# Two balls...

• Jul 20th 2006, 09:23 AM
Candy
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?
• Jul 20th 2006, 09:48 AM
CaptainBlack
Quote:

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 $\displaystyle KE_{initial}$, and momentum $\displaystyle p_{initial}$:

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

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

As linear momentum is conserved in the collision:

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

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

Hence:

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

so the final kinetic energy is:

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

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

RonL