EXAM III, PHYSICS 1403-002 (TT)
April 26, 2005
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!! PLEASE DO NOT write on the exam sheets, there will not be room!
2. 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.
3. The setup (PHYSICS) of a problem will count more heavily than the math of working it out.
4. 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: 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!!
A 8.5’’ x 11’’ sheet with anything on it & a calculator are allowed. Problem 1
(Conceptual Questions) IS REQUIRED! Answer any two (2) of the remaining
problems for a total of three (3) problems required. Problem 1 is worth 34 points.
Problems 2, 3, and 4 are equally weighted & worth 33 points each.
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 & EXPLAIN what the symbols mean!!
a. State Newton’s 2nd Law for Rotational Motion. Explain the meaning of any
symbols! (Note: The answer ∑F = ma will receive ZERO credit!)
b. State the two (2) conditions for static equilibrium. Explain the meaning of any
symbols! What are the Physical Principles (Laws of Physics!) from which these
conditions come? Stated another way, these conditions are special cases of which
Law or Laws?
c. See Figure. The round objects roll without slipping down an inclined plane, each
starting at the same height H above the horizontal. The box slides without
friction down the plane. All round objects have radius R. All objects, including
the box, have mass M. Moments of inertia: Hoop: I =
MR2, Cylinder: I = (½)MR2, Sphere: I = (2MR2)/5.
Obviously, the moment of inertia of the box is zero, since
it does not rotate! The objects are released, one at a time,
from height H. Which object arrives at the bottom with the
greatest speed? Why ? Which arrives with the smallest
speed? Why? What Physical Principle did you use to arrive at these
conclusions? (You may write equations, but explain the meaning
of the symbols. I want most of the answer in WORDS!)
NOTE: WORK ANY TWO (2) OF PROBLEMS 2., 3., or 4. !!!!!
2. The Figure shows the free body diagram of a uniform beam,
length L = 5.5 m, mass m = 50 kg. It is mounted by a hinge (left
of figure) on a wall. It is uniform, so its weight acts through its
center, a distance x = 2.75 m from each end. It is held in a
horizontal position by a wire making an angle θ = 35° with the
horizontal (right of figure). From its end, it supports a hanging
mass M = 500 kg. FT is the tension force in the wire. It & the
components FHx & FHy of the hinge force are unknown.
a. Compute the torque produced by the board’s weight (as if it
were acting alone!) about an axis passing through the hinge.
b. Compute the torque produced by the large mass’s weight (as if it were acting alone!) about
an axis passing through the hinge.
c. Write equations describing the equilibrium conditions for the beam. This doesn’t mean to
write the general conditions for equilibrium! It means to APPLY these conditions to the
beam & to write the equations resulting from this application. I don’t want abstract
sums! I want those sums expressed (written out!) in terms of the forces & torques for
this problem! Hint: Before doing this, it is helpful to first resolve the tension FT into
horizontal (x) & vertical (y) components FTx & FTy.
d. Use the results of part c to find the components FHx and FHy of the hinge force and the
components FTx and FTy of the tension in the wire.
e. Use the results of part d to compute magnitude AND direction of the tension force FT.
3. See Figure A. A pulley, mass M = 7.0 kg & radius R = 0.5 m is
above a well. The pulley wheel is a HOOP with moment of
inertia I = MR2. A cord is wrapped around the wheel & a
bucket, mass m = 3.0 kg, is attached to the other end. The bucket
is released & falls as the cord unwinds from the wheel, which
rotates around its axle. Neglect friction on the axle as the wheel
rotates. The bucket’s free body diagram is in Figure B. The
unknowns are the tension force FT in the cord, the bucket’s
downward translational acceleration a & the wheel’s angular
acceleration α. Hint: The bucket’s acceleration a is the same as the
A
tangential (translational) acceleration of a point on the wheel’s rim.
a. Write the equation resulting from applying Newton’s 2nd Law for rotational motion to the
pulley wheel. NOTE: Writing it in symbols, without substituting in numbers will receive
more credit than writing it with numbers in it! I don’t want an abstract sum! I want that
sum expressed (written out!) in terms of the torques (& forces) for this problem!
b. Write the equation resulting from applying Newton’s 2nd Law for translational motion to
the bucket. NOTE: Writing it in symbols, without substituting in numbers will receive
more credit than writing it with numbers in it! I don’t want an abstract sum! I want that
sum expressed (written out!) in terms of the forces for this problem!
c. Use the results of parts a & b (along with the above Hint) to compute (find numerical values!)
the tension force FT, the bucket’s acceleration a, & the wheel’s angular acceleration α.
d. If the bucket and wheel start from rest, compute the angular velocity ω of the wheel &
the velocity v of the bucket after the motion has lasted for 7 s.
e. Use the results of part d to compute the wheel’s rotational kinetic energy & angular
momentum after the motion has lasted for 7 s.
a
B
NOTE: WORK ANY TWO (2) OF PROBLEMS 2., 3., or 4. !!!!!
A

4. The Figure shows a ball on a track. It is a solid
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SPHERE of radius R = 0.4 m & mass M = 12.0 kg.
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2
It’s moment of inertia is I = (2MR )/5. It starts from
y1
rest at point A. It rolls without slipping to the right &
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down the track, passes point B & moves on to point C.
|
B

It continues to the right past point C, but that isn’t
part of this problem! The height difference between
points A & B, y1 in the figure, is unknown. The height difference between points B &
C is y2 = 11 m. When the ball reaches point B, the velocity of it’s center of mass is V
= 15 m/s. Use energy methods to answer the following!
a. Compute the translational kinetic energy of the sphere’s center of mass when it
has reached point B.
b. Compute the following for the sphere when it is at point B: The angular velocity
ω of rotation about an axis passing through the center of mass. The rotational
kinetic energy. The angular momentum.
c. Use the results of part b to compute the following for the sphere: It’s total kinetic
energy at point B. It’s initial gravitational potential energy at point A. The initial
height y1 at point A.
d. Calculate the following for the sphere when it reaches point C: The potential
energy. The total kinetic energy.
e. Suppose that the (constant) angular acceleration of the sphere as it moves from
point A to point B is unknown. However, the net torque on it during its motion
from A to B is τ = 10 m N. Compute the angular acceleration α and the time it
takes for the sphere to travel from point A to point B. (Hint: To find the time, you
also must use the angular speed ω found in part b).
C

|
y2
|
