User:Inconspicuum/Physics (A Level)/Rockets, Hoses and Machine Guns

We have already seen that force is the rate of change of momentum. This applies to continuous flows of momentum as well as to collisions:

$$F = \frac{dp}{dt} = v\frac{dm}{dt}$$

If I have a machine gun, explosions give the bullets of mass m momentum, causing them to move at a velocity v. This occurs several times each second - the momentum of the bullets is changing, and so there is a roughly continuous force acting on them. Momentum, of course, must be conserved. This results in a change in the momentum of the gun each time it fires a bullet. Overall, this results in a roughly continuous force on the gun which is equal and opposite to the force acting on the bullets.

If I have a tank of water and a hose, with a pump, and I pump the water out of the tank, a similar thing occurs - a force pushes me away from the direction of flow of the water. This force is equal to the flow rate (in kgs-1) of the water multiplied by its velocity. Bear in mind that 1 litre of water has a mass of about 1kg.

Rockets work on this principle - they pump out fuel, causing it to gain momentum. This results in a thrust on the rocket. When designing propulsion systems for rockets, the aim is to give the fuel as high a velocity per. unit mass as possible in order to make the system fuel-efficient, and to get a high enough change in momentum.