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Old Sep 18th 2016, 12:27 AM   #1
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Thermo Spoken Here's swing problem

On a previous post to this problem: Kids on a Swing | THERMO <i>Spoken Here!</i>

As far as I can tell the point of this problem was to point out that all gravitational potential energy is being converted to friction and therefore heat and the swing comes to rest at its equilibrium position.

So am I correct in assuming this problem is purely an exercise in static equilibrium and gravitational potential energy being lost to friction? I am not seeing any other subtle points jumping out at me here,
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Old Sep 18th 2016, 06:39 AM   #2
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There will be no energy lost to friction if there is no friction and friction only exist when at least one part is moving. So, no, this is not a "static equilibrium" problem.
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Old Sep 18th 2016, 10:36 AM   #3
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I would point out that there are other possible answers, depending on how the friction forces operate. In real life it's quite possible for the swing to "hang up" in a final position that is different from what you have calculated - if the torque about the pivot point due to gravity acting on the two boys is less than the value of friction force the swing stops. I think left unstated in your analysis is that you assume friction force diminishes with decreasing displacement, and/or velocity, much like in a classical mass/spring/damper problem, or one involving air resistance. But typically for a mechanical friction force one assumes it is constant independent of displacement. Therefore the swing may stop at some point other than the calculated static equilibrium point.
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Old Sep 18th 2016, 11:24 AM   #4
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Yeah, in response to @HallsOfIvy, I was not implying that this is *purely* a problem in static equilibrium but an exercise in static equilibrium *and* change in gravitational potential energy. I am guessing this could be calculated using the change in centre of mass of the swing system. The change in gravitational potential energy would be equal to the energy lost to friction.

as @ChipB pointed out, if the swing system "jams" before coming to complete rest then the centre of mass won't be at its lowest possible point before coming to rest. This would imply less energy lost to friction in that case.

Any other subtleties that I have missed here?

I have been spending some time studying differential equations and mechanical vibrations at the university of youtube. it seems that this is simply a damped simple harmonic motion system. Am I on right track here?
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