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Interesting Problem

This I feel is complete utter bollox. Relative to the hoop...the frame of referance known as the hoop is not an inertial frame. This means that the laws of physics are not invariant to the laws of physics in a rest frame (for those who did not do first year relativity... this means that classical change of reference frame laws of physics only work when you move from a frame of reference to another that is not accelerating relative to the first - else the maths doesn't work). So the only way to talk about the 'frame of reference' of the hoop (which is spinning - a type of constance acceleration) and using terms like 'energy' is by usage of something physists affectionately call General Relativity.
I think when you start talking about General Relativity the mass of the mass changes as it goes round...I'm not sure tho....
PS...Trust an imperial student to come up with that. >_<
Ask genius boy what his take on the question is...I heard he has a degree in physics already.

Reply 21

Gauss

OP

11

Technically the hoop should reach the stage where the mass reaches the lowest point of the hoop and is in contact with the floor.

However theoretically it can be shown that if one draws a straight line from the mass to the point of contact between the hoop and ground, then when the angle between this line and the ground goes below pi/4 the normal reaction between the hoop and the ground vanishes, i.e. the back of the hoop flips upwards. Thats why the "energy" goes missing.

This can be seen by considering a skier skiing on a slope that takes the path of a cycloid. As the skiier reaches the curve where the gradient approaches infinite he/she cannot remain on the path as they will fall off.

Anyhow, I consider myself more of a pure mathematician, and only found this problem interesting when introduced to it by Dr Frank Berkshire (Mehh, if you think this problem is complete bollox then take it up with Franky himself - I agree that the hoop is not an intertial frame, but we are not basing the laws of physics around this reference frame, just considering that the mass is never moving relative to the hoop).

Galois.

Reply 22

Mehh

8

Galois

but we are not basing the laws of physics around this reference frame, just considering that the mass is never moving relative to the hoop).

Galois.

I need a new definition of the term reference frame :confused:

Anyways, the term energy is just a random weird quantity we calulated and seems to stay constant reguardless. By definition in thermodynamics energy can't be destroyed or created. I fail to see where any energy is "stored" in the frame you suggested, thus thermodynamics appears to be broken (except only in a non inertial frame). Thus it doesn't seem to be a physics problem, hence I am confused why a term like 'energy' exists here.

Reply 23

Gauss

OP

11

Mehh

I need a new definition of the term reference frame :confused:

Anyways, the term energy is just a random weird quantity we calulated and seems to stay constant reguardless. By definition in thermodynamics energy can't be destroyed or created. I fail to see where any energy is "stored" in the frame you suggested, thus thermodynamics appears to be broken (except only in a non inertial frame). Thus it doesn't seem to be a physics problem, hence I am confused why a term like 'energy' exists here.

I tried to stress the fact that the energy does not get transferred (or stored) into the hoop.

The reason why the Conservation of Energy doesn't seem to hold is that the situation is impossible theoretically, yet praticially it should. The back of the hoop rises.

It's a nice paradox.

Galois.

Reply 24

El Stevo

11

sorry i'm late...;P is this situation analagous to a particle riding on a wave?

Reply 25

Gauss

OP

11

El Stevo

sorry i'm late...;P is this situation analagous to a particle riding on a wave?

Probably not so much a wave, although you can get away with saying a wave that moves in a cycloidian path.

Galois.

Reply 26

El Stevo

11

Galois

Probably not so much a wave, although you can get away with saying a wave that moves in a cycloidian path.

Galois.

water waves do that :smile:

Reply 27

Gauss

OP

11

El Stevo

water waves do that :smile:

Well there you go then :smile:

Reply 28

BCHL85

12

Well, I think K.E is not 0. If we consider motion of the mass, A, relative to the centre of the hoop, O, we'll see A is moving.
However, when I tried to find the energy of the mass relative to the ground, I ended up with paradox.
vOg is velocity of O relative to the ground.
vOg is always parallel to the groud.
vAg = vAO + vOg. (all are vectors)
Ofcourse vAO is perpendicular to OA.
When vAg = 0, -> vAO = -vOg
So vOA is parallel to the ground, i.e, OA is vertical.
That gives A is on the ground(if A is on the top, vAO = vOg)
It means when A is on the ground, velocity of A w.r.t the ground = 0, or at that time, K.E(A) = 0.
Also, P.E(A) = 0 at that instant -> total energy = 0 ??? Why it's like that? Did I have a mistake ?? :confused:

Reply 29

Newton

You have to consider both of the kinetic energies that the particle will have if we did not have a specific frame of reference, as the hoop turns obviously the displacement of it will result in linear kinetic energy, although if the hoop was our initertial frame this energy would not be considered, and so, the principle would imply that:

The total gravitational potential energy+ROTATIONAL kinetic energy=C.

Newton.

Interesting Problem

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