Physics 218 Honors; Secs. 201,202,203; Exam 2, FaH-09
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Section. No:
NOTE: Each problem is worth 20 pts
1. A block of mass mi sits on top of a block of mass m
2 which is on a horizontal
surface. The mss m
2 is pulled to the right with a force F as shown. The
coefficient of static friction between all surfaces is j.t. Assume that the magnitude
of F is just enough to start the blocks moving.
a) Draw free body diagrams for both blocks
b) Determine this minimum value ofF in terms of the masses, g ,and
c) Determine the tension T in the cord in terms of the same parameters
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2. A small bead of mass m is constrained to slide without friction inside a circular
vertical hoop of radius R which rotates about a vertical axis at a frequency f
a) Draw a free body diagram of the bead.
b) Determine the angle e where the bead will be in equilibrium- that is where it
will have no tendency to move up or down along the hoop
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3. A simple pendulum consists of a small object of mass m (the bob) suspended by a
cord of length L of negligible mass. A force F is applied in the horizontal direction
moving the bob very slowly so the acceleration is essentially zero. (NOTh that the
magnitude of F will need to vary with the angle 0 that the cord makes with the vertical at
any moment):
a) Draw a free body diagram of the bob.
b) Calculate the work done by the force F, to move the pendulum from 0=0 to 0= 0o
(Note: since the force is variable you must integrate to get it correct)
c) Calculate the work done by the gravitational force on the bob
d) What is the NET work done on the bob by both of these forces and can you use this
fact to explain why there is NO change in the kinetic energy of the bob?
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4. Stretchable ropes are are used to safely arrest the fall of rock climbers. Suppose one
end of a rope with unstretched length L is anchored to a cliff and a climber of mass m is
attached to the other end. When the climber is at a height L above the anchor point, he
slips and falls a distance 2L, after which the rope becomes taut and stretches a distance x
as it stops the climber. Assume the rope obeys Hooke’s law with a spring constant k.
Using the work-energy theorem, obtain an expression for x in terms of m, k, g, and L
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5. A caf a roller coaster of radius R is going around the circular track under
only the influence of gravity.
a) Draw free body diagrams of the car when it is at the top and bottom of the
track.
b) Find an expression for the “apparent weight” of the car when it is at the top of
the track. (in terms of VT, m, g, and R)
c) Find an expression for the “apparent weight” of the car when it is at the bottom
of the track. (in terms of VT, in, g, and R)
d) what is the difference in these apparent weights (bottom minus top)
e) What is the critical velocity for VT so that it just stays in contact with the track?
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