What is the tension in the line holding a helium-filled balloon?

[clutchstrike]

Homework Statement

An empty rubber balloon has a mass of .0120 kg. The balloon is filled with helium at a density of .181 kg/m^3. At this density the balloon is spherical with a radius of .500m. If the filled balloon is fastened to a vertical line, what is the tension in the line?

Homework Equations

Equations that I found:
volume of a sphere = 4/3(pi)(r^3)
density = mass/volume
Buoyant force = weight

The Attempt at a Solution

I attempted to set up a free body diagram, with two forces. One is the tension going up, and the other is weight going down. That would mean T = mg. since density = mass/volume, .181 kg/m^3 = mass / (4/3)(pi)(.5)^3. That gets a mass of .095g.
.095g(9.8 m/s^2) = .929 N. The correct answer is 5.57 N. So, I got it wrong.

 

[Doc Al]

The balloon floats--the string tension pulls the balloon down. What other forces act on the balloon?

Note: Buoyant force = weight of displaced fluid

 

[clutchstrike]

pressure?

 

[Doc Al]

pressure?

The pressure of the air is a force per unit area. The resultant force due to the air pressure is the buoyant force.

So far we have two forces acting on the balloon: tension and buoyant force. What's the third force?

 

[clutchstrike]

gravity?

 

[Doc Al]

gravity?

Right! The weight of the balloon is the third force.

So write an expression for the net force and use it to solve for the tension.

 

[clutchstrike]

But what is the equation for buoyancy, if there is no displaced fluid in the problem?

 

[Doc Al]

Sure there is: the displaced fluid is the air! It's the air that exerts the buoyant force on the balloon.