Automobile drives into a brick wall


by bmoore509
Tags: automobile, brick, drives, wall
bmoore509
bmoore509 is offline
#1
Oct5-10, 06:17 PM
P: 66
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 Hookes-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.
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Stonebridge
Stonebridge is offline
#2
Oct6-10, 03:00 AM
P: 649
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
bmoore509 is offline
#3
Oct6-10, 07:04 AM
P: 66
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
Stonebridge is offline
#4
Oct6-10, 08:23 AM
P: 649

Automobile drives into a brick wall


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


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