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:
“Walked forth to ease my pain
Along the shore of silver streaming Thames,
Whose rutty bank, the which his river hems,
Was painted all with variable flowers,”
—Edmund Spenser (1552?–1599)
“Compare the history of the novel to that of rock ‘n’ roll. Both started out a minority taste, became a mass taste, and then splintered into several subgenres. Both have been the typical cultural expressions of classes and epochs. Both started out aggressively fighting for their share of attention, novels attacking the drama, the tract, and the poem, rock attacking jazz and pop and rolling over classical music.”
—W. T. Lhamon, U.S. educator, critic. “Material Differences,” Deliberate Speed: The Origins of a Cultural Style in the American 1950s, Smithsonian (1990)