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!

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
    Gold Member

    Use the conservation of momentum equation.
     
  4. Nov 12, 2012 #3
    Worked like a charm, thank you.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Derive % change Kinetic energy eqn for inelastic collision
Loading...