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radagast_
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Homework Statement
http://img503.imageshack.us/img503/3535/11uv8.gif
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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