Find the maximum distance the spring will be compressed?

[ChloeYip]

Homework Statement

A spring of negligible mass has force constant k = 1800 N/m .

You place the spring vertically with one end on the floor. You then lay a 1.30-kg book on top of the spring and release the book from rest. Find the maximum distance the spring will be compressed.

Homework Equations

Potential energy of spring: 0.5kx^2
Potential engergy by gravity: mgh

The Attempt at a Solution

mgx = 0.5kx^2
mg = 0.5kx
x=0.01417m(take g=9.81)

But the answer is 12cm, what's wrong with my approach?
How can I obtain the correct answer?
Thank you.

 

[gneill]

Your approach looks okay to me. Could be a misprint in the text. Sometimes authors change the numbers in problems when they "refresh" a book for new editions and fail to update the answer key accordingly.

 

[ChloeYip]

Thanks