Mechanics

# Impulse momentum equation with examples and applications in real life

“Momentum of a body is the quantity of motion it possesses due to its mass and velocity.”We are aware of the fact that moving object possesses a quality by virtue of which it exerts a force on anything that tries to stop it.The faster the object is travelling ,the harder is to stop it.Similarly,if two objects move with the same velocity,then it is more difficult to stop the massive of the two.A bullet has a very small inertia due to its small mass.But why does its impact is so strong when it is fired from the gun? On the other hand,the impact of a loaded truck on a body coming its way is very large even if the truck is moving slowly.To explain such situations,we define a new physical quantity called momentum.

## How to calculate momentum?

This quality of the moving body was called the quantity of the motion of the body,by newton.This term is know called linear momentum of the body and is defined by the relation:

P = m×v

In this expression v is the velocity of the mass m.Linear momentum is therefore,a vector quantity and has the direction of velocity.

The SI unit of momentum is kgms-1 (kilogram metre per second).It can also be expressed as newton second (Ns).

## How is force related to momentum?

Consider a body of mass m moving with an initial velocity v.Suppose an external force F acts upon it for time t after which velocity becomes v and acceleration is produced in the body.If Pi and Pf be the initial momentum and final momentum of the body related to initial and final velocities respectively then:

Pi = mvi

and                                       Pf =mvf

Therefore    Change in momentum = final momentum – initial momentum

or           Pf – Pi= mv – mvi

Thus the rate of change in momentum is given by: The above equation defines force and states newton’s second law of motion as:

“When a force acts on a body,it produces an acceleration in the body and will be equal to the rate of change of momentum of the body.”This form of the second law is more general than the form F =ma ,because it can easily be extended to account for changes as the body accelerates when  its mass also changes.For example ,as a rocket accelerates ,it loses mass because its fuel is burnt and ejected to provide greater thrust.

## Impulse and momentum

Impulse is defined as:”The product of force and time for which it acts on a body.”

### examples

Sometimes we wish to apply the concept of momentum to cases where the applied force is not constant, it acts for very short time.For example,when a bat hits a cricket ball,the force certainly varies from instant to instant during the collision.In such cases,it is more convenient to deal with the product of force and time (F × t) instead of either quantity alone.The quantity F× t is called the impulse of the force,where F can be regarded as the average force that acts during time t.

## Equation of impulse and momentum

Impulse = F× t = mvf – mvi

Example:A 1500 kg car has its velocity reduced from 20 ms-1 to 15 ms-1 in 3 s. How large was the average retarding force?

Solution:By using equation of impulse:

F× t = mvf – mvi

F × 3.0 s =1500 kg × 15ms-1 – 1500 kg × 20 ms-1

Or  F = -2500 kg ms-2 = -2500 N

=-2.5 k N

In case of an accident ,a person not wearing seat belt will continue moving until stopped suddenly by something before him.This something may be a windscreen,another passenger or back of the seat in front of her/him. Seat belts are useful in two ways:

• They provide an external force to a person wearing a seat belt.
• The additional time is required to stretching seat belts.This prolongs the stopping time for momentum to change and reduces the effect of collision.

## Momentum and explosive forces

There are many examples where momentum changes are produced by explosive forces with in an isolated system. For example, when a shall explodes in mid air, its fragments fly off in different directions. the total momentum off all its fragments equals the initial momentum of the shell. suppose a  falling bomb explodes into two pieces. the momenta of the bomb fragments combine by vector addition equal to the original momentum of the falling bomb.