Find the maximum distance the spring will be compressed?

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SUMMARY

The maximum distance a spring compresses when a 1.30-kg book is placed on it can be calculated using the formula for potential energy. Given a spring constant (k) of 1800 N/m, the correct compression distance is 0.12 m (12 cm). The equation mg = 0.5kx is used to derive this result, where m is the mass of the book and g is the acceleration due to gravity (9.81 m/s²). The initial approach of setting mgx equal to 0.5kx² is valid, but the confusion may arise from a misprint in the problem statement regarding the expected answer.

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ChloeYip
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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.
 
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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.
 
Thanks
 

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