Automobile drives into a brick wall

bmoore509

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

An automobile of mass 3000 kg is driven into a brick wall in a safety test. The bumper behaves like a Hooke’s-law spring. It has an effective spring constant of 6 × 106 N/m, and is observed to compress a distance of 4.23 cm as the car is brought to rest. What was the initial speed of the automobile?
Answer in units of m/s.


2. Relevant equations
F=-kx
Ke=(1/2)mv^2
U=(1/2)kx^2
Kf+Uf=Ki+Ui
W=Kf-Ki+Uf-Ui

3. The attempt at a solution
I'm really not sure where to start. I tried doing KE=U but I know that's not right.

Stonebridge

The kinetic energy of the car is absorbed by the bumper.
Use the spring formula (F=kx) and spring constant given to calculate the energy "stored" in the bumper when compressed 4.23cm
Energy stored will be average force times distance compressed.
Equate this to the kinetic energy of the car before collision.

bmoore509

I got it. I had a way to do it but the answer never seemed right. I didn't think about the fact that I needed to convert the 4.23 cm.

I did:
F=-kx = -253800
W=Fd = -10735.74
W=-.5mv^2+.5kx^2
-10735.74=-.5(3000)v^2-.5(6X10^6)(0.0423^2)
V=1.89m/s

Stonebridge

Good.
It was just a case of putting ½Fx² equal to ½mv²
Kinetic energy lost by the car is "absorbed" by the bumper.