An impulsive force is a very great force acting for a very short time on a body, so that the change in the position of the body during the time the force acts on it may be neglected.

*Impulsive force and Impulse of a force*

*(i) Impulsive Force*

*An impulsive force is a very great force acting for a very short time on a body, so that the change in the position of the body during the time the force acts on it may be neglected.*

(e.g.) The blow of a hammer, the collision of two billiard balls etc.

*(ii) Impulse of a force*

*The impulse J of a constant force F acting for a time t is defined as the product of the force and time.*

(i.e) Impulse = Force x time

*J *=* F ** *x* t*

The impulse of force *F* acting over a time interval *t* is defined by the integral,

The impulse of a force, therefore can be visualised as the area under the force versus time graph as shown in Fig.. When a variable force acting for a short interval of time, then the impulse can be measured as,

*J = Faverage ** *x *dt ....(2)*

Impulse of a force is a vector quantity and its unit is N s.

*Principle of impulse and momentum*

By Newton's second law of motion, the force acting on a body = *m a* where *m* = mass of the body and *a* = acceleration produced

The impulse of the force = *F* x *t = (m a) t*

If *u* and *v *be the initial and final velocities of the body then, a = (v-u)/ t

Therefore, impulse of the force = m [(v-u)/t ] t = m(v-u) = mv-mu

Impulse = final momentum of the body - initial momentum of the body.

Impulse of the force = Change in momentum

(*i.e*) Impulse of the force = Change in momentum

The above equation shows that *the total change in the momentum* *of a body during a time interval is equal to the impulse of the force acting during the same interval of time. This is called principle of impulse and momentum.*

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