The product of mass and velocity of a body is called momentum.

Force and Laws of Motion Momentum

Mathematically , Momentum = mass × velocity P = mv

It is a vector quantity. Momentum is always directed in the direction of velocity. The unit of momentum is in S.I system kg m/s or NS.

Force and Laws of Motion Momentum

Here u1 > u2

Before collision :

Velocity of ball before collision

Momentum of ball A: PA = m1u1 Momentum of ball B: PB = m2u2

Total momentum before collision = m1u1 + m2u2

Suppose masses of two moving balls A and B are m1 and m2 and having initial velocities are u1 and u2.

Force and Laws of Motion Momentum

Balls collide to each other for time t.

Velocity of two balls

Force exerted by ball B on A during this interaction is FAB. As per Newton’s third law of motion Force acting on ball B due to ball A would be FBA.

Force and Laws of Motion Momentum

Let after collision their velocities become v1 and v2.

Momentum of ball A‘:, PA' = m1v1 Momentum of ball B‘: PB' = m2v2

Total momentum after collision = m1v1 + m2v2

Velocity of ball after collision

After collision

Force and Laws of Motion Momentum

Now according to Newton’s second law of motion :

1 1 1 1

2 2 2 2

'

'

A ABA

B BAB

P P m v m uF

t tP P m v m u

Ft t

1 1 1 1 2 2 2 2

1 1 1 1 2 2 2 2

1 1 2 2 1 1 2 2

AB BAF F

m v m u m v m u

t tm v m u m v m u

m v m v m u m u

Force and Laws of Motion Momentum

Final momentum = Initial momentum

Thus during interaction of two balls total momentum before collision is equal to total momentum after collision.

MomentumForce and Laws of Motion

A bullet of 40 g is fired horizontally from a pistol of 4 kg mass with velocity 300 ms-1. How much would be the velocity of pistol in backward direction after firing the bullet ?

Example

Contd.

Force and Laws of Motion Momentum

1 1 2 2 1 1 2 2

2

12

m v + m v = m u + m u

0.04 300 + 4v = 0.04 0 + 4 0

0.04 300v 3

4ms

Mass of bullet m1 = 40 g = 0.04 kgMass of pistol m2 = 4 kgInitial velocity of bullet u1 = 0 m/sInitial velocity of pistol u2 = 0 m/sFinal velocity of the bullet = v1 = 300 ms-1

Final velocity of the pistol v2 = ?According to law of conservation of momentum

Force and Laws of Motion Momentum