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In the lab the other day, my friend and I constructed a "simple" gauss cannon consisting of 1-3 metal balls lying side by side on a bend surface and one magnetic ball lying next to one of the other balls. Then we had a final metal ball that was send down towards the remaining balls on the surface.

If we only place the magnetic ball on the surface and push a single ball down the slope towards the magnetic ball it appears that the two balls collide and freeze on the spot. The same happens is we let 1-2 balls lie alongside the magnetic ball and push a ball down towards them. The "system" of balls will slide only a little before coming to rest (We reasoned this very small displacement was due to a higher friction of the non-rolling ball system). Finally if we lay 3 balls and 1 magnetic ball on the surface and pushed the last ball down towards them we experienced the Gauss Cannon effect, where the final ball in the row was send away with high velocity.

How do you physically describe the three cases above? Why do the single magnetic ball just "drain" all the kinetic energy (and where does it go?)? Why will there be no repulsion of the outert magnetic ball if we use 1-2 balls alongside the magnetic ball on the surface? And why WILL there be a repulsion if we increase the number of balls to 3 (alongside the magnetic ball)?

Thanks!

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As the trigger ball is moving towards the magnetic ball, at a close enough distance the magnetic ball starts moving towards the trigger ball, these motions nearly counteract each other and most of the momentum is converted into friction, sound and heat as the combined pair move back slightly making it seem like they have not changed position. If you did this on a friction-less surface you would probably get some left over combined momentum. (If you had a very high speed trigger ball this would not be the case, or a very weak magnetic ball, or a high friction or non-frictional surface).

With two balls, there is more momentum left over because the magnetic ball is not free to accelerate towards the trigger ball, since it is now dragging additional mass and additional frictional forces. But the magnetic force is strong enough to prevent the attached dragged ball firing off. Again, use a weaker magnet or a stronger trigger force and you will see it detach and fire off.

With additional drag balls, there could be a number of affects happening to do with the weaker magnetic attachment to the magnetic ball due to distance, the greater drag forces meaning the magnetic ball can hardly move at all, and the entire system will act much more like a non magnetic series of balls, but with the additional trigger force of the momentum plus the magnetic attraction of the virtually fixed magnetic ball. If you tried this with a stronger magnet ball, you would need more drag balls before they could fire off. The sideways movement is much increased because of conservation of momentum, until the final drag ball has enough momentum transferred to it to escape the magnetic pull.

A verbose and probably confusing answer but everything you saw was a consequence, as you rightly thought, of momentum, friction, sound and heat energies. (Plus a negligible loss of energy radiating in the distortion of the magnetic field).

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