A spring has a spring constant of 1350 N/m. You place the spring vertically with one end on the floor. You then drop a 1.3 kg book onto it from a height of 0.8 m above the top of the spring. Find the maximum distance the spring will be compressed. Express your answer with the appropriate mks units.

0.015m (downwards)

When the book is dropped on the top of the spring at that height, the potential energy () of the book is converted to elastic energy () on the spring thereby causing a compression on the spring. i.e

=

But;

The potential energy of the mass (book), is the product of the mass(m) of the book, the height(h) from which it was dropped and the acceleration due to gravity (g). i.e

= - m x g x h         [the -ve sign shows a decrease in height as the mass (book) drops]

Also;

The elastic energy () of compression of the spring is given by

= x k x c

Where;

c = compression length of the spring

k = the spring's constant

Substitute these values of and E into equation (i) as follows;

- m x g x h = x k x c             ----------------(ii)

From the question;

m =  1.3kg

h =  0.8m

Take g = 10m/s²

k =  1350N/m

Substitute these values into equation (ii) as follows;

- 1.3 x 10 x 0.8 = x 1350 x c

- 10.4 = 675c

Solve for c;

c = - 0.015 m          [The negative sign shows that the spring actually compresses]

Therefore, the maximum distance the spring will be compressed is 0.015m (downwards of course).