Impulsive force and Impulse of a force

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.