Conservation of energy and momentum in a gauss gun

[billy_button]

Hi, I'm doing a project on the Gauss gun and Newton's cradle. I'm trying to produce little models in MatLab and have come across some problems. Namely with the gauss gun, using different types of balls, hollow and solid (I've not even got round to adding acceleration from a magnet yet).

Currently I have a hollow ball hitting the pack and releasing a solid ball at the end. I have calculated the velocities of both, assuming energy is conserved, from the linear and rotational KE's, resulting in the solid ball leaving the pack with a higher velocity than the hollow ball hit it with. This means however, that momentum has not been conserved (off the top of my head I think the solid ball gained momentum??).

I'm now assuming that it must really be conserved and I need to look at the torque applied to stop and start each ball? Does this sound right and if so 1)how do I calculate the torque or angular acceleration at the instant of the collision? and 2)would the same torque be applied to the ball leaving the pack?

For 'ease' of calculations I have assumed perfectly elastic collisions and no losses due to friction/air resistance.

I'd be most appreciative of any help.

 

[mfb]

Why would you use torque in a linear arrangement of balls? Torque around what?

Momentum must be conserved, this should be one of the constraints in the equations, for each collision.