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Homework Help: Elastic Collision Problem

  1. Dec 26, 2017 #1
    1. The problem statement, all variables and given/known data
    Both object A and B have mass M and are moving.
    An object with mass of m and moving with velocity u collide with the object B elastically. (m < M)
    Find the following after m collide with B
    1) Velocity of m after bouncing back
    2) Velocity of B
    Then m collide with A and bounce back
    3) The highest value of M/m that velocity of m is lesser than or equal to that of B
    (Surface has no friction)
    2. Relevant equations

    3. The attempt at a solution
    Using the Law of Energy Conservation and the Law of Momentum Conservation

    ##\frac{1}{2} m u^2 = \frac{1}{2} m v_1^2 + \frac{1}{2} M v_2^2##

    ##m u = -m v_1 + Mv_2##

    After solving the equation, I get this

    ##v_1 = \frac{M - m}{M + m} u## (Answer for (1))

    ##v_2 = \frac{2 m}{M + m} u## (Answer for (2))

    Then object m hit object A. The velocity of m then change into

    ##(\frac{M - m}{m + M})^2 u##

    Velocity of m should be equal to that of B so m cannot reach B

    ##(\frac{M - m}{m + M})^2 u = \frac{2 m u}{m + M}##

    ##\frac{M}{m} = 2 + \sqrt{5}## (Answer for (3))

    Is that correct?
    Last edited: Dec 26, 2017
  2. jcsd
  3. Dec 26, 2017 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Looks fine.
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