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:
“There is not so variable a thing in nature as a lady’s head-dress.”
—Joseph Addison (1672–1719)
“Like Freud, Jung believes that the human mind contains archaic remnants, residues of the long history and evolution of mankind. In the unconscious, primordial “universally human images” lie dormant. Those primordial images are the most ancient, universal and “deep” thoughts of mankind. Since they embody feelings as much as thought, they are properly “thought feelings.” Where Freud postulates a mass psyche, Jung postulates a collective psyche.”
—Patrick Mullahy (b. 1912)