# Find the maximum distance the spring will be compressed?

• ChloeYip
In summary, the problem involves a spring with force constant k = 1800 N/m and a 1.30-kg book placed vertically on top of it. The goal is to find the maximum distance the spring will be compressed when the book is released from rest. Using the equations for potential energy of the spring and potential energy by gravity, the correct answer is found to be 12cm. However, there may be a misprint in the text that caused confusion and a different answer in the solution manual.
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.

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

## 1. What is the purpose of finding the maximum distance the spring will be compressed?

The purpose of finding the maximum distance the spring will be compressed is to understand the behavior of the spring and its potential energy. This information is important in designing and using springs in various applications such as in machinery, suspension systems, and toys.

## 2. How is the maximum distance of compression calculated?

The maximum distance of compression is calculated using Hooke's Law, which states that the force required to compress or stretch a spring is directly proportional to the distance the spring is compressed or stretched. This can be represented by the equation F = -kx, where F is the force, k is the spring constant, and x is the distance of compression.

## 3. What factors affect the maximum distance of compression of a spring?

The maximum distance of compression of a spring is affected by the spring's material, length, diameter, and number of coils. The spring constant also plays a role, as a higher spring constant will require more force to compress the spring and therefore result in a shorter maximum distance of compression.

## 4. Can the maximum distance of compression be exceeded?

Yes, the maximum distance of compression can be exceeded if the force applied to the spring is greater than the spring constant can handle. This can result in the spring being permanently deformed or even breaking.

## 5. How does temperature affect the maximum distance of compression of a spring?

Temperature can affect the maximum distance of compression of a spring by changing the material's stiffness and the spring constant. When a spring is exposed to higher temperatures, the material becomes more pliable and the spring constant decreases, resulting in a longer maximum distance of compression. Conversely, colder temperatures can make the spring stiffer and decrease the maximum distance of compression.

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