# Impulse Formula

## Impulse

A car is travelling at full speed. It crashes into the barrier, because of the negligence of the driver.

Here the huge force is applied on the wall by the car in a very little time interval which we term as an impulse.

Impulse is the big force acting for a very small interval of time. It is represented by J⃗ J→.

Impulse Formula is articulated as

J=F×t

Where,

• Force applied is given as F
• Time interval throughout which force is applied is given as t.

Impulse can also be articulated as the rate of change of momentum.

J=m×v

Where,

• Mass of the body is given as m
• The velocity with which the body is moving is given as v.

Velocity is articulated as

v=vf – vi

Where,

• Initial Velocity is given as vi
• Final Velocity is given as vf .

Therefore, the Impulsive force is articulated as

$$f=m\frac{v_{f}-v_{i}}{t}$$

Impulse is articulated in Kgms-1 and Impulsive force is articulated in Newton(N).

### Impulse-momentum formula

The Impulse-momentum formula is obtained from the impulse-momentum theorem which states that change in momentum of an object is equal to impulse applied on the object. The formula is given as follows:

 Impulse-momentum formula J=Δp When the mass is constant FΔt=mΔv When the mass is varying Fdt=mdv+vdm

As the SI unit of impulse and momentum are equal, it is given as Ns=kg.m.s-1

### Solved Examples

Below are some problems on impulse:

Example 1: A batsman knocks back a ball straight in the direction towards the bowler without altering its initial speed of 12 m/s. If the mass of the ball is 0.15kg, calculate the impulse imparted to the ball?

Given:
vi (Initial Velocity) = 12 m/s,

vf (Final Velocity) = -12m/s,

m (mass) = 0.15kg,

J (Impulse) = ?

Impulse is articulated as

J = mvf – mvi

= m(vf – vi)

= 0.15 Kg (-12 -12) m/s

J= -3.6N.

Example 2: A golfer hits a ball of mass 45g at a speed of 40m/s. The golf club is in contact with the ball for 3 s. Compute the average force applied by the club on the ball?

m (Mass)= 0.045 kg,

vi (Initial Velocity) = 0,

vf (Final Velocity) = 40m/s,

Impulse force F = ma = $$m\frac{v_{f}-v_{i}}{t}$$ $$=0.045 \times \frac{40}{0.003}$$

F= 600N