- #1

steve B. 98

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## Homework Statement

A cylindrical rod of length w carries a current I as shown(perpendicular to B) and is bathed in a field B perpendicular to the plane in which is a " shaped rail. The rod rolls without slipping on the rails, its length perpendicular to the two parallel rails and equal to the space between them. It starts at rest and rolls off after going a distance L. Show that its exit velocity is ##v = \sqrt{ \frac{4BLIw}{3M}}##

## Homework Equations

##F=B \times I w=BIw##

##\tau=r \times F##

##\tau=I\alpha##

## The Attempt at a Solution

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I start by taking the torque

##\tau=r \times BIw##

Using the moment of inertia for a cylinder I get

##\tau=Mr^2\alpha /2 ##

##\alpha=\frac{2BIw}{Mr}##

since the problem was rolling without slipping we get.

##a=\frac{2BIw}{M}##

Using ##v^2=0^2+2as##

##v=\sqrt{\frac{4BIwL}{M}}##

But this is off by a factor of ##\frac{1}{\sqrt{3}}##.

What did I do wrong, and some hints toward the solution would be nice.