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EXAM III, PHYSICS 1403
November 30, 2004, Dr. Charles W. Myles
INSTRUCTIONS: Please read ALL of these before doing anything else!!!
PLEASE put your name on each 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 and put them 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 125 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 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. 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. See Figure. A person, mass m = 85 kg, stands on a ladder which is
leaning against a wall as shown. The person is standing a horizontal
distance b = 0.70 m from the point where the ladder touches the
floor. The ladder touches the wall a vertical distance a = 3.8 m above
the floor. The wall is frictionless so the force f3 it exerts on the ladder
is horizontal as shown. The floor exerts both a horizontal frictional
force f2 and a vertical normal force f1 on the ladder as shown. Neglect
the ladder weight in what follows. (Hint: You don’t need to know
either the angle the ladder makes with the floor or the distance
between the wall and the point where it touches the floor to solve this
problem! Except for part e, you can solve this without using trig!)
a. Compute the torque produced by the weight of the person (as if it were acting
alone!) about an axis passing through the point where the ladder touches the floor.
b. Write equations which describe the conditions for equilibrium of the ladder. This
doesn’t mean to write the general abstract conditions for equilibrium! It means to
APPLY these conditions to the ladder and to write the equations which result
from this application.
c. Find the values of the unknown forces, f1, f2 and f3.
d. Compute the coefficient of static friction μs between the ladder and the floor.
e. Using vector addition, compute the magnitude AND direction of the resultant
force f = f1+ f2 that the floor exerts on the ladder.
3. See Figure. A yo-yo has outer radius R = 0.15 m. The radius of the inner
cylinder is r = 0.05 m. It’s moment of inertia is I = 1.9  10-3 kg m2. A
massless cord is wrapped around the inner cylinder and another massless
cord is wrapped around the outside, as shown. A small mass m = 0.05 kg
I
is attached to the outer cord as shown. The tensions T1 and T2 are
unknown. Starting from rest, the yo-yo rotates so that the small mass m
falls vertically. While m falls, the yo-yo rotates but doesn’t move
vertically. After m has fallen for 5 s, the angular speed of the yo-yo is ω
= 15 rad/s.
a. Compute the rotational kinetic energy and the angular momentum of the yo-yo
and the translational kinetic energy of the small mass after 5 s.
b. Compute the yo-yo’s angular acceleration α and the linear acceleration a of the
small mass.
c. Compute the net torque acting on the yo-yo. What physical principle did you use
to do this calculation?
d. Write the equations which result from applying Newton’s 2nd Law for rotational
motion to the yo-yo and Newton’s 2nd Law for translational motion to the small
mass.
e. Use the results of part d to find the values of the unknown tensions T1 and T2.
NOTE: WORK ANY TWO (2) OF PROBLEMS 2., 3., or 4. !!!!!
4. See Figure. A hollow SPHERE of radius R = 0.6 m & mass M = 8.0 kg starts from
the bottom of an inclined plane. It rolls without slipping up the plane until it stops at
height is H = 5.0 m above the bottom of the plane. The moment of inertia of the
sphere is I = (⅔)MR2.
H = 5.0 m
V
H=0
V=0
ω=0
V=?
ω=?
Before
After
a. Compute the gravitational potential energy of the sphere at its final position.
b. Use energy methods to calculate the initial linear speed V of the sphere center of
mass and the initial angular speed ω of the sphere at its initial position at the
bottom of the plane.
c. Compute the initial translational kinetic energy of the sphere’s center of mass.
Compute initial rotational kinetic energy of the sphere about an axis passing
through the center of mass. Compute the initial angular momentum about this
same axis.
d. Suppose that the (constant) angular acceleration of the sphere as it moves from its
lowest to its highest point is 8 rad/s2. Compute the linear (tangential) acceleration
of a point on the rim.
e. Using the angular acceleration of part d, calculate the net torque on the sphere
during its motion and the time it takes for the sphere to travel from the bottom to
the top. (Hint: To find the time, you also must use the angular speed ω found in
part b).