# 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?

Feb 22, 2016

The speed of the second ball is $1.3 \frac{m}{s}$
The kinetic energy lost in as heat was $177.3 J$

#### Explanation:

The momentum is conserved, then

${p}_{1} = {m}_{1} \cdot {v}_{1} = {p}_{2} = {m}_{2} \cdot {v}_{2}$

${v}_{2} = {v}_{1} \cdot {m}_{1} / {m}_{2}$ and replacing for the problems figures
${v}_{2} = 14 \frac{m}{s} \cdot \frac{2}{21} = 1.3 \frac{m}{s}$

The energy also is conserved

$E = {m}_{1} \cdot {v}_{1}^{2} / 2 = {m}_{2} \cdot {v}_{2}^{2} / 2 + Q$ where Q is the kinetic energy

lost in the impact, then

$Q = {m}_{1} \cdot {v}_{1}^{2} / 2 \cdot \left[1 - {m}_{1} / {m}_{2}\right]$ and replacing for the problems figures

$Q = \frac{2}{2} k g \cdot {14}^{2} {m}^{2} / {s}^{2} \cdot \left[1 - \frac{2}{21}\right] = 177.3 J$