# Homework Help: Helium Baloon question

1. Sep 17, 2007

### Kleptoma

1. The problem statement, all variables and given/known data
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

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

3. 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.

Last edited: Sep 17, 2007
2. Sep 17, 2007

### Kurdt

Staff Emeritus
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.

3. Sep 17, 2007

### 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

4. Sep 17, 2007

### Kurdt

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