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Another (probably very stupid) mechanics question

I initially got the correct answer to this question, but scribbled it out because I decided it did not take into account all the forces acting on the particle. The question I'm referring to is 8.b in the picture below:



My initial reasoning was as follows:
- At point A the EPE was 96.8J
- At point B the EPE was 28.8J
- Therefore, the loss of energy between A and B is 68J
- 68J/5m = 13.6N

The correct answer for the frictional force is 13.6N, but I thought that this was the sum of all resistive forces (not just friction) including the resistance caused by the elastic string. So I thought that the answer would be less than 13.6N. I mean, I'd expect the frictional force to be 13.6N if the particle became unattached from the string when it was released from A.

What's the flaw in this logic?
(edited 9 years ago)
I don't see what your logic is. What other resistive forces are you expecting there to be? The question is implicitly assuming that air resistance, for example, is negligible.

And what do you mean by "the resistance caused by the elastic string"? That doesn't make much sense to me.
Original post by atsruser
I don't see what your logic is. What other resistive forces are you expecting there to be? The question is implicitly assuming that air resistance, for example, is negligible.

And what do you mean by "the resistance caused by the elastic string"? That doesn't make much sense to me.


When you pull an elastic band back from a point, you feel resistance, right?
Original post by Brian Moser
When you pull an elastic band back from a point, you feel resistance, right?


The force that is extending the spring does work against the restoring force produced by the spring. However, when the spring is released, the restoring force does work on the mass at its end, and against any retarding forces, such as friction.

So when the spring is released, the force generated by the spring is in no way offering "resistance"; on the contrary, it's this force that is causing the motion to occur at all.
Original post by atsruser
The force that is extending the spring does work against the restoring force produced by the spring. However, when the spring is released, the restoring force does work on the mass at its end, and against any retarding forces, such as friction.

So when the spring is released, the force generated by the spring is in no way offering "resistance"; on the contrary, it's this force that is causing the motion to occur at all.


The fact that there is tension in the string when it reaches point B must mean that it is being stretched by the movement from point A to point B, doesn't it?

EDIT: Derp! Just realised how stupid I was being - the energy required to stretch the string is not lost from the system and is therefore already taken into account. My bad.
(edited 9 years ago)

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