Question

A light spring of constant 143 N/m rests vertically on the bottom of a large beaker of water.
A 5.12 kg block of wood of density 657 kg/m3
is connected to the top of the spring and
the block-spring system is allowed to come to
static equilibrium. What is the elongation ∆L of the spring?
The acceleration of gravity is 9.8 m/s2. Answer in units of cm.
Don't round answer.

Answer 1

Bouyancy force is

$$F=mg\left(\frac{\rho}{\rho_w}-1\right)$$

$$F=(5.12)(9.8)\left(\frac{1000}{657}-1\right)=26.2\ N$$

$$∆L=\frac{F}{k}=\frac{26.2}{143}=0.183\ m=18.3\ cm$$