Question

Determine the magnitude and direction of a force necessary to hold a concrete tube 30 cm on each side in equilibrium and completely submerged in
a.) mercury and
b.) seawater
Mass density of concrete cube = 2.40 g/mL

Answer 1

In seawater your concrete cube will falling down, since mass density of concrete (2.54) is greater than mass density of a seawater (1.2), namely
2.54>1.2,
so on your cube will act two vertical aligned forces:
1) the weight of your cube, which is directly downward;
2) the Archimede force, which is upward
I remember you, please, that Archimede force has modulus equals to the weight fluid, the seawater, displaced due to the presence in seawater of the cube.

Since density mass of mercury is 13.58 grams/cm^3, then we have:
13.58>2.40
so in m the case of mercury your cube will fall down .
As before the force acting on your cube can be calculated with the same reasoning. Even if the question can be more subtle, if the deepness at which you want to hold your cube is not neglectable

Answer 2

weight of concrete cube=
\[9.81*2.4*(30*10^{-2})^{3}\approx 636*10^{-3}Newton\]

Answer 3

You mean to say the weight of the cube should be equal to the tension?

Answer 4

weight of fluid displaced:
1) seawater:
\[9.81*1.2*27*10^{-3}\approx 318*10^{-3} Newton\]
2) mercury:
\[9.81*13.58*27*10^{-3}\approx 3600*10^{-3}Newtom\]

Answer 5

so in the caser of seawater, on your cube will act a force vertically aligned, downward, whose modulus is:

Answer 6

\[(636-318)*10^{-3} Newton\]
in the case of a mercury, on your cube will acts a force vertically aligned, upward, whose modulus is:
\[(3600-318)*10^{-3}Newton.\]
So I ask you sorry again, in the second case your concret cube will go towards the free surface in order to float, and will not falling down as wrongly as said before, since the density mass of concrete, is Greater than density mass of mercury.
A criterion to establish if a body immerged in a fluid will fall down, float, or stay in Equilibrium into that fluid is that:
1) if density mass of body is equals to density mass of fluid, the body will stay in Equilibrium into that fluid;
2) if density mass of body is greater than density mass of fluid, than body will fall down;
2) if density mass of body is less than density mass of fluid, then body will go to the free surface of fluid in order to float

Sorry again, I dsaid right the first time in the case of mercury