Physics of recoil

[dragonbait1a]

I'm trying to understand recoil (and physics generally) better. So I was thinking about the recoil of a 10mm auto round (because it is a nice round number caliber).

Assume a theoretical testing rig. A single shot firing apparatus, with no moving parts other then the bullet leaving the barrel, that recoils along a friction-less track in a vacuum. (Just to eliminate variables)

What would be the math to determine how far the apparatus would move for a given weight? How much weight would it have to have to not move at all? Round answers are fine.

Since it's a science question, I'm trying to express it in metric quantities. I thought that it's be nice and easy, but I just don't have the math to figure it out.

Rough stats:
a 12gram bullet with a radius of 5mm travelling 410 meters per second creating 987 joules.

http://en.wikipedia.org/wiki/10mm_Auto

Thanks for any input in advance.
RGB

[five.five-six]

it's the 3rd law of physics

[theicecreamdan]

frictionless track in a vacuum --> It will move forever.

For it to not move at all, its mass would need to be infinite.

[RobinGoodfellow]

Physics Question

It's been a while, but here goes ...

Assume conservation of momentum. The total momentum of the system prior to firing the bullet equals the total momentum of the system after firing the bullet.

P = mV, where

P = momentum (a vector)
m = mass
V = velocity (a vector)

But, velocity is zero before firing, so it is zero after firing.

Letting m1 = bullet mass (12 g), m2 = gun mass, and V1 = 410 m/s,

12 * 410 = m2 * V2

4920 / m2 = V2

So the velocity of the gun would be 4920 / the gun mass in grams.

For V2 = 0, m2 would have to be infinitely large if there is no friction.

[dragonbait1a]

RE Infinite movement.
I said I didn't know what I was doing

So if the gun was 4920g, it would move at ~1 meter a second?

RGB

[CaliforniaLiberal]

Your mechanism moving on a frictionless track in a vacuum would move forever. It would have to weigh an infinite amount to not move at all.

Perceived recoil is a whole different kettle of fish.

Generally I think you could say that the energy of the stuff leaving the barrel will equal the energy of the recoil. But the transfer of recoil energy can be stretched out over a longer period of time than the time the bullet travels through the barrel so perceived recoil is less than it would be if it were applied instantly.

http://www.chuckhawks.com/recoil_table.htm

http://en.wikipedia.org/wiki/Recoil

So it's your job now to read and figure this all out and come back and give us all a clearly understandable explanation, cause were a little fuzzy on precisely how it works.

[dieselpower]

frictionless track in a vacuum --> It will move forever.

For it to not move at all, its mass would need to be infinite.

so Gravity doesn't exist in a vacuum...really, are you sure

[Fjold]

In a frictionless world with no air resistance, the easiest way to look at it is to ratio the energy.

1/2 the mass of the bullet x the velocity of the bullet squared = 1/2 the mass of the gun x the velocity of the gun squared.

That will give you the velocity of the gun in the theoretical world.

[CaliforniaLiberal]

so Gravity doesn't exist in a vacuum...really, are you sure

So this frictionless track surrounded by vacuum is arranged so that the gun moves opposite to a gravitational force? I can't find that in the original post, are you sure that it's not set up far from gravitational influence or set up so that the track follows a curve so that it is always at a 90 degree angle to the force of gravity?

Please explain how the frictionless vacuum track is set up so that it is influenced by gravity.