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)
Famous quotes containing the words variable and/or mass:
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Whose rutty bank, the which his river hems,
Was painted all with variable flowers,”
—Edmund Spenser (1552?–1599)
“It is a mass language only in the same sense that its baseball slang is born of baseball players. That is, it is a language which is being molded by writers to do delicate things and yet be within the grasp of superficially educated people. It is not a natural growth, much as its proletarian writers would like to think so. But compared with it at its best, English has reached the Alexandrian stage of formalism and decay.”
—Raymond Chandler (1888–1959)