Written Challenge Problem, Fluid Statics:

Wooden cube, density $620k\frac{g}{m^3},$ is $0\mathrm{.}08$ m tall, $0\mathrm{.}12$ m wide, and $0\mathrm{.}12$ m thick. It floats in a liquid with density $900k\frac{g}{m^3}.$ A string attached to the bottom of the container prevents the cube from floating up to the surface. Find the tension in the string. $[8]$

Draw a pictorial representation of the problem.

Draw a free body diagram of the wooden cube.

Choose a coordinate system. What direction will you designate as positive?

Write out the Newton's second law $($net force$)$ equation for the wooden cube.

What variables in the force equation can you fill in from the given information?

Substitute the given information into he force equation as appropriate, and solve for the tension.

Comment briefly on whether your result is reasonably believable. If it is $-$ what sort of result could be easily identified as not believable for this problem?