Phy 231
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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?
answer/question/discussion:
Answer: minimum tension: 0N, maximum tension: 3N.
• Assuming that the tension in the rubber band is 100% conservative (which is not actually the case) what is its elastic potential energy at the 10 cm length?
answer/question/discussion:
Answer: PE=dW=Force*ds=3N*.2m=.6N.
3 N is the maximum force, not the average force. Clearly the max force occurs only at the max length, and lesser forces act as length decreases.
N * m does not give you N, it gives you Joules.
• If all this potential energy is transferred to the kinetic energy of an initially stationary 20 gram domino, what will be the velocity of the domino?
answer/question/discussion:
Answer: .6N=.5(.020kg)vf^2-.5(.0020g)(0), vf^2=60m/s/s. vf=7.7m/s.
N / kg give m/s^2, but sqrt(m/s^2) is not m/s.
The energy is in Joules, not Newtons, and when expressed in this unit your calculation will yield the correct units.
• If instead the rubber band is used to 'shoot' the domino straight upward, then how high will it rise?
answer/question/discussion:
Answer: vf^2=v0^2+2ads. 59m^2/s^2=0+2(9.8m/s/s)(ds), ds=59m^2/s^2 / 19.6m/s^2 = 3m.
At the speed you assumed this is correct.
However you should think in terms of energy conversion, not in terms of the equations of motion. Elastic PE becomes KE which then becomes gravitational PE.
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25 minutes
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