Max Mass on Helium Balloon: 4.40 x 10^-3 kg

[Kleptoma]

Homework Statement

A 1.10 g balloon is filled with helium gas until it becomes a 20.0 cm-diameter sphere.
What maximum mass can be tied to the balloon (with a massless string) without the balloon sinking to the floor?
Density of Air: 1.28 kg/m^3
Density of Helium gas : 0.18 kg/m^3
Volume of a sphere: V = 4/3*pi*r^3
g = 9.80 m/s^2

Homework Equations

Buoyant Force (Fb) = p (density) * V * g
Density = mass/volume
Fb = Wo = p (density of object) * V (Volume of object) * g

The Attempt at a Solution

Fb = Weight of the object + Mg (M is the mass to be solved)
(1.23)(4/3*pi*(0.1m)^3)(9.8) = (0.18)(4/3*pi*(0.1m)^3)(9.8) + M(9.8)
M = 4.40 * 10^-3kg

I am uncertain of whether the buoyant force is the force of air pushing upwards on the balloon, or whether it is the helium gas in the balloon. Nonetheless, I used air as the density to solve for the buoyant force.

Another possibility would be that:
T = Fb - mg
T = (1.23)(4/3*pi*(0.1m)^3)(9.8) - (0.0011kg)(9.8)
T = 0.0397 N
Therefore mass of the object = 0.0397N / 9.8 = 4.05 * 10^-3

I am doubtful of which solution is correct and if either solution is actually correct.
Thank you in advance.

 

[Kurdt]

The weight that the balloon can hold will be the buoyant force, minus the weight of the balloon. The buoyant force is equal to the weight of the displaced air.

 

[Kleptoma]

Thanks Kurdt. I know that the buoyant force is equal to the weight of the displaced air, which is represented by (1.23)(4/3*pi*(0.1m)^3)(9.8).
But I'm not sure how to calculate the weight of the balloon. Do I use the density of the helium gas and multiply it by Volume and gravity (Weight = D*V*g) or simply use Weight = mg

 

[Kurdt]

You'll need to use the density multiplied by the volume, and of course add it to the weight of the balloon.