# Archimedes Principle $\Delta M$ formula

i'm trying to determine a formula for $\Delta M=M-M_{apparent}$ in terms of $\rho_o , \rho_w , M$ for a fully submerged object and I have no idea where to begin. I have attempted to draw a force diagram but it did not help.

Just to correct you, there is no such thing as apparent mass. Mass is a constant here. The correct term used should be weight.

Let the mass be $M$. Then the weight will be $Mg$, and the apparent weight $Mg-\rho_{w}Vg$, where $V$ is the volume of the water displaced by the object.

Do take a look at the following diagram. The image here shows how the forces act.

Hence, $\Delta W$ is equivalent to the buoyant force, $\rho_{w}Vg$.

• Thank you, that makes more sense, I think I was just getting confused with the term 'apparent mass'. – Lucas Hasil Aug 28 '18 at 9:03

Use density = mass/volume

The most important thing here is finding the volume of the object, which is mass of the object divided by density of the object.

I think you can find the answer now, you have to work on it. Solving all of the problem is not allowed, and not good for you.