How many helium balloons does it take to lift a person?

[pinkerpikachu]

Homework Statement

How many helium-filled balloons would it take to lift a person? Assume the person has a mass of 76 kg and that each helium-filled balloon is spherical with a diameter of 33 cm.

Homework Equations

P = P₀ + ρgV

The Attempt at a Solution

I really don't know why this is confusing me, since it seems pretty straight forward. But, I know that the buoyant force has to be equal to at least the mass of the person (M) + the mass of the helium in all the balloons (m)

which means that F_B = Mg + mg

and the buoyant force is due to the helium, so, in order for the person to be lifted,

ρ_HegV = Mg + mg

so ρ_HeV = M + m

which is

ρ_HeV_He = M + ρ_airV_He

right?

So then M/(ρ_He - ρ_air) = V

but this would be negative...What I am doing wrong?

(I don't need help with the last part which is finding the number of balloons)

thanks!

 

[pinkerpikachu]

Wait, I have the density of the air and the helium switched, right? The buoyant force is due to the air and not the helium? Because the air is the fluid that it is in?

This is probably an easy question, but I'm pretty sleep deprived haha

 

[ehild]

Wait, I have the density of the air and the helium switched, right? The buoyant force is due to the air and not the helium? Because the air is the fluid that it is in?

Yes, exactly...

ehild