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## Homework Statement

Starting from rest, a railroad car rolls down a hill 20 m high and hits another identical car at rest. The cars lock together after the collision. What fraction of the first car's change in potential energy is converted into thermal energy in the collision?

## Homework Equations

ΔU

^{th}=mcΔT

V

_{g}=mgh

K=(1/2)mv

^{2}

## The Attempt at a Solution

My basic strategy here was that kinetic energy will not be conserved (due to the inelastic collision) so I need to find how much kinetic energy was lost and then the "lost" energy can be attributed to thermal energy. I can use conservation of energy equations to figure out how fast the car is going before the collision (v

_{1i})

ΔV

_{g}+ΔK=0

mgΔh+(1/2)mv

_{1i}

^{2}=0

mgh

_{i}=(1/2)mv

_{1i}

^{2}

Momentum is conserved, so

mv

_{1i}+mv

_{2i}=

2mv

_{f}.

That means that (1/2)v

_{1i}=v

_{f}

Then basically, K

_{i}=K

_{f}+U

^{th}Note here, that this is kinetic energy for a different portion of the problem

U

^{th}=K

_{i}-K

_{f}

U

^{th}=(1/2)mv

_{1i}

^{2}-(1/2)(2m)(v

_{f})

^{2}

U

^{th}=(1/2)mv

_{1i}

^{2}-(1/2)(2m)((1/2)v

_{1i})

^{2}

U

^{th}=(1/2)mv

_{1i}

^{2}-(1/2)(2m)(1/4)v

_{1i}

^{2}

U

^{th}=(1/4)mv

_{1i}

^{2}

U

^{th}=(1/2)((1/2)mv

_{1i}

^{2})

U

^{th}=(1/2)(mgh

_{i})

U

^{th}=(1/2)(V

_{g})

Anyway, I really feel as though I did something horrendously wrong here. Thanks for your time!