momentum(Urgent 20points!!!)

2010-03-07 8:20 pm
Momentum of a system is only conserved when no external forces act on it. However when a rocket is launched, it experiences force of gravity which is an external force. Why total momentum of rocket and the exhaust gases are conserved?

回答 (1)

2010-03-07 9:47 pm
✔ 最佳答案
Probably, I think you refer to the use of the momentum conservation equation as follows:

M.V = m.v
where M is the mass of rocket, with velocity V
m is the mass of exhaust gas, and v is the speed of exhaust.

In this equation, you may not be aware that the speed of exhaust is actually the speed of the exhaust relative to the rocket. It is not the absolute speed (relative to ground). That is to say, in applying the above equation, one refers to the total momentum referenced to the centre of mass of rocket and gas system.

Gravity acts on the system at its centre of mass and would alter the momentum of the centre of mass of the whole system. But when reference is made to the centre of mass itself, gravity would not cause any effect.

Just think of an example of a boy staying in a lift which is under free fall. If the boy throws out a ball from his hands inside the lift, he would find himself to recoil. He also finds that momentum conservation is followed should he measure his recoil speed and the speed of the ball inside the lift. These measured speeds are, apparently, speeds relative to the falling speed of the lift, and are not the actual speeds relative to the ground.


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