to slow down and eventually stop. The frictional force is Ff = 45 N.
(Note: How the box was shoved & the force used in shoving it AREN’T part of this
problem! The problem begins when the box has already been released & is moving to the
right with velocity v0!)
a. Sketch the free body diagram for the box, properly labeling all forces. Is there a force in
the direction of the motion (parallel to the velocity)? (Hint: The velocity v0 is NOT a force and
does not belong in a free body diagram!)
b. Compute the weight of the box and the normal force between it and the surface.
c. Compute the coefficient of friction μk between the box and the surface.
d. Compute the acceleration (magnitude and direction!) experienced by the box as it slows
down. What force causes this acceleration? What Physical Principle did you use to find
this acceleration?
e. The box stops a time t = 13 s after it is released. Compute the initial velocity v0 and the
distance from its release point that the box goes before coming to rest.
NOTE: Work any three (3) of Problems 4, 5, 6 and 7!
7. See Figure. A hollow sphere of radius R = 0.45 m & mass M = 8.0 kg starts from rest at
height H at the top of an inclined plane. The sphere’s moment of inertia is I = (⅔)MR2.
When it reaches the bottom, it’s angular velocity about its axis of rotation is ω = 20 rad/s.
y = H =?
V=0
ω=0
y = 0, V = ?
ω = 20 rad/s
Before
After
a. Compute the rotational kinetic energy & angular momentum (about an axis through the
center of mass) of the sphere when it reaches the bottom.
b. Compute the linear speed V of the sphere’s center of mass when it reaches the bottom.
c. Compute the translational kinetic energy of the center of mass and the total kinetic
energy of sphere the when it reaches the bottom.
d. Compute the gravitational potential energy of the sphere at its initial position and
compute it’s initial height H at the top of the incline. What Physical Principle did
you use to do this last calculation?
e. Consider the a point when the sphere is partway between the top and the bottom of the
incline. At that point, it is at a height y = 4.0 m (less than H!) above the bottom. Compute
the gravitational potential energy and 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!)
8. BONUS QUESTION!! During the semester, I did some demonstrations. If you were
present at any one of those times, please write a few short, complete, grammatically correct
English sentences telling about ONE of these times. 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 summer and good luck in the future!
v0 