Potential and Thermal Energy

vendredi 30 août 2013

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

ΔU^th=mcΔT

V_g=mgh

K=(1/2)mv²

3. 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_1i²=0

mgh_i=(1/2)mv_1i²

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_1i²-(1/2)(2m)(v_f)²

U^th=(1/2)mv_1i²-(1/2)(2m)((1/2)v_1i)²

U^th=(1/2)mv_1i²-(1/2)(2m)(1/4)v_1i²

U^th=(1/4)mv_1i²

U^th=(1/2)((1/2)mv_1i²)

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!