Question

A spring of negligible mass has force constant k = 1800 N/m .

You place the spring vertically with one end on the floor. You then drop a book of mass 1.40 kg onto it from a height of 0.900 m above the top of the spring. Find the maximum distance the spring will be compressed.

Take the free fall acceleration to be 9.80 m/s2 . Express your answer using two significant figures.

Answer 1

Let's define h = 0 at the top of the spring to make things a little easier though.

E tot = E ' tot

mgh1 = (1/2)kx^2 + mgh2

Note that x and h2 are actually the same thing here - and they are also both negative. (-x)^2 is still just x though.

mgh1 = (1/2)kx^2 - mgx

0 = (1/2)kx^2 - mgx - mgh1

0 = (1/2)(1800 N/m)x^2 - (1.40 kg)(9.80 m/s^2)x - (1.40 kg)(9.80 m/s^2)(0.900 m)

0 = 900x^2 - 13.72x – 12.348

x = -0.10976 or 0.125m

Minus one is the compressed distance.

So the spring will compress 0.11 m (2sf)