# A ball with a mass of 2 kg moving at 16 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?

Oct 28, 2016

In the first scenario, momentum conservation law will be applied.

#### Explanation:

from the law,
${m}_{1} {u}_{1} + {m}_{2} {u}_{2} = {m}_{1} {v}_{1} + {m}_{2} {v}_{2}$

here,
${m}_{1} = 2 k g$
${m}_{2} = 21 k g$
${u}_{1} = 16 m {s}^{- 1}$
${u}_{2} = 0 m {s}^{- 1}$
${v}_{1} = 0 m {s}^{- 1}$
we have to find ${v}_{2}$
if we put all the values in the equation, we will find,

$2 \cdot 16 + 21 \cdot 0 = 2 \cdot 0 + 21 \cdot {v}_{2}$
$\mathmr{and} , 32 = 21 {v}_{2}$
$\mathmr{and} , {v}_{2} = \frac{32}{21}$
$\mathmr{and} , {v}_{2} = 1.524 m {s}^{- 1}$

for the energy loss,
${E}_{i} = \frac{1}{2} \cdot 2 \cdot {16}^{2} + \frac{1}{2} \cdot 21 \cdot {0}^{2}$
$= 256 j$

${E}_{f} = \frac{1}{2} \cdot 2 \cdot {0}^{2} + \frac{1}{2} \cdot 21 \cdot {1.524}^{2}$
$= 24.387 j$

so, $\Delta E = {E}_{i} - {E}_{f}$
$= 256 j - 24.387 j$
$= 231.613 j$