# What Is Change in Momentum: How to Find, Facts and Problems, Examples

The article discusses about what is change in momentum and formulas about how to find change in momentum.

The change in momentum is a difference in motion. When an object is in motion, strikes, or collides with another object, the exerted force accelerates an object by varying its motion. The change in momentum is calculated using the Impulse formula or conservation of momentum.

The moving object is said to be in momentum. The amount of momentum gained by an object is proportional to its mass and velocity together. Hence, the change in one quantity can cause a change in momentum. That means, if you increase or decrease an object’s mass, then its momentum changes. Similarly, the momentum also changes when you increase or decrease its velocity.

The change in velocity means an object is accelerating, and we have learned that acceleration is caused by force. So greater the acceleration caused by force, the greater its change in momentum!!!

Suppose an object is at rest or does not have momentum, then it requires sufficient force to overcome the friction so that an object moves with some momentum. If an object is already in momentum and force is applied in the opposite direction, its momentum will decrease. But If force applies in the same direction, then momentum will increase.

A large force exerted over a short time causes a significant change in momentum. If the force is small but exerted over a long time, a significant change in momentum also occurs. That means when a force applies to an already gained momentum object for a certain period of time, its momentum changes.

## Change in Momentum Examples

The change in momentum examples explains how momentum changes when a force is acted upon.

## Long Jump

To attain momentum before jumping, the athlete runs a certain distance. Once the athlete gains some momentum after running, they apply force on the ground to jump that changes its momentum, and the athlete jumps forward. After the jump, the athlete needs to apply a large force again on the ground to stop their motion – which changes their momentum again.

## Hitting a Ball

The ball gains momentum when thrown by the bowler during sports like cricket or baseball. When a batter hits the ball with a bat, the applied force to the ball changes its momentum, and then a ball moves in the direction of an applied force. The ball’s momentum changes again when it is stopped or caught by the fielder.

## Driving Vehicle

Driving a vehicle such as a car or truck involves a continuous change in momentum. We apply a force on its accelerating paddle to speed up the vehicle. To stop the vehicle suddenly, we apply a force on its brake paddle, which changes the vehicle’s momentum as per applied force.

## Football or Rugby

In football or rugby, the striker accumulates maximum momentum when he dribbles or carries the ball near the goal coast by bypassing other players. The defenders near the goal coast then try to stop or change the striker’s momentum by tackling him.

## Playground Slides

When children start sliding on the playground slide from height, they achieve momentum downwards. But the friction present on the playground slide surface changes the momentum of sliding children by opposing their motion, preventing them from falling at the end of the slide.

## Change in Momentum Formula

The change in momentum formula is calculated using Newton’s second law of motion and kinematics equations of motion.

Newton’s second law displays that an object accelerates when a force applies. Since the force applied for a specific time interval changes an object’s motion, it also causes a change in momentum. The product of force and time interval is termed as ‘impulse’, which measures the change in momentum.

The first kinematics equation of motion is,

vf = vi + at

vf– vi = at

As per Newton’s second law, F = ma, a = F/a

vf-vi=(F/m)*t

m(vf– vi) = Ft

mΔv=Ft

Whereas RHS in the above equation is termed as ‘Impulse’ (denoted by J) and LHS is the formula of Momentum Change (ΔP)

Therefore, we can also write as,

J=Ft=mΔv=ΔP…………. (*)

Impulse = Change in Momentum

The equation (*) is also known as ‘Impulse –Momentum change equation’

The more significant the impulse, the more significant the momentum change.

The strength of force applied to an object depends on how long it acts. The concept of impulse quantifies the effect of force.

## Calculate Impulse applied by the defender.

Given:

m = 40kg

vi = 10m/s

vf = 15m/s

t = 0.10s

To Find:

1. Pi =?
2. Pf =?
3. ΔP =?
4. F =?

Formula:

1. P = mv
2. ΔP = Pf –Pi
3. Ft = ΔP

Solution:

The initial momentum of a striker is calculated as,

Pi = mvi

Pi = 40 x 10

Pi = 400

The initial momentum of striker is 400kg.m/s

The final momentum of a striker is calculated as,

Pf = mvf

Pf = 40 x 15

Pf = 600

The final momentum of striker is 600kg.m/s

The change in momentum of a striker is calculated as,

ΔP = Pf –Pi

ΔP = 600 – 400

ΔP = 200

The change in momentum of a striker is 200kg.m/s.

The force applied by the defender to stop the striker is calculated using the impulse-momentum Change formula.

Ft = ΔP

Substituting all values,

F(0.10) = 200

F = 200/0.10

F = 2000

The force applied by the defender is 2000N.

The impulse by defender is calculated as,

J = Ft

J = 2000 x 0.10

J = 200

The impulse by defender on striker is 200N.s.

## How to Calculate Momentum Change?

The momentum change is calculated using the law of conservation of momentum.

When an external force acts on an object, we can compute its momentum change by impulse formula. But when there is no external force, the total momentum of colliding objects remains the same. That’s how we can calculate the momentum change due to collision using conservation of momentum.

Suppose two objects have a momentum P1 and P2 due to their masses m1 and m2 and velocity u1 and u2. Due to collision, their momentum changes to P1’ and P2’ since their velocity changes to v1 and v2

As per conservation of momentum,

m1u1 + m2u2 = m1v1 + m2v2

Since we want to calculate change in momentum, rearranging terms m1 on LHS and m2 on RHS,

m1u1 – m1v1 = m2u2 – m2v2

P1f– P1i = P2f-P2i

ΔP1 = ΔP2

Momentum change in object 1 = Momentum change in object 2

## Calculate the change in velocity of the second ball after the collision.

Given:

m1 = 5kg

m2 = 3kg

u1 = 8m/s

u2 = 15m/s

v1 = 5m/s

To Find:

1. ΔP1 =?
2. v2 =?

Formula:

1. ΔP1 = P1f– P1i
2. m1u1 – m1v1 = m2u2 – m2v2

Solution:

The change in momentum of first ball is calculated as,

ΔP1 = P1f– P1i

ΔP1 = m1u1 – m1v1

Substituting all values,

ΔP1 = 5 x 8 – 5 x 5

ΔP1 = 40 – 25

ΔP1 = 25

The momentum change of first ball is 25kg.m/s

The velocity change of second ball after collision is calculated as,

m1u1 – m1v1 = m2u2 – m2v2

Substituting all values,

25 = 3 x15 – 3v2

25 = 45 – 3v2

v2 = -20/3

v2 = -6.66

The velocity change of the second ball is -6.6m/s.