Conservation of momentum / energy problem?
In my answer to a question here, involving firing a gun in space, I am thinking I may have been incorrect about something.
If you were to have a large vacuum chamber and fire a bullet while standing on the floor, and another while sitting on a magnetically levitated platform, would the muzzle velocities of the two bullets be the same (assuming identical mass slugs and identical charges in the cartridges)?
I'm not sure whether kinetic energy imparted to the marksman and the bullet are the same, or if it's momentum. I know that regardless, momentum must be conserved, but I forget how to calculate the amount of momentum in this situation...
I used the following values in my example:
mass of bullet: 115grain =~ 0.00745kg
muzzle velocity of bullet: 360m/s (this is a typical value when fired within the atmosphere, but it doesn't matter for my question)
Anyone less rusty than me in dynamics able to straighten me out on this one?
Forgot to list assumed mass of marksman = 100kg (including the mass of the platform)
My gut tells me that the bullet fired while standing will be much faster than the one fired from the mag-lev platform, but I can't come up with the reasoning for it.
magnetically levitated platform isolates the shooter from the earth (simulating floating in free space). Standing with a solid footing means that the bullet is pressing against the mass of the earth.