Finding the Equilibrium of a Spring in Water with a Connected Block

[songoku]

Homework Statement

A light spring with a force constant k = 160 N/m rest vertically on the bottom of a large beaker of water (a). A 5 kg block of wood (density = 650 kg/m^3) is connected to the spring, and the block-spring system is allowed to come to static equilibrium (b). What is the elongation \Delta L of the spring?

Homework Equations

F = kx

The Attempt at a Solution

I don't have idea to start. The spring rests on the bottom so when the mass is connected, I think the spring should be compressed rather than become longer. Maybe we should consider external force (I doubt this myself because there is no such thing in the question).
And why does the question mention density? The only thing I can come up with is to find volume of the block and I absolutely clueless what to do with the volume...

Thanks

 

[kuruman]

What keeps the wood from floating to the surface of the water? Draw a free body diagram of the block.

 

[songoku]

Hi kuruman

Maybe I get it. From the free body diagram, there are 3 forces that acts on the block which are weight, upthrust, and the restoring force from the spring.

\rho *g*V + kx = mg

From the above equation, I got x = - 16.5 cm. I want to ask why I got negative value?
Maybe I should use : restoring force = - kx, instead of kx ?

Thanks

 

[kuruman]

If up is positive and down is negative and the sum of all the forces must be zero,

+ρgV - kx - mg = 0

The buoyant force is up, gravity is down and the spring force is down because the spring stretches up to keep the block from floating to the surface.

 

[songoku]

Hi kuruman

Oh I see. The direction of the restoring force is downward

Thanks a lot for your help