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Thread: Two balls...

  1. #1
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    Exclamation 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?
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  2. #2
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    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
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