Your 'cq_1_15.1' 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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Seed question 15 - 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?
answer/question/discussion:
At minimum (8cm) there is no tension exerted and at maximum (10cm) the tension is 3 N
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:
Force * ds
Force = 3N
Ds = 10cm-8cm = 2cm
But since I need to work in meters
2cm = .02m
3N * .02m = .06J of PE
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:
KE = 1/2m*v^2
KE = .06J
Very good. Your only error is that you used the maximum tension to calculate the work.
The minimum tension during the stretching process is 0 N, at the beginning when the length is 8 cm. The maximum is 3 N, at then end when the length is 10 cm. There is no reason to prefer the 0 N force to the 3 N force; they are both equally applicable to the stretching process. The reasonable conjecture is that the average force is equal to the average of these equally applicable forces, so the average force is (0 N + 3 N) / 2 = 1.5 N.
This will give you half the work you calculated here.
m = 20g but since J = Newtons * meters and Newton = kg * m/s^2 I think it would be easier if I change the mass from grams to kilograms. 20g = .02kg ( I think)
So…
.06J = ½ (.02kg)*v^2
.06J = .01kg * v^2
.06J/.01kg = 6 = v^2
v = 2.45m/s
If instead the rubber band is used to 'shoot' the domino straight upward, then how high will it rise?
answer/question/discussion:
Force of rubber band = 3N
PE of rubber band = .06J
Mass of domino = .02kg
Work done by domino = Fnet of all forces against the domino * displacement.
The forces against the domino include gravity and air resistance (no friction). I hope I can assume no air resistance, since I don’t know a standard for it and it isn’t stated. So Fnet against domino is force of gravity or .02kg * 9.8m/s^2 = 0.196N
Because the PE of the rubber band will be transferred to the domino as KE then the work done by the domino = .06J.
DW = fnet * ds
.06J = 0.196N * ds
Ds = .3 m = 30cm
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30 minutes.
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I realized when I was done that I should have been working in meters - not cm. While working I had already caught the changing g to kg, but I didn't catch the necessary conversion from m to cm until I finished.
Excellent. You had only one error (though that error affected a couple of your other answers); be sure to see my note so you'll understand the error.
&#Let me know if you have questions. &#