Systems of Particles
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Conservation of Momentum in a System of Particles: |
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The momentum can be expressed in terms of the CM
as well. For the system of many
particles the total momentum would be p = p1+p2+..….+pn = m1v1+m2v2+…..+mnvn.
Then the
velocity of center of mass would be given by,
vcm = (m1v1+m2v2+…..+mnvn)/M.
Here, M is the total mass of the system. Thus the momentum of the whole system is p = Mvcm.
Then the external force acting on the system can be written as:
Now, for no external force we can write:
Then the total momentum is constant, i.e. p = constant. Hence the momentum is conserved for a
many particle system as well.
Systems of Variable Mass:
would involve the differentiation of mass as well. Now, the net force is given by,
The best example for a variable mass system is the rocket+gas system. In this case, the rocket
expels gas in high speed as it moves in forward direction due to the reaction force of the gas. We
care about the motion of the rocket. However, we do not care about the movement of gas in the
backward direction. If the whole system is considered, then momentum is conserved for the
rocket+gas system.
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