Question

State law of conservation of momentum and prove it by using third law of motion.
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Answer 1

Answer:

For two or more bodies in an isolated system acting upon each other, their total momentum remains constant unless an external force is applied. Therefore, momentum can neither be created nor destroyed.

Answer 2

Answer:

Law of conservation of momentum states that total momentum of system remains conserved in the absence of external force.

Consider a system of two particles, A and B. Let's say they interact with each other and 'A' experts a Force Fba on 'B' and in reaction, 'B' exerts a force Fab on 'A'.

Now, according to the second law of motion,

Fba= Mb x d/dt(Vb) = d/dt(Mb x Vb)

Fab= Ma x d/dt(Va) = d/dt(Ma x Va)

where Mb and Ma are masses of 'B' and 'A' respectively, and similarly Vb and Va their velocities in that order. d/dt denotes the derivative.

Now, adding the above two equations,

Fab + Fba = d/dt (Ma x Va) + d/dt(Mb x Vb)

Note that according to the third law of motion, these forces Fab and Fba are equal and opposite, so Fab= -Fba

Hence, 0= d/dt(Ma x Va) + d/dt(Mb x Vb) = d/dt(Pa + Pb)

where Pa and Pb are the linear momenta of 'A' and 'B' respectively.

Hence, Pa + Pb= constant (since the derivative is zero)

Therefore, The sum of the linear momenta of the bodies is constant.