MOMENTUM

Momentum is defined as being the product of the mass of an object and its velocity.

p = m.v

mass in kg

velocity in m.s-1

momentum in kg.m.s-1 or N.s

Momentum is a VECTOR quantity because velocity is but mass is not. We must, therefore, always state a direction and take it into account in all calculations.

When a resultant force is applied to a body it accelerates. This means that its velocity and hence its momentum change. How much the velocity changes depends upon both the mass of the body and the size of the resultant force applied.

Newton’s second law can therefore be re-written as:

The resultant force applied to a body is equal to the rate of change of momentum, and that this change occurs in the direction of the applied force.

Fnet = m.a

Fnet = m.(vf - vi)

Δt

Fnet = m,vf - m.vi

Δt

t

Fnet.Δt = m.vf - m.vi = Δp

Fnet.Δt is called impulse.

From the above equation we can see that the change in momentum of a particular mass depends upon both the size of the resultant force and the length of time it is applied.

A small force applied for a long time will have the same effect as a large force applied for a short time.

e.g 1.All sports’ coaches encourage players to follow through in order to keep the racquet, bat or club on the ball as long as possible. This will ensure the greatest change in momentum.

2.Artillery use long barrels to keep the expanding gases pushing the round for as long as possible.

3.When catching a cricket ball one usually moves the hands back as one catches so that the force applied to the ball ( and hence the force the ball applies to the hand) will be as small as possible to lessen the pain.

4.Rockets can reach huge speeds in space because the thrust is applied for a long time.

PRINCIPLE OF CONSERVATION OF LINEAR MOMENTUM

In an isolated system the total momentum remains constant in both magnitude and direction. (Isolated means that no external forces are acting on the system.)

Therefore if mass m1 and mass m2 collide then:

pfinal = pinitial

m1.vf1+ m2.vf2 = m1.vi1 + m2.vi2

NOTE:momentum is conserved in all collisions, regardless of whether or not heat is produced.

kinetic energy (EK = ½m.v2)is only conserved when the collision is perfectly elastic.

WORKED EXAMPLES

1.A cricket ball of mass 0,2 kg is moving at a velocity of 30 m.s-1. Calculate the average force exerted by

i)the wicket-keeper, if he stops the ball in 0,3 s.

ii)the bat, if the batsman hits the ball back to the bowler at a velocity of 20 m.s-1 and if the ball is contact with the bat for 0,1 s.

2.A 320 g ball travelling at 15 m.s-1 strikes a stationary 400 g ball. After the collision the 400g ball moves off at 8 m.s-1.

i) What is the final velocity of the 320 g ball?

ii) Calculate the total kinetic energy before and after the collision. Is it an elastic collision?