Question

State the relation between the momentum of a body and force acting on it?

Answer 1

Hint: First apply the concept that force of the body is the product of its mass and acceleration. And we know that the acceleration is the rate of change of velocity in a unit time. Thus the product of mass and its velocity is the momentum acting on a body. Then we will get the relation between force and momentum of a body.

Formula used:
According to Newton’s second law,
$F=ma$
where, F is the force
m is the mass of the body
and a is the acceleration.

Complete step by step answer:
According to Newton’s second law of motion,
$F=ma$ ………..(1)
where, F is the force
m is the mass of the body
and a is the acceleration.
We know that,
Acceleration, $a=\dfrac{dv}{dt}$
Thus the acceleration is the rate of change of velocity in a unit time.
Substituting the value of acceleration in equation (1) we get,
$F=m\dfrac{dv}{dt}$
Here the numerator term is the product of mass and change in velocity which is equal to the change in momentum. Hence equation becomes,
$\Rightarrow F=\dfrac{dp}{dt}$
where, dp is the change in momentum.
Therefore we get the relation between force of a body and momentum acting on it.
Here force and momentum are directly proportional. Hence, momentum of the body increases with increase in the applied force.

Note:
Force and momentum are directly proportional. Hence, momentum of the body increases with increase in the applied force. This relation is derived from Newton's second law of motion. Thus rate of change of momentum and the force applied are directly proportional to each other. And also momentum always depends on two factors. That is, mass and velocity.