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2-body collision: Min and Max speed

  1. Dec 31, 2012 #1
    1. The problem statement, all variables and given/known data

    A ball of mass M travelling at non-relativistic speed v elastically collides with a stationary ball of mass m.

    (a)Show that the maximum speed which the second ball can have is:

    2Mv/(M+m)


    (b)What is the minimum speed?


    3. The attempt at a solution

    (a)
    Method 1

    Go into ZMF frame:

    step 1: find VCM
    step 2: u2' = u2 - VCM
    step 2: pi = pf = 0
    step 3: v2' = -u2
    step 4: go back into lab frame by adding VCM

    Method 2

    1)Speed of approach = speed of separation
    2)conservation of momentum
    3)done.

    But the puzzling thing is that why is this the maximum speed? Isn't this the actual acquired speed?

    (b)
    Do we assume a head-on collision? If it is a head-on collision won't the speed be the same as part (a)?

    assuming a non head-on collision by including angles and stuff doesn't help..
     
  2. jcsd
  3. Dec 31, 2012 #2

    mfb

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    Staff: Mentor

    If you assume a head-on collision where the second ball travels in the initial direction of ball 1, this is the maximal speed.
    Every other collision will give a lower speed.
     
  4. Jan 1, 2013 #3
    so for part (b) it isn't a head-on collision?
     
  5. Jan 1, 2013 #4

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Right ;)
     
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