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## Homework Statement

http://img503.imageshack.us/img503/3535/11uv8.gif [Broken]

a cylinder with a given radius [tex]R[/tex] rolls to the right without slipping ([tex]\omega= \frac{v}{R}[/tex]). It hits a nail fixed to the pillar. find [tex]h[/tex], the height of the nail above the floor, in which the cylinder will roll back without slipping.

[tex]I=\frac{MR^2}{2}[/tex] for the cylinder.

- The nail applies lateral force only.

- the collision with the nail is ellastic, there's no loss of kinetic E whatsoever.

- express [tex]h[/tex] with [tex]R[/tex] only.

## Homework Equations

conservation of linear momentum, conservation of angular momentum.

[tex]J=r\times P[/tex]

## The Attempt at a Solution

OK.

there is no loss of kinetic energy. so if v is the speed before the collision and u is the speed of the ball after, [tex]v=-u[/tex].

Thus, there is impact as follows: [tex]2mv=\Delta P[/tex]

Also, I want the cylinder to roll backwards still with the term of not-slipping - [tex]\omega=\frac{v}{R}[/tex] so it's the same with angular momentum: [tex]2F\mu*R=\Delta J[/tex]

Now, I was thinking about solving this with [tex]J=(h-R)\times P[/tex], but then I don't know what to do with [tex]F\mu[/tex].

I'd appreciate help in this :)

Thanx.

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