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
[tex]\begin{gathered} U_s=U_B \\ \frac{1}{2}kd^2=mg(h+d) \end{gathered}[/tex]*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
[tex]\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}[/tex]Hence, the maximum distance by which the spring will be compressed is d = 0.12 m
