EXAM II, PHYSICS 1403-003 (MWF)
April 6, 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 a few complete and grammatically correct ENGLISH SENTENCES!
You may supplement these with equations, but keep them to a
both
minimum and EXPLAIN what all symbols mean!!!
start
a. State the Principle of Conservation of Mechanical Energy.
here!
b. State the Law of Conservation of Momentum.

c. See figure. 2 water slides are shaped differently, but start at
the same height, h. 2 riders, Paul & Kathleen, start from
rest at the same time & at height h, but on different slides.
(The figure shows them at different heights because it shows
them AFTER they have started down!) The slides are
frictionless. Which rider is travelling faster at the bottom?
What physical principle did you use to answer this? Which
rider gets to the bottom first? Why ? (Answer in WORDS!!)
d. Answer the following for 5 BONUS POINTS! During our discussion about
energy conservation, I did a demonstration which illustrates part of the answer to
part c. about the people on the water slides. Briefly describe this demonstration.
(If you were in class the day I did this, you probably will be able to answer this.
However, if you “cut” class that day, as many of you often do, you probably
won’t be able to answer it!)
NOTE: WORK ANY TWO (2) OF PROBLEMS 2., 3., or 4.!!!!!
2. See figure of a frictionless track that
v=0
marbles can be rolled down. The circular

v=?
|
loop near the middle has radius R = 0.55 m.

|

The right end of the track rises to height y =
H
R
0.45 m. A marble, mass m = 0.15 kg, is put
|
v=?
on the track and released from rest at height


H at the left of the figure. When it reaches
the right end of the track, it’s velocity is v = 4.0 m/s.
a. Compute the potential energy, the kinetic energy, & the total mechanical energy
of the marble when it reaches the right end of the track.
b. Compute the potential energy of the marble at the left end of the track & the
height H from which it must be released from rest in order for it to reach the right
end of the track with the velocity of v = 4.0 m/s.
c. Compute the potential energy, the kinetic energy, & the velocity of the marble
when it has reached the bottom part of the track just before it starts onto the loop.
d. Compute the potential energy, the kinetic energy, & the velocity of the marble
when it has reached the top of the loop.
e. What physical principle did you use to do these calculations?
f. 5 POINT BONUS!! Parts a-d are theoretical. However, an experiment is done
& when the marble is released from the height H found in part b, it’s velocity at
the right end of the track is measured as v = 3.3 m/s instead of 4.0 m/s.
This means the track isn’t frictionless! In this case, compute the work done by
friction as the marble moves from the left end of the track to the right end. Hint:
I’m NOT asking for the frictional force! I’m asking for the work (energy!) due to
friction. You don’t need to know the friction coefficient or the track length!
3. See figure of Problem 2! Consider the marble in Problem 2 with mass m = 0.15 kg,
on the track described in that problem. Other than the figure, this is independent of
Problem 2! You DON’T need to solve Problem 2 to solve this! The circular loop at
the middle of the track has radius R = 0.55 m. Consider the marble when it is at the
top of the loop. For Parts a-d, assume that it’s velocity there is v = 3.5 m/s.
a. Compute the marble’s centripetal acceleration and the “centripetal force” on it at
that point.
b. Sketch the free body diagram for the marble at the top, properly labeling all
forces. Don’t forget the (downward!) normal force FN from the track!
c. Write the equation resulting from applying Newton’s 2nd Law to the marble in the
vertical direction at the top. Writing it in general, without numbers substituted in
will get more credit than writing it with numbers in!
d. Use the equation found in part c to compute the normal force on the marble at the
top of the loop.
e. For this part only, obviously the velocity at the top is NOT v = 3.5 m/s as given
above! Compute the minimum velocity the marble must have at the top of the
loop to just make it around the loop without falling off at the top. (Hint: The
minimum velocity there will be the one for which the normal force FN between
the track & the marble is zero!)
v = 4.0 m/s
y = 0.45 m


 y

h
NOTE: WORK ANY TWO (2) OF PROBLEMS 2., 3., or 4.!!!!!
4. See figures. In a pool game, two balls undergo an elastic
collision as one approaches the other from the rear. Figure a
shows them before the collision and figure b shows them
a
after the collision. The masses are m1 = 0.5 kg & m2 = 0.3
kg. The initial velocity of m1 is v1 = 5.0 m/s & that of m2 is v2
= 3.0 m/s. Both velocities are in the same direction as in
figure a. After the collision, their velocities v1´ & v2´ are both
b
still in the same direction, as in figure b.
a. Compute the total momentum p1 + p2 of the two balls before the collision.
Compute the total kinetic energy KE1 + KE2 of the two balls before the collision.
b. Compute the total momentum p1´+ p2´ of the two balls after the collision.
Compute the total kinetic energy KE1´ + KE2´of the two balls after the collision.
What physical principles did you use to find these results? Is kinetic energy
conserved in this collision?
c. Calculate the velocities v1´ & v2´ of the balls after the collision.
d. Compute the impulse that was delivered to m2 by m1. Stated another way,
compute the change in momentum of m2 due to the collision.
e. If the collision time was Δt = 8  10-3 s, use the results of part d to compute the
average force exerted by m1 on m2.