CONSERVATION OF MOMENTUM

When two particles collide they exert equal and opposite impulseson each other.

It follows that for the two particles, the total change in momentumis zero.

Hence the changes in momentum are equal and opposite.

The law of conservation of momentum states that when there areno external forces acting on a system, the total momentum of thesystem is constant.

For a collision:

The total momentum before a collision = the total momentum after.

Example 1: A railway truck of mass 2 tonnes and moving with speed 4 ms–1 along a horizontal track, collides with a stationarytruck of mass 1.2 tonnes. The trucks couple together and move off at v ms–1. Find v.

BA

Before:

After:

2000 1200

4 0

v v

Note: 1 tonne = 1000 kg

Using the principle of Conservation of Momentum:

( 2000 × 4 ) = 2000v

8000 = 3200v

So, v = 2.5

+ ( 1200 × 0 ) + 1200v

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 thatA 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 BA

Before:

After:

m

6 0

0 3

By Conservation of Momentum: 12 + 0 =

m = 4i.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)

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 twicethat of A. Find the impulse given to A by B.

w

7 –1

2w

3 1 BA

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

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 BA

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 ) 2v0 = 2v + 6

Summary of key points:

This PowerPoint produced by R.Collins ; Updated Apr. 2009

When two particles collide they exert equal and opposite impulseson each other.

The law of conservation of momentum states that when there areno external forces acting on a system, the total momentum of thesystem 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