Question

A ball with a mass of `5 kg` moving at `2 m/s` hits a still ball with a mass of `6 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

Energy lost, `E_(heat)= 1. dot 6 J`

Explanation:

Step 1: To calculate the velocity of the second ball after the hit.
This part of the question is regarding Conservation of Momentum.
Momentum `vec p=m vec v`. (It is a vector quantity).
Initial momentum, second ball being stationary

`vec p_i=m_1 vec v_1`
`p_i=5 times 2`
`implies p_i=10` in the direction of `vec v_1`

Final momentum, first ball stops
`vec p_f=m_2 vec v_2`
Equating both `vec p_i` and `vec p_f`
`10=6 times vec v_2`,

As the direction of initial momentum is that of direction of motion of first ball, therefore, direction of final momentum is also the same.
Therefore, direction of motion of second ball after hit is also the same as that of the first ball.
`|vec v_2|=10//6`
Step 2: To calculate amount of kinetic energy lost as heat energy. Using law of Conservation of energy where `KE= 1/2 m v^2`

KE before hit = KE after hit + Energy lost as heat

Before hit, second ball is still, hence its Kinetic Energy is zero. Similarly for first ball which stops after hit.

`KE_i =KE_f+E_(heat)`
`1/2 5 times 2^2=1/2 6. (10/6)^2+ E_(heat)`
Rearranging
`E_(heat)=10-8. dot 3`