# Homework Help: Compressed spring, doubling speed of impact

1. Feb 28, 2012

### shrutij

1. The problem statement, all variables and given/known data
A 0.211 kg shoe is dropped onto a vertically oriented spring with a spring constant of 102 N/m. The shoe becomes attached to the spring upon contact, and the spring is compressed 0.117 m before coming momentarily to rest.
If the speed of the shoe just before impact is doubled, what is the maximum compression achieved by the spring?

3. The attempt at a solution
Before this question, I figured out the speed the shoe was travelling at just before it hit the spring to be 2.08 m/s, which was correct. I also figured out the work done by the spring force to be -0.698 J and the work done by the weight of the shoe to be 0.242 J.
I know that when speed doubles, K.E. quadruples, which means the net work done must increase by 4 as well.
Wnet= Wgrav+Wspring=0.242 -0.698=-0.456 J.
I found the new K.E. to be 1.826 J (with doubled speed).
When I equate KE to Wnet, I get a quadratic: m*g*x -0.5*k*x^2= -1.826 J (new K.E.)
Is there no other way other than solving this quadratic to get to the new compression?

2. Feb 28, 2012

### SammyS

Staff Emeritus
There may be some other way, but what's wrong with solving the quadratic equation?

3. Mar 1, 2012

### shrutij

I tried solving the quadratic equation, but didn't get the right answer. Can someone tell me where I went wrong with my approach?
thanks