This may sound dumb to some folks, but lets say I fire a gun. 1000N of force goes into the bullet, and another 1000N of force goes into my body. Even if i strap the gun to the ground, it will just apply 1000N of force to move the earth by a tiny amount. Because of this, does it mean that it isn’t possible to have 2000N of force going to the bullet with the same parameters as before?
In: Physics
Both the gun and the bullet are pushed with the same force.
But the bullet ends up moving a *lot* faster as it’s smaller.
The amount of energy an object has increases with the square of speed, so the smaller the bullet compared to the mass of the gun, the greater proportion of kinetic energy ends up in the bullet compared to the gun.
For an example that gives some nice round numbers.
M16 muzzle velocity is pretty close to 1000m/s with a bullet mass around 4g (0.004kg) – lot of variation by ammo type but those make nice working numbers.
That’s 4kgm/s of momentum (mass x velocity), and around 2000J of energy (0.5 x mass x velocity^2)
An M16 has a mass of around 4kg. So that 4kgm/s it receives due to Newton’s Third Law will move it at 1m/s. That’s 2J.
Now, not all the energy ends up in the round as there is wastage elsewhere, but in terms of efficiency from Newton’s Third Law, that gives you 99.9%. That’s one of a number of reasons why shooting a gun doesn’t kill you with the recoil.
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