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Two objects have unequal masses, m1>m2; which object has greater momentum?

  1. Oct 23, 2011 #1
    Two objects have unequal masses, m1 > m2. If their kinetic energies are equal, which has the greater momentum?

    This is the way I approached this problem. I know that,
    Momentum = mass*velocity
    K = 1/2mv^2


    So, I solved for v since it is the only unknown in these two equations.
    k = 1/2mv^2
    2k/m = v^2
    √2k/m = v

    And plugged it into the first equation for momentum.
    Momentum = m√2k/m
    = √m^2*√2k/m
    = √m^2 2k/m
    = √2k m

    However, since 2k is a constant between the two massess I removed them from the equation giving me Momentum = √m

    Since m1>m2 I thought it was safe to say that the momentum of object 1 is greater than the momentum of object 2; however, I was wrong. According to the answer the momentum of m2 is greater than m1 so I'm just wonder, why?

    Is my math wrong, am I not suppose to join these two equation? If somebody can help I would greatly appreciate it. Thank you for taking the time to review my question.
     
  2. jcsd
  3. Oct 23, 2011 #2

    Delphi51

    User Avatar
    Homework Helper

    Fascinating problem and solution!
    You have momentum = constant * sqrt(m).
    So the one with the bigger m has the bigger momentum.
    Makes sense.

    Another approach is the say ½m1v1² = ½m2v2²
    so m1*v1 = m2*v2²/v1
    momentum1 = m2*v2*v2/v1
    momentum 1 = momentum2*v2/v1
    The first line ½m1v1² = ½m2v2² with m1 > m2 implies v1 < v2
    so v2/v1 is larger than 1 and momentum1 must be larger than momentum2.

    Your conclusion has been found correct by two methods . . .
    A single counterexample can disprove the textbook answer.
    Say m1=4, v1 = 1, m2=1, . Then v2 = 2 to make the energies equal.
    p1 = 4*1 = 4, p2 = 1*2 = 2.
     
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