- #1
nathangrand
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1. Homework Statement
A cylindrical hoop rests on a rough uniform incline. It is released and rolls
without slipping through a vertical distance h0. It then continues up a perfectly
smooth incline. What height does it reach?
2. Homework Equations
GPE=mgh
Rotational Ke =0.5Iw2
Linear Ke = 0.5mv2
Moment of inertia of the hoop, I = mr2 where r is the radius, and m the mass
Friction Force = UN where U is the coefficient of friction, N the normal reaction force
3. The Attempt at a Solution :
Ok..I'm sort of thinking now that at bottom of the slope, mgh0=Ke[Rot] +Ke[Lin]
mgh0={{0.5Iw2}}+0.5mv2
mgh0= {{0.5mv2}} + 0.5mv2 by using v=wr and equation for I
So half the energy is as rotational kinetic energy?
This rotational energy will have to be dissipated as the hoop rolls up the other slope and comes to rest
meaning that only half the energy -- the translational half -- is available for climbing the slope
and hence why the hoop only reaches half the height it started at (I have the answers!)
Can't help but thinking this is a bit of a rubbish explanation and very fudged..can someone tell me if my thinking is right and explain?
Any help appreciated as always guys :)
A cylindrical hoop rests on a rough uniform incline. It is released and rolls
without slipping through a vertical distance h0. It then continues up a perfectly
smooth incline. What height does it reach?
2. Homework Equations
GPE=mgh
Rotational Ke =0.5Iw2
Linear Ke = 0.5mv2
Moment of inertia of the hoop, I = mr2 where r is the radius, and m the mass
Friction Force = UN where U is the coefficient of friction, N the normal reaction force
3. The Attempt at a Solution :
Ok..I'm sort of thinking now that at bottom of the slope, mgh0=Ke[Rot] +Ke[Lin]
mgh0={{0.5Iw2}}+0.5mv2
mgh0= {{0.5mv2}} + 0.5mv2 by using v=wr and equation for I
So half the energy is as rotational kinetic energy?
This rotational energy will have to be dissipated as the hoop rolls up the other slope and comes to rest
meaning that only half the energy -- the translational half -- is available for climbing the slope
and hence why the hoop only reaches half the height it started at (I have the answers!)
Can't help but thinking this is a bit of a rubbish explanation and very fudged..can someone tell me if my thinking is right and explain?
Any help appreciated as always guys :)
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