class 051205
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Intro Prob Set 8: Remainder of Problems
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Read Chapter 7 Sections 5-6 and
8
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Chapter 7 Problems 47, 48, 50
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Read Chapter 8 Sections 1-4
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Chapter 8 Problems 6, 9, 16, 20,
23, 26
Chapter 8 Problems 52, 53, 58,
61, 65
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Read Chapter 9, Sections 1-4
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Chapter 9 Problems 6, 13, 19,
24, 30-33
Intro Prob Set 9: Problems 7-11
Intro Prob Set 9: Problems 12-18
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Read Chapter 11, Sections 1-4
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Chapter 11 Problems 6, 14, 19,
24, 29, 31
Experiment:
Rotate a strap with magnets located near the ends of the strap
on a die, using a rubber band string to apply a nearly uniform force over a
short distance.
Assume the rubber bands have a 'force constant' of
k = (.7 N / cm) / (number of bands in string).
Determine the following:
- the force and the torque exerted by the bands,
- the angular displacement through which the force is exerted
- the angular displacement through which the system coasts as
it comes to rest
Organize your data into a table and submit one table from each
group.
Determine the force behavior of your rubber band system:
- Suspend 2, 4, 6, 8, ... dominoes and measure the length of
your rubber band chain for each
- Each domino has a mass of 18 grams. Use this to
figure out the force exerted by the rubber band at each length and graph force
vs. length.
- Figure out the area beneath your force vs. length graph
from the unstretched length to the length at which the rubber band was
released in the rotation experiment.
Analyze your system:
- Figure out the initial velocity (the velocity immediately
after the rubber band releases) of your system for each trial, using the
angular acceleration you previously observed for this system (observed angular
accelerations range from about .3 to about .6 rad/s^2, depending on whom you
ask).
- The moment of inertia of your system is about 18,000 g
cm^2. Figure out its initial KE (the KE immediately after the rubber
band releases).
- Compare this result with the area beneath your force vs.
length graph.
Figure out torque vs. angular position:
- Graph the torque exerted by the rubber band on the system
vs. the angular position of the system, from the initial position to the
position at which the rubber band releases.
- Find the area beneath this curve and see how it compares
with previous results.
Using a new rubber band system consisting of thin rubber
bands:
- Suspend 1, 2, 3, 4, 5 and 6 dominoes and measure the length
of the system for each number.
- Obtain your force vs. length graph for this system.
- Determine the natural oscillatory frequency of the system
when it supports 1, 2, 3 and 4 dominoes in a 'bag' made from a single sheet of
8.5 x 11 paper.
- Fit the best possible straight line to your force vs.
length graph and use this line to determine the approximate force constant of
your system.
- Compare your oscillatory frequencies to the ideal
frequencies predicted by omega = sqrt(k / m), where k is the force constant, m
the mass of the suspended dominoes, and omega the angular frequency of the
harmonic motion.
Graph oscillatory frequency T vs. suspended mass M (the paper
bag has mass 5 grams).
Graph log(T) vs. log(M), fit the best possible straight line
to your data and determine the slope and vertical intercept of your straight
line. After you submit your results Monday we'll figure out what this
information tells you.
On your first trial, how long was the rubber band chain before
you released it, and how long was it when it slipped off the peg and stopped
exerting a force on the system?
When you suspended dominoes from the rubber band chain, you
got a graph of force vs. length. What is the force corresponding to the
length of the chain before release? What is the area beneath the force vs.
length curve up to that point?
What was the angular displacement of the system between
release and the point where the rubber band slipped off?
On your first trial, what was the total angular displacement
of the system before it came to rest?
Assuming angular acceleration of magnitude .5 rad/s^2, what
was the initial angular velocity of the system?
What therefore was the initial angular KE of the system
(recall moment of inertia is about 18,000 g cm^2)?
What is average torque * angular displacement for the torque
exerted by the rubber band?