Question

A spring with a force constant k = 200 N/m is attached to the bottom of a large beaker which is then filled with water (figure (a)). A block of pine wood with a mass of 4.10 kg and a density of 630 kg/m³ is connected to the spring and the block-spring system comes to equilibrium as shown in figure (b). Determine the elongation ΔL of the spring.

Answer 1

There has been no water in the beaker, wood block would have had compression governed by
F = - k ΔL = mg = 4.1g

due to water filled scenario, block will also be subjected to bouyancy force upwards - the net force on spring will decide the extension or compression.

apparent weight of block = W' = mg - [V d(water)*g]
where V = volume of block = m/d(wood)
W' = mg - m[(d(water)/d(wood)) * g]
W' = 4.1*9.8 - 4.1[(1000/630) *9.8]
W' = 40.2 N- 63.84 N=-23.6N

this is upward pull on the spring>
restoring force = + 23.6 N downwards
so there will be extension in spring

ΔL = 23.6/k = 23.6/200 = 0.118 meter
extension