1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Simple Elastic Collision

  1. Nov 27, 2009 #1
    1. The problem statement, all variables and given/known data

    I can't believe I cannot get this! I am trying to help out my gf with this problem:

    A 5 kg ball moving at 2 m/s to the right collides with a 7.5 kg stationary ball. If the collision is elastic, what are the final velocities of the 2 balls?

    2. Relevant equations

    Momentum is Conserved
    KE is conserved


    3. The attempt at a solution

    Momentum

    [itex](m_1v_1)_o+(m_2v_2)_o = (m_1v_1)_f+(m_2v_2)_f[/itex]

    [itex]\Rightarrow (5)(2) + (7.5)(0) = 5v_{1f} + 7.5v_{2f} [/itex]

    [itex]v_{1f} = 2 - 1.5v_{2f} \qquad (1)[/itex]

    Energy

    [itex]0.5(m_1v_1^2)_o+0.5(m_2v_2^2)_o = 0.5(m_1v_1^2)_f+0.5(m_2v_2^2)_f[/itex]

    [itex]\Rightarrow (5)(2)^2 = 5v_{1f}^2 + 7.5v_2f}^2[/itex]

    [tex]v_{1f} = \sqrt{4 - 1.5v_{2f}^2} \qquad (2)[/tex]


    From (1) and (2), we have

    [tex]2 - 1.5v_{2f} = \sqrt{4 - 1.5v_{2f}^2}[/tex]

    [itex]\Rightarrow 4 - 3v_{2f} + 2.25v_{2f}^2 = 4 - 1.5v_{2f}[/itex]

    [itex]\Rightarrow 3.75v_{2f}^2 - 3v_{2f} = 0 = (3.75v_{2f} - 3)v_{2f} [/itex]

    [itex] \Rightarrow v_{2f} = 0.8 m/s[/itex]

    Which is incorrect.

    What the heck am I missing? I feel like such an amateur right now! :redface:
     
  2. jcsd
  3. Nov 27, 2009 #2
    It's a simple arithmetic mistake... you didn't square the binomial correctly in...

    (2 - 1.5v_2f) ^ 2

    the cross term is -6v_2f not -3v_2f.
     
  4. Nov 27, 2009 #3
    Oh jeesh....thank you Elvex!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Simple Elastic Collision
  1. Elastic collision (Replies: 6)

Loading...