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Change in Velocity after a Collision

  1. Feb 17, 2016 #1
    1. The problem statement, all variables and given/known data
    Kevin and Jake collide in the air. If Kevin undergoes a 4.2 kg*m/s change in momentum, what is Jacob’s change in velocity if he has a mass of 83.2 kg?

    2. Relevant equations
    p=mv
    MV+mv=MV'+mv'

    3. The attempt at a solution
    I tried the simplest way possible...
    p=mv
    v=p/m
    v=4.2/83.2
    v=0.050m/s (incorrect)

    I feel like conservation of momentum plays a role here, but I can't figure out how... I'm not great at questions where I'm given such little information...
     
  2. jcsd
  3. Feb 17, 2016 #2

    SammyS

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    Just conservation of momentum

    MV+mv=MV'+mv'

    and a little algebra, rearranging.

    Which variables are for Kevin? which for Jake ?
     
  4. Feb 17, 2016 #3
    Big letters for Kevin, small for Jake.
    MV+mv=MV'+mv'
    So I'm solving for:
    v'=(MV+mv-MV')/m

    My question now is how on Earth do I get velocities for them? Or can I just plug in the 4.2 for MV'?
     
    Last edited: Feb 17, 2016
  5. Feb 17, 2016 #4

    SammyS

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    One step at a time.

    You are given Kevin's change in momentum.

    How do express that with your chosen variables?

    That should be related in a simple way to Jake's change in momentum..
     
  6. Feb 17, 2016 #5
    If Kevin's momentum changes by 4.2, then so will Jake's?

    & Kevin's change in momentum could be shown as MV'-MV=4.2?
     
  7. Feb 17, 2016 #6

    SammyS

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    So solve the conservation of momentum equation for MV'-MV .
     
  8. Feb 17, 2016 #7
    Alrighty,

    MV'-MV=mv-mv'
    4.2=mv-mv'
     
  9. Feb 17, 2016 #8

    SammyS

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    Right.

    That's actually the negative of the change in Jake's momentum.

    Alternatively, that could be written as:
    4.2 − (mv' − mv) =0 ,

    where (mv' − mv) is the change in Jake's momentum.​
     
  10. Feb 17, 2016 #9
    Okay, so how would one solve for v' without v? Do we assume that v is 0?
     
  11. Feb 17, 2016 #10

    SammyS

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    What does the question ask for?
     
  12. Feb 17, 2016 #11
    OOOHHHHHHH
    Okay I've got it now!
    change in velocity = v'-v

    4.2=mv-mv'
    4.2/83.2=mv-mv'
    0.05=v-v'
    -0.05=v'-v

    I was so close at the beginning!
    Thanks for your help, I'm glad I just didn't try the negative answer in the beginning, now I understand how to get there! :)
     
  13. Feb 17, 2016 #12

    SammyS

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    Some typo / omission .
    4.2/83.2 = (mv-mv')/m

    Otherwise OK.
     
  14. Feb 17, 2016 #13

    SammyS

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    The equation in post #3 wasn't too far off. It did have a major typo which it looks like you fixed..
    Rearranging gives:

    v' = (MV−MV' + mv)/m

    = (−(MV' − MV) + mv)/m

    = −(MV' − MV)/m +v​
     
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