# Derive % change Kinetic energy eqn for inelastic collision

## Homework Statement

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

## Homework Equations

%Δ = 100 * ( ( measuredfinal - measuredinitial ) / measuredinitial )

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

## 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.

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lewando
Homework Helper
Gold Member
Use the conservation of momentum equation.

Use the conservation of momentum equation.
Worked like a charm, thank you.