EXAM III, PHYSICS 1403
July 28, 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! Yes, this wastes
paper, but it makes my grading easier!
2. PLEASE show all work, writing the essential steps in the solutions. 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: I HAVE 55 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!!
An 8.5’’ x 11’’ piece of paper with anything written on it and a calculator are allowed. NOTE:
Problem 1 consists of Conceptual Questions and IS REQUIRED! You may work any three (3) of
the remaining four problems for four (4) problems total for this exam. Each problem is equally
weighted and worth 25 points, for a total of 100 points on this exam.
1. THIS PROBLEM IS MANDATORY!!! CONCEPTUAL QUESTIONS: Answer
briefly, in complete, grammatically correct English sentences. Supplement your
answers with equations, but keep these to a minimum. Explain what the symbols
mean!! Answer ALL questions!
a. State the Work-Energy Principle.
b. State the Principle of Conservation of Mechanical Energy.
c. State the Law of Conservation of Momentum.
d. Explain: Elastic Collision, Center of Mass.
e. 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 on different slides. (NOTE! The figure shows them at different
heights because it shows them AFTER they have started down! They start
from the SAME height, h.) 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!!)
f. For 5 BONUS POINTS(!!), answer the following: During class
discussion about mechanical energy conservation, I did a demonstration to try to
illustrate the answer to part e. Briefly describe this demonstration. (If you were in
class the day I did this demonstration, likely will be able to answer this. If you
“cut” class that day, as several of you are now habitually doing, you probably
won’t be able to answer it!)
NOTE: WORK ANY THREE (3) OF PROBLEMS 2., 3., 4., or 5.!!!!!
NOTE: Some of the answers to the following are large numbers! PLEASE express
your answers in scientific (powers of 10) notation for such numbers. Thanks!
2. A car, mass m1 = 1,200 kg moving at velocity v1 = 20 m/s rear-ends a truck, mass
m2 = 3,000 kg, moving in the same direction at a velocity v2 = 10 m/s. Make the (very
unrealistic!) assumption that this is a perfectly elastic one dimensional collision.
After the collision, their velocities are v1´ and v2´.
a. Compute the total momentum p1 + p2 and the total kinetic energy KE1 + KE2 of
the 2 vehicles before the collision.
b. Compute the total momentum p1´+ p2´ and the total kinetic energy KE1´ +
KE2´ of the 2 vehicles after the collision. What Physical Principles did you use?
c. Calculate the velocities v1´ and v2´ of the vehicles after the collision.
d. Compute the impulse delivered to the truck by the car (to m2 by m1). Stated
another way, what was the change in the momentum of the truck, m2 due to the
collision with the car, m1?
e. If the collision time was Δt = 0.05 s, use the results of part d to compute the
average force exerted by the car on the truck. What Physical Principle did you
use?
3. See figure. Use energy methods to solve this!!! NO credit will be given for force
methods! You don’t need to force components or the incline angle θ to solve
this! A block, mass m = 3 kg, is on a horizontal, frictionless surface. It is pressed
against an ideal spring, of constant k = 900 N/m, and is initially at rest, as on the
right of the figure at point A. At point A, the spring is compressed a distance x = 0.3
m from its equilibrium position. The block is released and it moves first to point B,
which is at the bottom of a frictionless incline. It then moves up the incline and
stops at point C at the right of the figure, a at height h above the original position.
a. Compute the elastic (spring) potential energy of the block at point A.
b. Compute the kinetic energy the block at point B. What Physical Principle did you
use?
c. Compute the speed of the block at point B.
d. Compute gravitational potential energy of the block at point C and the height
h at which it stops. What Physical Principle did you use?
e. Compute the velocity of the block when it is at height y = 0.8 m above the
horizontal surface (above point B and below point C).
NOTE: WORK ANY THREE (3) OF PROBLEMS 2., 3., 4., or 5.!!!!!
NOTE: Some of the answers to the following are large numbers! PLEASE express
your answers in scientific (powers of 10) notation for such numbers. Thanks!
4. See figure. A roller coaster car, mass m = 3,500 kg, is
shown a portion of a roller coaster ride. The height
difference between points A and B is 45 m. The height
difference between points B and C is 38 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. What physical principle did
you use?
c. Compute the speed of the car at point B.
d. Compute the kinetic energy and speed of the car at point C.
e. 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 vB = 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? (Hint: I’m asking for
WORK here, not for the frictional force! You don’t need to compute the
frictional force to answer this!)
5. See figure. A railroad engine, mass M = 50,000 kg, traveling at a speed of 20 m/s
strikes a car, mass m = 3,000 kg, which is at initially at rest because it is stuck in the
crossing (the people in the car have run away from it!). After the collision, the railroad
engine and the car STICK TOGETHER (it is a perfectly Inelastic Collision!) and move
off down the tracks.
v = 20 m/s
Before Collision
V=?
After Collision
a. Compute the initial momentum and kinetic energy of the engine.
b. Compute the momentum of the engine-car combination as they move away
from the collision. What physical principle did you use to find this?
c. Compute their speed immediately after the collision.
d. Compute the kinetic energy of the engine-car combination immediately after
the collision. Was kinetic energy conserved? Was momentum conserved?
Explain (using brief, complete, grammatically correct English sentences!).
e. Compute the impulse delivered to the car by the engine. If the collision time
was Δt = 3 x 10-2 s, compute the average force exerted by the engine on the
car. What physical principle did you use?