# Math Help - Two balls...

1. ## Two balls...

Two balls with masses of 2.0 kg and 6.0 kg travel toward each other at speeds of 12 m/s and 4.0 m/s, respectively. If the balls have a head-on, inelastic collision and the 2.0-kg ball recoils with a speed of 8.0 m/s, how much kinetic energy is lost in the collision?

2. Originally Posted by Candy
Two balls with masses of 2.0 kg and 6.0 kg travel toward each other at speeds of 12 m/s and 4.0 m/s, respectively. If the balls have a head-on, inelastic collision and the 2.0-kg ball recoils with a speed of 8.0 m/s, how much kinetic energy is lost in the collision?
You have initial kinetic energy $KE_{initial}$, and momentum $p_{initial}$:

$KE_{initial}=\frac{2.12^2+6.4^2}{2}=192\ \mathrm{J}$

$p_{initial}=2.12+6.(-4)=0\ \mathrm{kg.m.s^{-1}}$.

As linear momentum is conserved in the collision:

$p_{final}=p_{initial}=0=2.(-8)+4.v$,

where $v$ is the final velocity of the second particle.

Hence:

$v=4\ \mathrm{m/s}$,

so the final kinetic energy is:

$
KE_{final}=\frac{2.8^2+6.4^2}{2}=112 \ \mathrm{J}
$
,

so $80\ \mathrm{J}$ are lost

RonL