when two bodies ,one heavy and other lighter are pushed with same force for same time what will be the momentum,large ,small or equal and why?

 When two bodies, a heavy one and a light one, are acted upon by the same force for the same time, the lighter body builds up a higher velocity than the heavy one. But the momentum they gain is the same in both cases. This important connection between force and momentum was recognized by Sir Isaac Newton and expressed by him in a second law of motion.

 

Newton's second law of motion

The rate of change in momentum of a body is proportional to the applied force and takes place in the direction in which the force acts.

 

Suppose a force F acts on a body of mass m for a time t, and causes its velocity to change from u to v.

The momentum changes uniformly from mu to mv in time t, therefore, the rate of change of momentum = mv – mu / t.

By Newton’s second law, the rate of change of momentum is proportional to the applied force and hence,

F is proportional to mv – mu / t

factorizing         F is proportional to m ( v – u ) /t

But   ( v – u ) /t  = change in velocity / time = acceleration = a

            Therefore      F is proportional to ma

            Thus,             F = constant * ma.

It is this equation which enables us to define an absolute unit of force. If m= 1 kg and a = 1 m / s², the value of the unit of force is chosen so as to makeF = 1 when the constant = 1 .

The SI unit of force is called the Newton ( N ), and is the force which produce an acceleration of 1 m / s² when it acts on a mass of a kg.

Thus,

F = ma.