EXAM II, PHYSICS 1403
April 2, 2004
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 ,
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.
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 sentences with equations, but keep these to a minimum !!
a.
State the Principle of Conservation of Mechanical Energy.
b.
State the Law of Conservation of Momentum.
c.
See figure. Two water slides are shaped differently, but start at the same height, h . Two riders, Paul and Kathleen, start from rest at the same time and at the same 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 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 demonstration, 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.
The figure shows a roller coaster car, mass m = 3,000 kg, on a portion of a roller coaster ride. The height difference between points A and B is 35 m . The height difference between points B and C is 23 m . The car starts from rest at point A . Take the y = 0 point to be point B . For parts a., b., and c., assume that the roller coaster track is frictionless . a.
Compute the gravitational potential energy of the car at points A, B, and C . b.
Compute the kinetic energy of the car at point B . Compute its speed there.
What physical principle did you use to do this calculation? c.
Compute the kinetic energy and speed of the car at point C . d.
Parts a., b., and c.
assume that the track is frictionless. However, the measured speed of the car at point B is found to be v
B
= 20 m/s . This is less than the speed that you (should have) computed in part b. This means that friction cannot be neglected. In this case, how much WORK is done by friction when the car moves from point A to point B ? What physical principle did you use to compute this work?
3.
See the figure.
Two bumper cars in an amusement park undergo an elastic collision as one approaches the other from the rear.
Their masses are m
1
= 475 kg and m
2
= 600 kg.
Their initial velocities are both in the same direction, as in fig. a) . The initial velocity of m
1 is v
1
= 5.1 m/s and that of m
2 is v
2
= 3.9 m/s . After the collision, their velocities v
1
´
& v
2
´
are both still in the same direction, as in fig. b) . a.
Compute the total momentum p
1
+ p
2 of the two cars before the collision.
Compute the total kinetic energy KE
1
+ KE
2
of the two cars before the collision. b.
Compute the total momentum p
1
´+ p
2
´ of the two cars after the collision.
Compute the total kinetic energy KE
1
´ + KE
2
´ of the two cars after the collision.
What physical principles did you use to find these results? Is kinetic energy conserved in this collision? c.
Calculate the velocities v
1
´ & v
2
´ of the cars after the collision. d.
Compute the impulse that was delivered to m
2
by m
1
. (Stated another way, compute the change in momentum of m
2 due to the collision.) e.
BONUS!! 5 EXTRA POINTS!!
If the collision time was
 t = 3

10 -2 s , use the results of part d to compute the average force exerted by m
1
on m
2
.

NOTE: WORK ANY TWO (2) OF PROBLEMS 2., 3., or 4.!!!!!
4.
See figure . A ball, mass m = 1.5 kg is twirled at constant speed v at the end of a massless string in a vertical circle of radius r = 1.2 m .
The period for this uniform circular motion is T = 1.3 s . Free body diagrams for the ball at the top and at the bottom of the circle are shown. a.
Compute the speed v of the ball. b.
Compute the ball’s centripetal acceleration. c.
Compute the “centripetal force” on the ball. d.
When the ball is at the top (point A in the figure) compute the tension F
TA
in the string. e.
When the ball is at the bottom (point B in the figure) compute the tension F
TB in the string.