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

Apollo 15 launches itself to the moon by means of the change in momentum of its fuel.

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.