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Math Help - Calculating Energy Loss in a collision

  1. #1
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    Calculating Energy Loss in a collision

    Hi guys, I have a simple question involving the collision of 2 particles of different masses. Particle 1 of mass m is travelling with speed u towards particle 2 of mass 3m which is initially at rest. I have been asked to calculate the energy loss in the impact, however in my notes there is only an example of calculating the energy loss when there is the 'special case' where the masses are the same, which is to use the formula



    How would I construct the above equation given the different masses I have?

    Thanks
    Last edited by Hamster Jam; January 3rd 2010 at 08:09 AM. Reason: typo
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Hamster Jam View Post
    Hi guys, I have a simple question involving the collision of 2 particles of different masses. Particle 1 of mass m is travelling with speed u towards particle 2 of mass 3m which is initially at rest. I have been asked to calculate the energy loss in the impact, however in my notes there is only an example of calculating the energy loss when there is the 'special case' where the masses are the same, which is to use the formula



    How would I construct the above equation given the different masses I have?

    Thanks
    The energy lost is equal to the difference in the before and after kinetic energies.

    \Delta KE=\frac{m u}{2} + \frac{(3m) 0}{2} - \frac{m v_1}{2}-\frac{(3m) v_2}{2}



    You have enough information to calculate the before KE but insufficient for the after.

    CB
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  3. #3
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    The previous question asks me to find the speed acquired by v2 after the collision. I have done this by plugging in my values into the conservation of momentum formula and the law of restitution formula, and solving for v2, so that



    So I have v2. Does this mean I can calculate the energy loss?
    Last edited by Hamster Jam; January 7th 2010 at 07:16 AM. Reason: typo
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  4. #4
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    Do you have the coefficient (e) or are you assuming elastic and therefore =1?

    If that is correct you can use the conservation equations to calculate the kinetic energy loss.

    You cannot lose energy per se.
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  5. #5
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    It is quite a theoretical natured module, I just have 'e'. I have tried working it out but I'm going round in circles and getting very messy answers, could anyone tell me how to go about calculating energy loss?
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  6. #6
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    Like CB said the more general equation you are looking for is:

    \Delta KE=\frac 12 m_1u_1^2+\frac 12 m_2u_2^2-\frac 12 m_1v_1^2-\frac 12 m_2v_2^2

    where

    m_1=m
    m_2=3m
    u_1=u
    u_2=0

    Now you just need to calculate v_1 and v_2, make the substitutions and out pops the answer.
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