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Elastic Momentum

  1. Mar 6, 2009 #1
    1. The problem statement, all variables and given/known data

    Two elastic balls, one with mass m = 50 g and the other with mass M = 3m experience a head-on elastic collision after initially traveling in opposite directions at the same speed v = 15 m/s.

    Use the conservation of momentum strategy to obtain symbolic expressions and numerical values
    for the velocities of the two balls after the collision. (One of the answers is 3E1.)

    2. Relevant equations

    Mi1Vi1+Mi2Vi2=Mf1Vf1+Mf2Vf2

    3. The attempt at a solution

    Well I know that the initial Velocities are going to be the same so

    M1+M2(Vi)=M1Vf1+M2Vf2

    Would be correct

    I'm not sure how you would solve this problem because you are looking for 2 unknowns?

    Thanks for any help
     
  2. jcsd
  3. Mar 6, 2009 #2

    LowlyPion

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  4. Mar 6, 2009 #3
    The Kinetic Energy is conserved

    So I guess KEi=KEf

    or

    KEi=1/2M1Vi1^2+1/2M2Vi2^2
    KEf=1/2M1Vf1^2+1/2M2Vf2^2

    Where would I go from there?
     
    Last edited: Mar 6, 2009
  5. Mar 6, 2009 #4

    LowlyPion

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    Weren't you complaining about having 2 unknowns?

    So don't you have 2 equations?
     
  6. Mar 6, 2009 #5
  7. Mar 6, 2009 #6

    LowlyPion

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  8. Mar 9, 2009 #7
    Ok, I used this equation:

    Vi1+Vi2=Vf1+Vf2
    Vi1-Vi2=Vf1-Vf2

    which would mean

    15m/s + -15m/s=Vf1+Vf2
    0=Vf1+Vf2
    or
    Vf1=-Vf2

    and

    15m/s- -15m/s=Vf1-Vf2
    15+15
    30m/s=Vf1-Vf2

    30m/s=Vf1-Vf1

    what am I doing wrong?
     
  9. Mar 9, 2009 #8

    LowlyPion

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    One mass is 3 times the other.
     
  10. Mar 9, 2009 #9
    Oh yeah, good point
     
  11. Mar 9, 2009 #10
    I'm trying to take that into account but i'm still lost I think it's because I'm really rusty on Algebra
     
  12. Mar 9, 2009 #11

    LowlyPion

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    Also try using the equations at the link I supplied.

    Kinetic energy ... you know that ½mv² thing is also conserved.
    Momentum is conserved.

    Write them out carefully and solve..
     
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