Impulse of a Force

When two bodies collide, the force acts for small time and varies with time. In such case, the net effect of force is measured by the impulse of the force.

According to Newton’s second law of motion, \[F=\frac{dP}{dt}\] \[Fdt=dP\] During the collision, let a force $F$ acts for time $t$ and the momentum changes from $P_1$ to $P_2$. Then, \[\int_0^tF\;dt=\int_{P_1}^{P_2}\;dP\] \[\int_0^tF\;dt=P_2-P_1\] Force $F$ varies with time. So, this integral is the impulse of the force. It is denoted by $I$. \[∴I=\int_0^tF\;dt=P_2-P_1\]
Thus, impulse of force is the total change in the momentum of the body during the collision. 

If $F_{\text{av}}$ is the average force, then $F_{\text{av}}$ can be considered as a constant. \[I=\int_0^tF_{\text{av}}\;dt\] \[I=F_{\text{av}}\int_0^tdt\] \[I=F_{\text{av}}t\] \[∴I=F_{\text{av}}t=P_2-P_1\]
Therefore, impulse of a force can also be defined as the product of the average force and the time for which the force acts.
​Impulse is a vector quantity and its SI unit Newton second $(Ns)$.


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