1. CONSERVATION OF MOMENTUM

2. When two particles collide they exert equal and opposite impulses on each other. It follows that for the two particles, the total change in momentum is zero. Hence the changes in momentum are equal and opposite. The law of conservation of momentum states that when there are no external forces acting on a system, the total momentum of the system is constant. For a collision: The total momentum before a collision = the total momentum after.

3. Example 1: A railway truck of mass 2 tonnes and moving with speed 4 ms –1 along a horizontal track, collides with a stationary truck of mass 1.2 tonnes. The trucks couple together and move off at v ms –1. Find v. B A Before: After: 2000 1200 40 vv Note: 1 tonne =1000 kg Using the principle of Conservation of Momentum: ( 2000 × 4 )= 2000v 8000 = 3200v So, v = 2.5 + ( 1200 × 0 )+ 1200v

4. Example 2: A particle A of mass 2 kg is moving with speed 6 ms –1 when it collides with a stationary particle B. Given that A is brought to rest by the collision and that B moves off with speed 3 ms –1, find the mass of B. Find also the impulse on B given by A. 2 B A Before: After: m 60 0 3 By Conservation of Momentum: 12 + 0 = m = 4 i.e. The mass of B is 4 kg. Impulse on B = “mv – mu”I = m(3) The impulse is 12 Ns. = 4(3) – 0 0 + 3m – m(0)

5. Example 3: Two particles A and B of masses 3kg and 1kg respectively are moving towards each other along the same straight line, with speeds 7ms –1 and 1ms –1 respectively. After impact the particles move in the same direction with the speed of B being twice that of A. Find the impulse given to A by B. w 7 –1 2w 3 1 B A Before: After: By Conservation of Momentum:( 7 × 3 )3w 21 – 1 = 5w w = 4 Impulse on A =Change in momentum= “mv – mu” 3 (– 4 ) –= –12 + 21= 9 i.e. Impulse = 9 Ns I = 3 ( – 7 ) + ( 1 × –1 ) = + 2w

6. Example 4: A gun of mass 2kg fires a bullet of mass 40g. Given the bullet is fired at 150 ms –1, find the speed of the recoil of the gun. 2 B A Before: After: 0.04 0 0 v 150 Using the principle of Conservation of Momentum: 0 + 0 = –6 = 2v The speed of the recoil is 3 ms –1. + ( 0.04 × 150 ) 2v 0 = 2v + 6

7. Summary of key points: This PowerPoint produced by R.Collins ; Updated Apr. 2009 When two particles collide they exert equal and opposite impulses on each other. The law of conservation of momentum states that when there are no external forces acting on a system, the total momentum of the system is constant. For a collision: The total momentum before a collision = the total momentum after. Impulse = Change in momentum = Final momentum – Initial momentum = mv – mu