Calculate the bouyancy of two spheres joined by a rope submerged in seawater

[jnuz73hbn]

Homework Statement

Spheres in total 2, of equal volume are connected with a ship's rope (is not very long, nevertheless of unknown length, the rope is weightless) in sea water (Rho= 1200kg/m3). Both spheres sink down with constant speed. The lower sphere consists of magnesium (Rho= 1750 kg/m3). Underwater, the ship's rope is now cut. The upper sphere K1 moves with the same constant velocity (as it sank together with the lower sphere) v upwards again. We have not given the radius, the velocity, the mass or the value of the volume, how can we now find out, for example, what the density of the upper sphere is?

Relevant Equations

Fb= rho* g*h

m * g = mAl * g
V * ρ * g = VAl * ρAl * g
V * ρ * g = V * ρAl * g
ρ = ρAl
this does not work at all, because the upper ball must have a density smaller than that of seawater 1200kg/m3 or not?

 

[erobz]

Homework Statement: Spheres in total 2, of equal volume are connected with a ship's rope (is not very long, nevertheless of unknown length, the rope is weightless) in sea water (Rho= 1200kg/m3). Both spheres sink down with constant speed. The lower sphere consists of magnesium (Rho= 1750 kg/m3). Underwater, the ship's rope is now cut. The upper sphere K1 moves with the same constant velocity (as it sank together with the lower sphere) v upwards again. We have not given the radius, the velocity, the mass or the value of the volume, how can we now find out, for example, what the density of the upper sphere is?
Relevant Equations: Fb= rho* g*h

m * g = mAl * g
V * ρ * g = VAl * ρAl * g
V * ρ * g = V * ρAl * g
ρ = ρAl
this does not work at all, because the upper ball must have a density smaller than that of seawater 1200kg/m3 or not?

I think something is off with this question, but maybe I'm mistaken.

What do you get for the EOM of the two sinking spheres ( constant velocity $v$ ), and the EOM for the sphere that rising at $v$?

 

[jnuz73hbn]

I think something is off with this question, but maybe I'm mistaken.

What do you get for the EOM of the two sinking spheres ( constant velocity $v$ ), and the EOM for the sphere that rising at $v$?

The balls are in equilibrium of forces

 

[erobz]

The balls are in equilibrium of forces

Correct. So what is the EOM that describes the two balls sinking?

 

[BvU]

Please explain your symbols. You have two situations:

1. balls connected and sinking
2. balls disconnected and one sinking, one rising

set up equations with clear symbols for each ball & case.Use $\LaTeX$

 

[haruspex]

The balls are in equilibrium of forces

Right, but what are those forces?

 

[erobz]

I think something is off with this question, but maybe I'm mistaken.

@jnuz73hbn Just so you know the problem is ok, but it's a little sneakier than I originally suspected.