FINAL EXAM, PHYSICS 1306
August 8, 2003. 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!!
2. PLEASE do not write on the exam sheets, there will not be room!
3. PLEASE show all work, writing down the essential steps in the solution of a problem. Write the
appropriate formulas first, then put in numbers. Partial credit will be LIBERAL, provided that the
essential work is shown. Organized, logical, easy to follow work will receive more credit than
disorganized work.
4. The setup (PHYSICS) of a problem will count more heavily than the math of working it out.
5. PLEASE clearly mark your final answers and write neatly. If I can’t read or find your answer, you
can't expect me to give it the credit it deserves.
6. You will lose credit if you don’t show the units of an answer or if the units are wrong.
PLEASE FOLLOW THESE SIMPLE DIRECTIONS!! THANK YOU!!
An 8.5’’ x 11’’ piece of paper with anything written on it and a calculator are allowed.
Problem 1 (Conceptual Questions) and IS REQUIRED! Work any 3 of the remaining four problems for
four (4) problems total. Each problem is equally weighted and worth 25 points, for a total of 100 points.
1. THIS PROBLEM IS MANDATORY!!! CONCEPTUAL QUESTIONS: 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 Archimedes’ Principle (for computing the buoyant force on an object in a fluid).
Explain the meaning of any symbols!
b. Briefly define the following terms related to a simple harmonic oscillator: Period,
frequency, amplitude.
c. In the Figure, the round objects are rolling without slipping
down an inclined plane of height H above the horizontal. The
box is sliding without friction down the slope. All round
objects all have the same radius R. All objects have the same
mass M. The moments of inertia are: Hoop: I = MR2,
Cylinder: I = MR2, Sphere: I = (2MR2)/5. The four objects
are released, one at a time, from the height H. Which object
arrives at the bottom with the greatest (linear) speed V? Why ? Which 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!)
NOTE: WORK ANY THREE (3) OF PROBLEMS 2., 3., 4., or 5.!!!!!
2. See figure. It takes 20 J of work to stretch an ideal spring a distance
1.5 m from its equilibrium position.
a. Determine the spring constant k of the spring.
A mass m = 2.5 kg is attached to the spring and is pulled a distance x = 2.0 m from its
equilibrium position and released from rest. Neglect friction. Determine:
b. The amplitude of the motion.
c. The period, the frequency, and the angular frequency of the motion.
d. The maximum speed.
e. The maximum acceleration of the mass and the maximum force it experiences.
f. The total mechanical energy.
g. The speed, the kinetic energy, and the potential energy when x = 1.0 m.
h. Write an expression for the position x as a function of time x(t). (Note: ZERO credit
will be given if you use an equation from Chapter 2!).
NOTE: WORK ANY THREE (3) OF PROBLEMS 2., 3., 4., or 5.!!!!!
3. A cord has mass m = 0.6 kg and length L = 6 m. For parts a and b, a
transverse traveling wave is set up in the cord, as in the first figure.
The wave velocity is v = 35 m/s.
a. Compute the tension in the cord.
b. If the frequency of this wave is f = 180 Hz, compute the
wavelength.
In c, d, and e, the ends of the same cord as in a and b are tied to
supports and a standing wave is set up. (See second figure). The cord
has the same length and wave velocity as in a & b. Otherwise, c and d
are independent of a and b.
c. What is the longest possible wavelength (the fundamental) of such
a standing wave?
d. What is the fundamental frequency of this cord?
e. Compute the frequencies and wavelengths of the 2nd, 3rd, and 4th harmonics.
4. See Figure. A sphere of radius R = 0.7 m and mass M = 8.0 kg starts from rest at the top of
an inclined plane. Initially, the height is H = 10.0 m above the bottom of the plane. The
sphere’s moment of inertia is I = (2MR2)/5.
y=H
V=0
=0
y=0
V=?
=?
Before
After
a. Compute the gravitational potential energy of the sphere at its initial position.
b. Use energy methods to calculate the linear speed V of the center of mass and the
angular speed  of the sphere when it reaches the bottom of the plane.
c. Compute the translational kinetic energy of the center of mass of the sphere when it
reaches the bottom of the plane.
d. Compute the rotational kinetic energy of the sphere when it reaches the bottom of the
plane. Compute the angular momentum (about an axis passing through the center of
mass) of the sphere when it reaches the bottom.
e. Suppose the constant angular acceleration on the sphere as it moves from its highest
point to its lowest point is 9 rad/s2. Compute the net torque on the sphere during its
motion. What Physical Principle did you use to do this last calculation?
NOTE: WORK ANY THREE (3) OF PROBLEMS 2., 3., 4., or 5.!!!!!
5. For a. and b. , see first figure. A balloon is filled with a volume V = 2,000 m3 of a
gas of unknown density G so that, in air, it will lift a load (excluding the mass of
the gas, but including the mass of the empty balloon) of mass mload = 1560 kg. The
air density is air = 1.29 kg/m3.
a. Compute the density G of the gas. (Hint: This is NOT the same as the density
of the load!)
b. Calculate the buoyant force of the air on the balloon (neglecting the volume of
the load). What Physical Principle did you use to do these computations?
For c., d., and e., see second figure. Gasoline at a pressure of P1 = 3 x 105 N/m2
at street level is pumped in a pipe up a height h = y2 – y1 = 25 m above the street.
At ground level, the velocity of the gasoline is v1 = 0.5 m/s and its circular cross
section pipe has radius 0.25 m. The pipe tapers down to a radius of 0.1 m when it
gets to the top. Density of gasoline:  = 680 kg/m3.
c. Compute the volume flow rate of gasoline in the pipe.
d. Compute the velocity of the gasoline in the pipe at the top.
e. Compute the pressure on the gasoline at the top. What Physical
P1, v1, r1 
Principle did you use to do this computation?
 P2, v2, r2


h



6. BONUS QUESTION!!! During the session, I did a few 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 rest of the summer and good luck in the future!