Interesting Problem Watch

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Gauss
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#1
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Say we have a very very light hoop (assume it has no mass) and we place a mass on it. The hoop moves from left to right. Also assume the ground is infinitely rough, so that the hoop rolls and doesn't slip.

When the mass is directly above the normal reaction between the hoop and ground it has P.E. mgh. The mass is not moving, it's simply "placed" on the hoop. So total energy is mgh (since KE = 0).

When the hoop moves enough, so that the mass is directly at the lowest point of the hoop, it has zero PE. Since it's not moving, it has no KE.

But where has the mgh gone? Energy is conserved of course, so where did it go? :p:

Galois.
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SsEe
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#2
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Do you mean that somebody holds the hoop and turns it 180 degrees or it's given a nudge when the mass is at the highest point so it rolls by itself? If the first then there's probably energy changes with the person moving it (don't know what though). If the second then wouldn't it keep moving (so have KE=mgh when the mass is at the lowest point)? Surely? I'm not 100% sure what you're asking.
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Gauss
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#3
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(Original post by SsEe)
Do you mean that somebody holds the hoop and turns it 180 degrees or it's given a nudge when the mass is at the highest point so it rolls by itself? If the first then there's probably energy changes with the person moving it (don't know what though). If the second then wouldn't it keep moving (so have KE=mgh when the mass is at the lowest point)? Surely? I'm not 100% sure what you're asking.
Sorry for the ambiguity.

No body has pushed the hoop, the hoop is not accelerated. It is moving with constant velocity to the right.

The mass is not moving itself, though it's on something that's moving.

Galois.
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naivesincerity
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#4
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(Original post by Galois)
Say we have a very very light hoop (assume it has no mass) and we place a mass on it. The hoop moves from left to right. Also assume the ground is infinitely rough, so that the hoop rolls and doesn't slip.

When the mass is directly above the normal reaction between the hoop and ground it has P.E. mgh. The mass is not moving, it's simply "placed" on the hoop. So total energy is mgh (since KE = 0).

When the hoop moves enough, so that the mass is directly at the lowest point of the hoop, it has zero PE. Since it's not moving, it has no KE.

But where has the mgh gone? Energy is conserved of course, so where did it go? :p:

Galois.

Why does it have no K.E??? When the mass reaches the bottom the PE has gone down to zero and the KE has gone to mgh surely???

Fascinating fact:Galois died very young in a swordfight/dual, having already devised methods for solving polynomials by radicals, and Inventing group theory..
Clever Bloke!!!
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Gauss
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#5
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(Original post by naivesincerity)
Why does it have no K.E??? When themass reaches the bottom the PE has gone down to zero and the KE has gone to mgh surely???
The mass is fixed on the hoop. It has no KE.

The mass has no velocity itself.
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naivesincerity
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(Original post by Galois)
The mass is fixed on the hoop. It has no KE.

The mass has no velocity itself.
Then the KE's gone to the hoop??...oh god i should know this!!!
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Gauss
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#7
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(Original post by naivesincerity)
Then the KE's gone to the hoop??...oh god i should know this!!!
None of the energy is transfered into the hoop im afraid.

Hint: Consider the path that the mass makes.
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Bezza
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#8
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(Original post by Galois)
The mass is fixed on the hoop. It has no KE.

The mass has no velocity itself.
If the mass is moving, it has KE, regardless of what it's attached to
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Gauss
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#9
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(Original post by Bezza)
If the mass is moving, it has KE, regardless of what it's attached to
No I was told in this case (when presented with the problem) that the mass has no KE.
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Bezza
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#10
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(Original post by Galois)
No I was told in this case (when presented with the problem) that the mass has no KE.
how can a moving mass have no KE? Do you mean initially or something?
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naivesincerity
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#11
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OH **** it ,its too late at night for this !!! havent done any maths for ages
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Gauss
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#12
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(Original post by Bezza)
how can a moving mass have no KE? Do you mean initially or something?
You're considering relative Energy.

The mass, relative to us, is moving and has KE. But the mass itself, relative to the hoop, is fixed and never moving. It gains PE when reaches a certain point, but then loses it at another point. Where does the enery go?
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naivesincerity
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#13
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(Original post by Galois)
You're considering relative Energy.

The mass, relative to us, is moving and has KE. But the mass itself, relative to the hoop, is fixed and never moving. It gains PE when reaches a certain point, but then loses it at another point. Where does the enery go?
I dont get this..The mass has potential energy at the top point, at the bottom it loses it again,its kinetic energy is zero relative to the hoop, and its potential energy relative to the hoop is the same as it is relative to us, as the hoop has no potential energy,its on the ground...
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Gauss
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#14
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(Original post by naivesincerity)
I dont get this..The mass has potential energy at the top point, at the bottom it loses it again,its kinetic energy is zero relative to the hoop, and its potential energy relative to the hoop is the same as it is relative to us, as the hoop has no potential energy,its on the ground...
Yes exactly...so what don't you get?

Try and see what happens to the normal reaction of the hoop with the ground, and the path the mass makes. That should help.
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Bezza
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#15
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(Original post by Galois)
You're considering relative Energy.

The mass, relative to us, is moving and has KE. But the mass itself, relative to the hoop, is fixed and never moving. It gains PE when reaches a certain point, but then loses it at another point. Where does the enery go?
Relative to the hoop it's potential energy will always be the same too then won't it? I don't really understand what the question is - relative to us, it's PE changes and so does it's KE so what's the problem?
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Gauss
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#16
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#16
(Original post by Bezza)
Relative to the hoop it's potential energy will always be the same too then won't it? I don't really understand what the question is - relative to us, it's PE changes and so does it's KE so what's the problem?
It's PE will always be changing relative to the hoop since it's circulating around the centre.

The problem is is that at certain parts of the motion the energy dissapears, and then re-apears, which is nonsense.
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naivesincerity
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#17
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When the hoop moves enough, so that the mass is directly at the lowest point of the hoop, it has zero PE(the mass you mean?). Since it's not moving, it has no KE( moving relative to the hoop?).
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Bezza
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#18
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(Original post by Galois)
It's PE will always be changing relative to the hoop since it's circulating around the centre.

The problem is is that at certain parts of the motion the energy dissapears, and then re-apears, which is nonsense.
umm, not really sure about that. pe = mgh is gravitational potential energy which is relative to the ground

what's the answer then - explain it to us all
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naivesincerity
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#19
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Well the only conclusion i can come to is that as "h" decreases, and Energy(for the mass relative to us=KE+PE), then PE of the mass relative to us decreases, KE of the mass relative to us increases and is transferred to the hoop!
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naivesincerity
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#20
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Might as well tell us..so much for Galois, thought he was a pure mathematician!!! mechanics was my worst point in maths!!!
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