FINAL EXAM III, PHYSICS 1408-001, December 11, 2007, 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!
PLEASE show all work, writing the essential steps in the problem solution. 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.
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 51 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) AND EITHER Problem 2 (Vibrations) OR Problem 3 (Fluid Dynamics) ARE
REQUIRED! NOTE: Work any two (2) of Problems 4., 5., 6. for four (4) problems total. Each problem is
equally weighted & worth 25 points, for a total of 100 points on this exam.
1. MANDATORY 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 with ONLY
symbols, with no explanation about what they mean, will receive NO credit!)
a. State Newton’s 1st Law of Motion (for translations). How many objects at a time does it
apply to? State Newton’s 3rd Law of Motion (for translations). How many objects at a time
does it apply to?
b. State the Principle of Conservation of Mechanical Energy. Which kinds of forces are
required to be present in order for this principle to hold?
c. State the Principle of Conservation of Momentum. Under what conditions is momentum
conserved?
d. State Newton’s 2nd Law for Rotations. (∑F = ma will get ZERO credit!).
e. State Archimedes’ Principle (for the buoyant force on an object partially or completely submerged
in a fluid).
f.
2.
State Newton’s Universal Law of Gravitation.
NOTE: Work EITHER Problem 2 (Vibrations) OR Problem 3 (Fluid Dynamics).
(Vibrations) See figure. It takes 20 J of work to stretch an ideal spring a distance x = 0.6 m from its
equilibrium position.
a. Calculate the spring constant k of the spring. (Hint: This statement is about work or ENERGY, not
about force! You can’t use a force relation to calculate k!)
A mass m is attached to this spring. It is pulled a distance x = A from its
equilibrium position & is released from rest. It undergoes simple harmonic
motion. Observation shows that x as a function of time is x(t) = Acos(ωt) =
(1.2 m) cos(12t). That is, the amplitude A = 1.2 m & the angular frequency ω
= 12 s-1. (Note: Answers to the following attempting to use the constant
acceleration kinematic equations from Ch. 2 will get ZERO credit!) Neglect friction. Calculate:
b. The frequency f , the period T of the motion, and the mass m.
c. The mass’s maximum speed vmax and total mechanical energy E.
d. The maximum force on the mass & the maximum acceleration it experiences.
e. The mass’s potential energy, kinetic energy and speed v when x = +1.0 m.
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5.
NOTE: Work EITHER Problem 2 (Vibrations) OR Problem 3 (Fluid Dynamics).
(Fluid Dynamics) For part a., answer using more WORDS than symbols! ZERO CREDIT will be given if
you write an equation without defining the symbols!
a. State Bernoulli’s Principle (for flowing fluids).
For parts b to e, see figure. A fluid of density ρ = 2  103 kg/m3 moves through a
horizontal circular pipe of radius r1 = 0.4 m at a speed of v1 = 2.5 m/s under a pressure
P1 = 3.0 x 105 N/m2, as on the left. The pipe narrows to radius r2 = 0.2 m as on the
right. (Area of circle of radius r: A = πr2). Calculate:
b. The volume flow rate of the fluid AND the speed v2 of the fluid in the narrow part of the pipe.
c. The pressure P2 in the narrow part of the pipe.
d. If a circular sheet of thin plastic of radius r = r1 = 0.4 m were placed inside the wider part of the pipe (at
the left) perpendicular to the direction of the fluid flow, it obviously would stop the flow. The fluid
flowing from the left of this sheet would then obviously exert a force to the right on it. Calculate this
force. (Hint: Use the definition of pressure in terms of force.)
NOTE: Work any two (2) of Problems 4., 5., 6.!
See figure. A helicopter, mass M = 2.0  104 kg, moves upward with acceleration a. It is lifting an object,
mass m = 4.0  103 kg, which is connected to it’s bottom by a massless cable. The upward force on the
helicopter exerted by the air on the rotors is F = 4.0  105 N. The tension in the cable is T, which acts down

on the helicopter & up on the object. The free body diagrams for the helicopter &

object are in the figure. The 2 unknowns in this problem are the acceleration a & the
 a
F
cable tension T. (Hints: The motion is vertical, but a is obviously NOT g downward,
but a upward! If it were g downward, the object would be in free fall & T would be
zero! Also, T can’t possibly be mg, or a would be zero!).
Mg
a. Apply Newton’s 2nd Law to the helicopter & the object to find the two equations

T
needed to solve for a & T. Writing these without substituting in numbers, will


receive more credit than writing them with numbers substituted in!
b. Using the equations from part a, calculate a & T.

For the following, assume that all forces in the problem are constant, so that the
T
acceleration a is constant. Once the cable is tight, the upward velocity of the system is
vi = 5 m/s. Consider this system after it has moved upward a distance y = 10 m.
c. Calculate the velocity vf of the system at that point. (Hint: You can use a
mg
kinematic equation from Ch. 2!)
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d. Calculate the Work done in this process by the lifting force F = 4.0  105 N.
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e. Calculate Net Work done in this process (Hint: Rather than calculate the work due to each force
separately & adding them, it may be easier to use the Work-Kinetic Energy Theorem!)
NOTE: Work any two (2) of Problems 4., 5., 6.!
The figure is a compound wheel. The inner wheel radius is r1 = 0.4 m. The outer wheel radius is r2 = 0.75
m. (They are bolted together, so they can rotate rigidly together). Two equal forces, F1 = F2 = 50 N, are applied as
shown. F1 is applied tangent to the inner wheel in the direction shown (down in figure). F2 is applied at the
top of the outer wheel, at an angle of 60° with respect to the dashed vertical line in the figure
F2
(30° with respect to the tangent to the larger wheel at that point). The moment of inertia of
the compound wheel is I = 2.55 kg m2. (Hints: This means that I = (½)MR2 is should NOT be
used! To solve this problem, the wheel mass is NOT needed! The gravity acceleration g, is irrelevant!)
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b.
c.
d.
Calculate the torque, τ1 due to F1 & the torque, τ2 due to F2. Be sure to include the signs
of these in your answers. (Hint: Sign convention: A torque which, if it acted alone,
would cause a counterclockwise rotation is considered positive & a torque which, if it
acted alone, would cause a clockwise rotation is considered negative.) Calculate the net
torque τnet on the compound wheel.
F1
Calculate the wheel’s angular acceleration α. What physical principle did you use to do
this? Calculate the tangential acceleration atan of a point on the outer rim (at radius r2).
The wheel starts from rest at time t = 0, compute the angular velocity ω after t = 8 s.
Calculate the rotational kinetic energy and the angular momentum of the wheel at t = 8 s.
6.
NOTE: Work any two (2) of Problems 4., 5., 6.!
See figure. A block, mass m = 8 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 = 8 kg
vB = 8 m/s 
A
B
M = 12 kg
v=0
C
stick together!
V=?
D
a. Calculate the kinetic energy and the momentum of m at point B.
b. Calculate 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 = 0.25
m (less than xA!) from the spring’s equilibrium position. The spring is still touching m at that point!
Calculate the elastic potential energy and the kinetic energy of m at that point. (NOTE: ZERO credit
will be given if you set kinetic energy = potential energy 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 = 12 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. Calculate 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. Calculate the kinetic energy of the two stuck together masses at point D. Is kinetic energy
conserved in the collision? Why or why not?
7.
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. (3 points) See figure. The round objects roll without slipping down an inclined
plane. The box slides with no 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) 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 this box.
v
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!
c. (3 points) See figure. A straw of length L is put into a fluid of density . A finger is put over
the top so that no air can get in or out, & the straw is lifted out of the fluid. It retains the fluid
such that the distance from the finger bottom to the top of the fluid is h. Does the air in the
space between the finger & the fluid top have a pressure P that is 1) greater than, 2) equal to, or
3) less than the atmospheric pressure PA outside the straw? Explain the reasoning you used to
get this answer!
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.