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.