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Elastic collision in one dimension

  1. Jul 28, 2009 #1
    1. The problem statement, all variables and given/known data
    A Pendulum weighs .5kg and has a string length of 70cm swings from a horizontal position downwards to hit a block that weighs 2.5 kg and is on a frictionless plain. Calculate the speed of both the ball and the block after the elastic collision.


    2. Relevant equations
    mgh=.5mV^2
    conservation of momentum
    m1V= m1V1+m2V2
    conservation of kinetic energy
    .5m1V^2=.5m1V1^2+.5m2V2^2


    3. The attempt at a solution

    I used the first equation to solve for the initial velocity of the pendulum, which is 3.7m/s.
    From here comes the elastic collision part.
    I try to use both conseravation equations and substitute for one of the variables by solving for either V1 or V2 in either equation and thus substituting. However, when i try to solve it that way it ends up canceling out.
    I know there is an equation for one dimension elastic collisions, but my professor says we can't use it unless we write the derivation of it, and that is a tedious thing to do and is rather lengthy.

    Please help, ask questions if things are unclear
     
  2. jcsd
  3. Jul 28, 2009 #2

    rl.bhat

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    Homework Helper

    You can rewrite eq.(1) as
    m1v - m1v1= m2v2...(3)
    Similarly you can rewrtie eq.(2) as
    m1v^2 - m1v^21= m2v^22..(4)
    From 3 and 4 you can get
    (v - v1)/v^2 - v1^2= v[/SUB]2[/SUB]/v[/SUB]2[/SUB]^2
    After simplification you get
    (v + v1) = v2
    Substitute the value of v2 in equation (1) and solve for v1.
     
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