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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?
The minimum tension is when the length is 8cm and the maximum is when the tension is at length 10cm. The tension at 10cm is 3N. At length 8cm, the rubber band has not moved so the force is 0N
answer/question/discussion:
How much work is required to stretch the rubber band from 8 cm to 10 cm?
Work = force * displacement
Work = 3N * 10cm
The 3 N force is achieved only at the end of the stretch. The rubber band does not exert a 3 N force for the entire distance.
The force is not exerted through a 10 cm displacement. The displacement is only the 2 cm from the 8 cm length to the 10 cm length.
Work is the product of the force in the direction of the displacement and the displacement.
To stretch the rubber band requires a displacement of the one or both ends, with stretching forces exerted in the directions of any displacements. So to stretch the rubber band requires positive work.
The total displacement is 10 cm - 8 cm = 2 cm.
The force changes linearly with displacement, from 0 N to 3 N, so the average force is (0 N + 3 N) / 2 = 1.5 N.
The work is therefore force * displacement = 1.5 N * 2 cm = 3.0 N * cm.
Work =30J
answer/question/discussion:
During the stretching process is the tension force in the direction of motion or opposite to the direction of motion?
Tension force opposes the direction of motion
answer/question/discussion:
Does the tension force therefore do positive or negative work?
Tension force will actually do no work because it deals with Newtons third law. Tension will go both ways.
If an end of the rubber band moves while under tension, then the tension force does work. By Newton's third law the work done by the tension force is equal and opposite to the force exerted by the stretching agent against the tension, so one will do positive work and the other negative; but that doesn't make either zero.
You said above that the tension force opposes the direction of motion. It therefore exerts a force along the line of motion and does work. Is the work positive or negative?
answer/question/discussion:
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?
I do not know how to calculate this problem
This should be equal and opposite to the work done by tension as the rubber band was stretched.
answer/question/discussion:
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?
KE = 1/2mv^2
Use whatever v was found to be. Everything else we already know.
answer/question/discussion:
At this point how fast will the domino be moving?
I do not know how to solve this problem.
answer/question/discussion:
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15 minutes
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