I mean in the example with the balloons

You are about 100kg and you occupy about 0.07 m^3
Each balloon will be n x 0.01 m^3 so for every balloon you add the amount of volume will increase but the amount of mass increase will be smaller and you will reach a threshold where the combined density will be lower than 1.2kg/m^3 at which point you will ascend

Shall we move on to 3 now?

Why would mass be smaller

mass to volume ratio decreases

sorry

Each balloon has the same amount of helium

man(100 / 0.07) + n x (0.001 / 0.01)

density = mass / volume

by adding more ballons you are increasing the volume, but the total mass does not increase significantly, in fact the amount of mass you are adding is less than the equivalent amount of mass you would be adding if you added balloons of air.

Ok let's use easier numbers I am lost

One balloon is 3 kilos

man = 100kg mass, 0.07 m^3 volume

n = number of balloons

0.0001kg = mass of balloon full of helium

0.01 m^3 = volume of balloon

Ok

so do you concur that were I to attach a sufficient number 'n' of helium balloons to myself, I would ascend, yes?

So mass of one balloon is 0.0001/0.01

I mean density

about that

Density of two balloons is 0.0002/0.02

depends on what sort of balloon you're using, what material, rigid or inflatable

Or simplified the same thing

wrong

density of two balloons is 0.0001/0.01 + 0.0001/0.01

What

No.

which is the same as 0.0002/0.01

The mass increases, not the density.

What's 1/2 + 1/2 ?

You have to do the mass and the volume of the ENTIRE system

The total buoyant force increases, though.

and even forgetting the math it's common sense that volume increases

By adding a second balloon, you've doubled both the mass and the volume, so they cancel each other out.

the mass increase so does the volume, however the increase in mass is much much less than the increase in mass would be if you were to fill the balloons with air

that doesn't matter

it could be infinitely less

as long as the ratio stays the same...

Which it obviously does if the helium balloons are identical.

Air has a density of about 1.2kg/m^3, however helium at room temperature at standard air pressure is about 0.164kg/m^3 and hydrogen is lower about 0.1kg/m^3