How much kinetic energy is lost in the collision? (See full question below)

A snooker ball, having a mass of 0.04 kg and initially moving with a speed of
2ms^-1 strikes a stationary ball of the same mass. After the collision, the two balls are both moving with equal speeds at equal angles of 30° to the original direction of the incident ball. How much kinetic energy is lost in the collision?

1 Answer
May 13, 2018

0.026J

Explanation:

Start with a diagram.

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We need to find the final speed of the balls; let this be v for now.

By the conservation of momentum
Momentum before = momentum after

2xx0.04+0=0.04vcos30+0.04vcos30

0.08=0.08vcos30
1=vcos30
v=1/cos30
v=2/sqrt3
v=1.15ms^-1

Now we can work out the kinetic energies.

KE_"before"=1/2xx0.04xx2^2
=0.08J

KE_"after"=1/2xx0.04xx(2/sqrt3)^2+1/2xx0.04xx(2/sqrt3)^2
=0.04xx(2/sqrt3)^2
=0.04xx4/3
=4/75

DeltaKE=0.08-4/75
=0.026J