Question

A spring of negligible mass has a force constant of 1600 N/M you place the spring vertically with one end on the floor you then drop a 1.2 kg book onto it from a height of 0.8 a o e the top of the spring find the maximum distance the spring will be compressed

Answer 1

Given data

*The given force constant of spring is k = 1600 N/m

*The given mass of the book is m = 1.2 kg

*The given height is h = 0.8 m

The formula for the maximum distance by which the spring will be compressed is given by the conservation of energy as

$\begin{gathered} U_s=U_B \\ \frac{1}{2}kd^2=mg(h+d) \end{gathered}$

*Here U_s is the spring potential energy.

*Here U_B is the book potential energy.

*Here g is the acceleration due to the gravity

Substitute the known values in the above expression as

$\begin{gathered} \frac{1}{2}(1600)d^2=(1.2)(9.8)(0.8+d) \\ 800d^2=9.408+11.76d \\ d=0.116\text{ m} \\ \approx0.12\text{ m} \end{gathered}$

Hence, the maximum distance by which the spring will be compressed is d = 0.12 m