Question

A ball with a mass of `9 kg` moving at `3 m/s` hits a still ball with a mass of `21 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

Use conservation of momentum and conservation of energy
`v_2' = 9/21 3 = 9/7 m/s`
energy lost to collision = 40.5-17.36 = 23.14 J

Explanation:

Momentum of the system before collision:
`m_1v_1 + m_2v_2 = m_1v_1'+ m_2v_2'`
`m_1 = 9 kg; m_2 = 21 kg; v_1 = 3 m/s; v_2 = 0; v_1' = 0`
`v_2' = m_1/m_2v_1` substitute
`v_2' = 9/21 3 = 9/7 m/s`
now kinetic energy before
`KE = 1/2mv^2; KE_i = 1/2 9 (3)^2 ; KE_f = 1/2 21 (9/7)^2`
`KE_i = 1/2 9*9 = 40.5 J; KE_f = 1/2 3 (9)^2/7 = 17.36 J`
energy lost to collision = 40.5-17.36 = 23.14 J