You place the spring vertically with one end on the floor. You then drop a book of mass 1.10 kg onto it from a height of 0.600 m above the top of the spring. Find the maximum distance the spring will be compressed.

max_x = 3.59850 / √k

Explanation:

HI!

We can solve this problem using the conservation of the energy.

The energy of the initial state - before the book is drop is:

Vi = mgxi

When the book is just above the srping some of this energy will be converted into kinetic energy (the book is moving), and all of this kinetic energy will be transferred into the spring and it will be compresed.

The kinetic energy the book has before toching the spring:

K = Vi - Vf = mg (xi - xf) = (1.10 kg) * (9.81 m/s^2) * (0.6 m) = 6.4746 kg m^2/s^2

The energy of the spring is:

Vs = (1/2) kx^2

Where k is the spring constant in units (kg/s^2)

The spring will compressed a distance x:

x^2 = (2/k) K = (12.9492/k)