1. 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.

2. Force and Laws of Motion Momentum

3. Here u 1 > u 2 Before collision : Velocity of ball before collision Momentum of ball A: P A = m 1 u 1 Momentum of ball B: P B = m 2 u 2 Total momentum before collision = m 1 u 1 + m 2 u 2 Suppose masses of two moving balls A and B are m 1 and m 2 and having initial velocities are u 1 and u 2. Force and Laws of Motion Momentum

4. Balls collide to each other for time t. Velocity of two balls Force exerted by ball B on A during this interaction is F AB. As per Newton’s third law of motion Force acting on ball B due to ball A would be F BA. Force and Laws of Motion Momentum

5. Let after collision their velocities become v 1 and v 2. Momentum of ball A‘:, P A ' = m 1 v 1 Momentum of ball B‘: P B ' = m 2 v 2 Total momentum after collision = m 1 v 1 + m 2 v 2 Velocity of ball after collision After collision Force and Laws of Motion Momentum

6. Now according to Newton’s second law of motion : Force and Laws of Motion Momentum

7. Final momentum = Initial momentum Thus during interaction of two balls total momentum before collision is equal to total momentum after collision. Momentum Force and Laws of Motion

8. 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

9. Mass of bullet m 1 = 40 g = 0.04 kg Mass of pistol m 2 = 4 kg Initial velocity of bullet u 1 = 0 m/s Initial velocity of pistol u 2 = 0 m/s Final velocity of the bullet = v 1 = 300 ms -1 Final velocity of the pistol v 2 = ? According to law of conservation of momentum Force and Laws of Motion Momentum