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Math Help - 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
    Grand Panjandrum
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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 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:

    <br />
KE_{final}=\frac{2.8^2+6.4^2}{2}=112 \ \mathrm{J}<br />
,

    so 80\ \mathrm{J} are lost

    RonL
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