# Machine Gun Momentum Question

## Homework Statement

A machine gun is attached at one end of a 10m long stationary flatcar and fires towards the other end. Determine the average recoil fore on the gun if it fires 240 rounds/min, the mass of the bullets is 25g and the muzzle velocity is 900m/s. If each bullet is in the 0.5 long barrel for 2x10^-3 seconds after discharge, estimate the peak force on the gun. If the bullets are absorbed by a target at the other end of the car, and the 10^3 kg flatcar moves without friction, how fast and in what direction does the flatcar move?

2. Relevants Equations:

240 rounds/min = 4 rounds/s

## The Attempt at a Solution

I found the average recoil force using this:

F=$$\Delta$$mv = (4 rounds/s)(0.025kg)(900m/s)=90 N

I'm actually not even sure if 25g is the mass of one bullet or the total mass, but surely 25g can't be the mass of all the bullets.

Then I'm not sure how to estimate the peak force. I know the max F is supposed to occur at 1x10^-3 s.

For the last part, I know that the total momentum is conserved

p=p'
0=(mass of car)(v of car) + (mass of bullets)(v of bullets)

so the car should be moving backwards...except the bullets are fired continuously over time, so i don't know what to put down for the mass. and i'm not even sure if the force applied by the bullets is constant, if it's not, then a is not constant? so i would have to take the deriv of a to find the speed of the car?

Any help is appreciated, thanks. =)

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