Question

A ball with a mass of `5 kg` moving at `9 m/s` hits a still ball with a mass of `10 kg`. If the first ball stops moving, how fast is the second ball moving? How much kinetic energy was lost as heat in the collision?

Answer 1

v= 4,5 m/s
kinetic energy lost =101,25 J

Explanation:

the first ball has a momentum: `Q= mv= 5 kg 9 m/s = 45 kgm/s` .
The second, still ball, has no momentum.
Both for an elastic collision, both for an inelastic collision the total momentum doesn't change so the second ball's speed will be:
`v_2= (45 kgm/s)/(10kg) = 4,5 m/s.`
initial kinetic energy = `1/2 m(v_1)^2 = 1/2 5Kg (9(m/s))^2= 202,5 J`
finall kinetic energy= `1/2 m(v_2)^2 = 1/2 10Kg (4,5(m/s))^2= 101,25 J`
kinetic energy lost = initial kinetic energy -finall kinetic energy = 101,25 J

If the collision were elastic the kinetic energy wouldn't change, but it may be possible only if the second ball, before the collision had a speed of 2,25 m/s against the first ball