What is the elongation of the spring ?

Question

A light spring of constant 180 N/M rests vertically on the bottom of a large beaker of water. A 4.12 kg block of wood of density 680 kg/m^3 is connected to the top of the spring and the block-spring system is allowed to come to static equilibrium. what is the elongation of the spring ? answer in units of cm.

Answer 1

I assume the block is completely submerged

Since Volume * density = mass, then
Volume= mass/density

The boyant force is equal to the difference in density times volume
Water is 1000kg/m^3
so diff =1000-680
or 320

320*V*g=force
=320*9.81*4.12/680
19 N
since F=k*x
x=F/k
=100*19/180
10.6 cm

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Answer 2

Calculate the weight of the block of wood.
(Easy, it's mg)

Calculate the buoyant force of the block.
Archimedes says: buoyant force equals the weight of the displaced water
= volume * density of water * g

That volume is just the mass of wood divided by its density.

The spring must exert a force equal to the difference between the weight and the buoyancy to keep the block static. So just subtract.

Once you have the force, calculate the displacement using hooke's law:

F = kx. You calculated F. They give you k.