How Fast is the Shoe Moving Before It Hits the Spring?

[fernancb]

Homework Statement

A 0.222 kg shoe is dropped onto a vertically oriented spring with a spring constant of 101 N/m. The shoe becomes attached to the spring upon contact, and the spring is compressed 0.110 m before coming momentarily to rest.

What work is performed by the weight of the shoe while the spring is being compressed? = 0.239 J

What work is done by the spring force? = 0.611 J

Here is my problem:
At what speed is the shoe traveling just before it hits the spring?

Homework Equations

Ek = 0.5 mv^2
W = Fd
W = E

The Attempt at a Solution

W = Ek
= 1/2 mv^2
0.239 = 1/2 (0.222)v^2
v = 1.47 m/s

What am I doing wrong?

 

[gneill]

W = Ek
= 1/2 mv^2
0.239 = 1/2 (0.222)v^2
v = 1.47 m/s

What am I doing wrong?

Once the shoe hits the spring, the weight of the shoe is only doing part of the work to compress the spring. The kinetic energy that the shoe brought with it is doing the rest.