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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.
** CQ_1_14.1_labelMessages **
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.
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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: ->->->->->->->->->->->-> :
The minimum tension seems to be 0 Newtons while the maximum tension seems to be at 3 Newtons. This would make the average tension to be 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: ->->->->->->->->->->->-> :
First I am going to convert centimeters to meters. 2 cm * (1 m / 100 cm) = 0.02 m
`dwnet = Fnet * `ds = 3 Newtons * 0.02 m = 0.06 Joules
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You know that minimum and maximum tensions.
Your calculation here assumes the maximum tension throughout. You could equally well have chosen the minimum tension, which would have given you a result of 0 Joules.
The work is found by multiplying the average tension, not that max or min tension, by the displacement. In this case you don't know for sure what the average tension is, since you don't know how the tension varies with length. It is reasonable, without further information, to use the average of the minimum and maximum tensions.
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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: ->->->->->->->->->->->-> :
I think that the tension force is in the direction of motion.
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If you pull on the end of the rubber band, the tension in the rubber band pulls back, in the direction opposite your pull. Since stretching the rubber band required a pull in the direction of motion, the tension is in the opposite direction.
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Does the tension force therefore do positive or negative work?
answer/question/discussion: ->->->->->->->->->->->-> :
I think the tension force does positive 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.
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Again assuming that the tension force is conservative, how much work does the tension force do on the domino?
answer/question/discussion: ->->->->->->->->->->->-> :
I believe it would do the same amount of work before of 0.06 Joules.
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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: ->->->->->->->->->->->-> :
The `dKE is equal to the `dW, so I think it would have a kinetic energy equal to 0.06 Joules.
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At this point how fast will the domino be moving?
answer/question/discussion: ->->->->->->->->->->->-> :
Fnet = m * a
a = Fnet / m = 3 Newtons / .02 kg = 150 m/s^2 (which sounds a bit extreme of a number for this problem)
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It's very good that you're thinking about what is reasonable.
This is the acceleration at the maximum tension, which is 15 times the acceleration of gravity. You are used to lesser accelerations, on the order of the acceleration of gravity, so this might well seem like an unreasonable result. However as it turns out it is very easy to exert a 3 Newton force (that's less than a pound) on a 20 gram mass. The acceleration you would get significantly exceeds that of gravity, and this is in fact a reasonable result.
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Check my notes. You'll understand, but also read through the discussion at the link below. No need for a revision unless you have questions.
&#See any notes I might have inserted into your document, and before looking at the link below see if you can modify your solutions. If there are no notes, this does not mean that your solution is completely correct.
Then please compare your old and new solutions with the expanded discussion at the link
Solution
Self-critique your solutions, if this is necessary, according to the usual criteria. Insert any revisions, questions, etc. into a copy of this posted document. Mark any insertions with &&&& so they can be easily identified.If your solution is completely consistent with the given solution, you need do nothing further with this problem. &#
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