Variable Mass
When a system expels mass in one direction, the force the expelled mass applies to the system is called thrust; the force the system applies to the mass being expelled is of equal magnitude but opposite direction.
Consider for example a rocket. The momentum of the rocket (including the remaining fuel) changes due to two effects: one is the applied thrust, the other one is the reduction of mass:
where
- p is the momentum of the rocket including the remaining fuel
- dp is the infinitesimal change of the momentum of the rocket including the remaining fuel; it is the negative of the momentum of the mass being expelled, just after expulsion (the total momentum does not change)
- m is the mass of the rocket including the remaining fuel (it decreases when mass is expelled)
- dm is the infinitesimal change of the mass of the rocket including the remaining fuel, so the negative of the mass being expelled
- v is the velocity of the rocket
- ve is the velocity of the just expelled mass relative to the rocket (effective exhaust velocity), hence:
- ve + v is the velocity of the just expelled mass
- F is the thrust
- dJ is the infinitesimal impulse exerted on the rocket
Read more about this topic: Impulse (physics)
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