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Seed question 14.1
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:
This is either an easy question or a tricky one. The rubber band begins exerting a tension force at 8cm so the minimum force would be zero and the max at 10cm is 3N. The average tension force would be (0N + 3N )/2 = 1.5N
However, the question asks BETWEEN 8 and 10cm, so the minimum wouldn’t be zero, because it starts exerting a force at 8. I don’t know what the smallest unit of measure for a Newton would be, but the minimum would be zero + the smallest unit of measure for a Newton.
How much work is required to stretch the rubber band from 8 cm to 10 cm?
answer/question/discussion:
I think you would use the end force to calculate this.
DW = Fnet * ds
Change cm to m (2cm = .02m)
DW = 3N * .02m = .06J
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 in the opposite direction of the motion during the stretching process. The tension is trying to return the rubber band to rest.
Does the tension force therefore do positive or negative work?
answer/question/discussion:
If the motion during the stretching process is considered positive, then the tension force is negative.
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?
As long as it is conservative and there are no other forces acting on the rubber band then the amount of work done by the rubber band on the domino would be the same as the amount of work done on the rubber band to stretch it (conservable).
DW = 3N * .02m = .06J
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 same as above. .06J
At this point how fast will the domino be moving?
answer/question/discussion:
KE = 1/2m * v^2
.06J = ½(.02kg) * v^2
.06J = .01 * v^2
6 = v^2
2.45 m/s^2 = vf
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<30mins
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