What is the acceleration of a rod in a rail gun?

[matt747]

Hi I'm trying to come up with an expression for the accleration of the rod in Rail Gun.

The conducting rod is free to slide on two parallel rails with negligible friction. At the right end of the rails, a voltage source of strength "V" in series with a resistor of resistance "R" makes a closed circuit together with the rails and the rod. The rails and the rod are taken to be perfect conductors. The rails extend to infinity on the left.

There is a uniform magnetic field of magnitude B, pervading all space, perpendicular to the plane of rod and rails. The rod is released from rest, and it is observed that it accelerates to the left.

I'm trying to find the acceleration based on the following variables:

V (voltage)
B (magnetic field)
v (velocity of the rod)
L (Length of the rod)
R (Resistance)
m (mass)

http://mp.pearsoncmg.com/probhtml/16467_a.jpg

Thanks,

Matt

 

[kuruman]

You need to find the current $I$ in the rail using Ohm's law and then find the magnetic force on the rail using $\vec F=I\vec L\times \vec B$. Finally, Newton's law will give you the acceleration. If you have seen Faraday's law, you need to write a differential equation taking the back emf into account.