November 2, 2004
Dr. Charles W. Myles
INSTRUCTIONS: Please read ALL of these before doing anything else!!!
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!
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 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.
in a few complete and grammatically correct English sentences. 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. A ball, mass m, is twirled at the end of a string in a vertical circle
of radius r and constant speed v. Free body diagrams for the ball at the top
and at the bottom of the circle are shown. Is the tension FTA that the string
exerts on the ball at the top of the circle (point A) less than, more than, or
equal to the tension FTB at the bottom of the circle (point B)? Explain your
answer using Newton’s 2nd Law with centripetal acceleration.
d. See figure. Two water slides are shaped differently, but they 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 traveling faster at the
bottom? What physical principle did you use to answer this? Which rider
gets to the bottom first? Why ? (Answer in words!!)
e. Answer the following for 5 BONUS POINTS! During our energy
conservation discussion, I did a demonstration which illustrates the answer
to part d 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: Answer any two (2) of problems 2, 3, & 4!!!
2. See figure. A Ferris wheel moves in a vertical circle of radius r = 10 m
at a constant speed v = 5 m/s. A rider of mass m = 50 kg is sitting in one
of the cars. This person experiences a normal force FN due to the car seat
pushing upward on their body. The free body diagrams for the rider at the
top and at the bottom are shown in the figure. The normal force is labeled
FN at both the top and the bottom. However, this does NOT imply that
FN necessarily has the same numerical value at the two places (it might
or it might not)! Part of this problem is to compute FN at the two places!
a. Compute the period of the circular motion of the Ferris wheel.
b. Compute the centripetal acceleration experienced by the rider.
c. Compute the centripetal force on the rider.
d. Use Newton’s 2nd Law with centripetal acceleration to compute the normal force
FN between the rider and the car seat at the top of the ride.
e. Use Newton’s 2nd Law with centripetal acceleration to compute the normal force
FN between the rider and the car seat at the bottom of the ride.
3. See figure. A mass m = 4.0 kg slides with initial velocity v = 3 m/s across a
horizontal, frictionless surface until it encounters a spring with constant k = 250 N/m.
It comes to rest after compressing the spring a distance x. (Hint: In the following,
PLEASE remember to take square roots properly!)
Initially, v = 3 m/s
Finally, x = ?, v = 0
a. Compute the initial kinetic energy of the mass (left hand figure).
b. Compute the potential energy of the spring-mass system at the final position and
the distance x the spring is compressed there (right hand figure). What physical
principle did you use to find these results?
c. Compute the force (magnitude and direction) the spring exerts on the mass at the
final position (right hand figure) where the mass has stopped moving.
d. Compute the potential energy of the spring-mass system and the distance the
spring has been compressed when the mass’s speed has slowed down to 1 m/s.
(This is not shown in the figures! This occurs sometime after the mass touches the
spring, but before it has come to rest in as in the right hand figure!)
e. The mass in the left hand figure was given its initial velocity by sliding it from
rest down a frictionless inclined plane from a height h. (This is not shown in the
figures! This happened sometime before the situation shown in the left hand
figure!) Compute the potential energy the mass had at the top of the inclined
plane and the height h from which the mass started. What physical principle did
you use to find these results?
NOTE: Answer any two (2) of problems 2, 3, & 4!!!
4. See figure. A bullet, mass m = 0.035 kg, traveling at a speed
v = 350 m/s, strikes and becomes embedded in a block of wood,
mass M = 1.5 kg, which is at initially at rest on a horizontal
v = 350 m/s
surface. The block-bullet combination then to moves to the right
across the surface.
a. Compute the momentum and kinetic energy of the bullet before it hits the
b. Compute the momentum of the bullet-block combination as they move away
from the collision. Compute their speed V immediately after the collision.
What physical principle did you use to find these?
c. Compute the kinetic energy of the bullet-block combination immediately after
the collision. Was kinetic energy conserved? Explain (using brief, complete,
grammatically correct English sentences!). (Hint: Please THINK before
answering this! Compare the kinetic energy computed here with that
computed in part a!)
d. Compute the impulse Δp delivered to the block by the bullet. If the collision
time was Δt = 2  10-3 s, compute the average force exerted by the bullet on
the block. What physical principle did you use to find this force?
e. After the collision, the bullet-block combination moves across the horizontal
surface until it stops some distance away from the collision point. Assuming
that work done by the frictional force between the block and the surface is
what causes them to stop, how much work is done by friction in this process?
(Hint: I’m not asking for the frictional force here! I’m asking for the WORK
[energy!] associated with friction! To answer this, you DON’T need to know
the frictional force or the distance it takes to stop!)
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