Problem 1: Hunter in the Forest (25 points)

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PHYSICS 218 Final Exam Fall, 2006 STEPS
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• __________________________________________________
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• No calculators are allowed in the test.
• Be sure to put a box around your final answers
  and clearly indicate your work to your grader.
• All work must be shown to get credit for the
  answer marked. If the answer marked does not
  obviously follow from the shown work, even if the
  answer is correct, you will not get credit for
  the answer.
• Clearly erase any unwanted marks. No credit will
  be given if we cant figure out which answer you
  are choosing, or which answer you want us to
  consider.
• Partial credit can be given only if your work is
  clearly explained and labeled. Partial credit
  will be given if you explain which law you use
  for solving the problem.
• Put your initials here after reading the above
  instructions

For grader use only Problem 1 (20)
___________ Problem 2 (20) ___________ Problem 3
(10) ___________ Problem 4 (20)___________ Problem
5 (15) ___________ Problem 6 (20)___________ Tot
al (105) ___________

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Problem 1 (20 points)
y
x
F
3
Problem 2 (20 points)

• A spring with negligible mass exerts a restoring
  force , if it is
  stretched or compressed ( and are known
  constants). A block of mass m is pushed against
  the spring so that the spring is compressed by
  amount of A. When the block is released, it
  moves along a frictionless, horizontal surface
  and then up the incline that has coefficient of
  friction .
• Find the potential energy of the system before
  the block is released.
• How far does the block travel up the incline
  before starting to slide back down?

N
mg
4
Problem 3 (10 points)
5
Problem 4 (20 points)

• A car in an amusement park rides without
  friction around the track. It starts with
  velocity V0 at point A at height H.
• Find the velocity of the car at point B. Denote
  it as .
• What is the radius R that the car moves around
  the loop without falling off.

C
1) Conservation of energy
2) To find the maximum radius, we need to find
the magnitude of critical velocity for the car
not to fall off the track. From the second law at
point C
From conservation of mechanical energy at points
A and C
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Problem 5 (15 points)
Two masses, and , are attached by a
massless, unstretchable string which passes over
a pulley with radius R and moment of inertia
about its axis I. The horizontal surface is
frictionless. The rope is assumed NOT to slip as
the pulley turns. Find the acceleration of mass
.
x
y
7
Problem 6 (20 points)
A bullet of mass m is fired with velocity of
magnitude into a block of mass M. The
block is connected to a spring constant k and
rests on a frictionless surface. Find the
velocity of the block as a function of time.
(Assume the bullet comes to rest infinitely
quickly in the block, i.e. during the collision
the spring doesnt get compressed.)
x
k
M