Question

A ball with a mass of `2 kg` moving at `14 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

The speed of the second ball is `1.3m/s`
The kinetic energy lost in as heat was `177.3J`

Explanation:

The momentum is conserved, then

`p_1 = m_1*v_1 = p_2 = m_2*v_2`

`v_2 = v_1*m_1/m_2` and replacing for the problems figures
`v_2 = 14m/s*2/21 = 1.3m/s`

The energy also is conserved

`E= m_1*v_1^2/2 = m_2*v_2^2/2 + Q` where Q is the kinetic energy

lost in the impact, then

`Q = m_1*v_1^2/2*[1-m_1/m_2]` and replacing for the problems figures

`Q= 2/2kg*14^2 m^2/s^2*[1-2/21]=177.3J`