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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
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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