Question

You place the spring vertically with one end on the floor. You then lay a 1.60 kg book on top of the spring and release the book from rest. Find the maximum distance the spring will be compressed.

Answer 1

Answer:

Compression in the spring, x = 3.7 cm

Explanation:

It is given that,

Mass of the book, m = 1.6 kg

It can be assumed the spring constant of the spring is, k = 840 N/m

As the book moves down, the change in potential energy of the book is converted to spring potential energy of compression. The mathematical expression is as follows :

$\dfrac{1}{2}kx^2=mgx$

$x=\dfrac{2mg}{k}$

$x=\dfrac{2\times 1.6\ kg\times 9.8\ m/s^2}{840\ N/m}$  

x = 0.037 meters

or

x = 3.7 cm

So, the spring is compressed to a distance of 3.7 cm. Hence, this is the required solution.