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PHY 121
Your 'cq_1_14.1' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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A rubber band begins exerting a tension force when its length is 8 cm. As it is
stretched to a length of 10 cm its tension increases with length, more or less steadily,
until at the 10 cm length the tension is 3 Newtons.
Between the 8 cm and 10 cm length, what are the minimum and maximum tensions, and what
do you think is the average tension?
answer/question/discussion: ->->->->->->->->->->->-> : ->->->->->->->->->->->-> :
Minimum tension is 0 Newtons; maximum tension is 3 Newtons. This would make the average
tension 1.5 Newtons.
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How much work is required to stretch the rubber band from 8 cm to 10 cm?
answer/question/discussion: ->->->->->->->->->->->-> : ->->->->->->->->->->->-> :
work = F * `ds
3N * 2 cm = 3 N * .02 cm = 0.06 Joules
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The 3 N force is exerted only at the 10 cm length. It is not applied through the entire
2 cm.
You need to use the average force to get this result.
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During the stretching process is the tension force in the direction of motion or
opposite to the direction of motion?
answer/question/discussion: ->->->->->->->->->->->-> : ->->->->->->->->->->->-> :
The tension force would be opposite the direction of motion. The motion is going out
and the tension is pulling it back.
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Does the tension force therefore do positive or negative work?
answer/question/discussion: ->->->->->->->->->->->-> : ->->->->->->->->->->->-> :
That means that the tension force would do negative work.
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The rubber band is released and as it contracts back to its 8 cm length it exerts its
tension force on a domino of mass .02 kg, which is initially at rest.
Again assuming that the tension force is conservative, how much work does the tension
force do on the domino?
answer/question/discussion: ->->->->->->->->->->->-> : ->->->->->->->->->->->-> :
The tension force would do -.06 Joules of force
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Assuming this is the only force acting on the domino, what will then be its kinetic
energy when the rubber band reaches its 8 cm length?
answer/question/discussion: ->->->->->->->->->->->-> : ->->->->->->->->->->->-> :
When the rubber band reaches its 8 cm length the potential energy is .06, so kinetic
energy would be -.06.
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At this point how fast will the domino be moving?
answer/question/discussion: ->->->->->->->->->->->-> : ->->->->->->->->->->->-> :
.5mv^2 = 0.06 J
mv^2 = 2 * 0.06 J
v^2 = .12 J / m
v^2 = .12 J / .02 kg
v^2 = 6
v = 2.4 cm/s
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I don't see any modifications here.
In any case the average force is 1.5 N so the work is 3 N cm which is .03 J, and the velocity will be about 1.7 cm/s.
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