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Homework Help: Derive % change Kinetic energy eqn for inelastic collision

  1. Nov 11, 2012 #1
    1. The problem statement, all variables and given/known data
    We did a lab in my PHYS with Caclulus I class involving a collision of cart A (given an initial push) and cart B (initially at rest) on a relatively smooth surface. *At the moment of the collision, the two carts become attached, providing a completely inelastic collision*. One of the post-lab questions asks the following:

    Derive the equation below from first principle (don't work backwards from the answer). Start from the definition of %Δ and then plug in what you know about this type of collision (you may include that mass B starts from rest).

    %Δ Ksystem = ( -mB / (mA + mB) ) * 100

    ^eqn I need to derive




    2. Relevant equations
    %Δ = 100 * ( ( measuredfinal - measuredinitial ) / measuredinitial )

    And I assume I should use K = 0.5mv^2



    3. The attempt at a solution
    %ΔKsystem = 100 * ( ( Ksysf - Ksysi ) / Ksysi )

    %ΔKsystem = 100 * ( ( KAf + KBf ) - ( KAi + KBi ) ) / ( KAi + KBi )

    Since cart B is initially at rest, it has no Ki:

    %ΔKsystem = 100 * ( ( KAf + KBf ) - ( KAi ) ) / ( KAi )

    I will omit all of the one-halves (0.5's) as I replace all "K"s with (0.5)mv^2, since they will all clearly cancel out:

    %ΔKsystem = 100 * ( mAvAf2 + mBvBf2 - mAvAi2 ) / ( mAvAi2 )

    And I'm drawing a blank at this point.
     
    Last edited: Nov 11, 2012
  2. jcsd
  3. Nov 11, 2012 #2

    lewando

    User Avatar
    Homework Helper
    Gold Member

    Use the conservation of momentum equation.
     
  4. Nov 12, 2012 #3
    Worked like a charm, thank you.
     
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