(adsbygoogle = window.adsbygoogle || []).push({}); 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 K_{system}= ( -m_{B}/ (m_{A}+ m_{B}) ) * 100

^eqn I need to derive

2. Relevant equations

%Δ = 100 * ( ( measured_{final}- measured_{initial}) / measured_{initial})

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

3. The attempt at a solution

%ΔK_{system}= 100 * ( ( K_{sysf}- K_{sysi }) / K_{sysi})

%ΔK_{system}= 100 * ( ( K_{Af}+ K_{Bf}) - ( K_{Ai}+ K_{Bi}) ) / ( K_{Ai}+ K_{Bi})

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

%ΔK_{system}= 100 * ( ( K_{Af}+ K_{Bf}) - ( K_{Ai}) ) / ( K_{Ai})

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:

%ΔK_{system}= 100 * ( m_{A}v_{Af}^{2 }+ m_{B}v_{Bf}^{2 }- m_{A}v_{Ai}^{2}) / ( m_{A}v_{Ai}^{2})

And I'm drawing a blank at this point.

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

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