# Hot air balloon - Archimedes Principle

1. Feb 26, 2014

### Attis

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

A hot air balloon with V = 500 m^3 is floating in the air without moving. The air outside the balloon has a density of 1,20 kg/m^3, and the hot air inside the balloon has a density of 0,75 kg/m^3. Calculate the total mass of the hot air balloon.

2. Relevant equations

Archimedes Principle F0 = ρVg

3. The attempt at a solution

I googled the answer to this question, so I already know how to solve it:
F0 = (1,20 -0,75) * 500 = 225 kg

What I don´t understand is why g wasn´t integrated into this answer? How come the answer isn´t (1,20-0,75)*500 * 9,82 =2210 kg?

2. Feb 26, 2014

### ehild

The buoyant force is ρVg, but you made it equal with mass, which is wrong.

Fo has to be equal to the weight, that is, ρ(outside)Vg=ρ(inside)Vg+Mg where M is the mass of the balloon and cargo, without the air inside the balloon.
You can divide the whole equation with g.

ehild

3. Feb 26, 2014

### voko

I do not think you described the problem as stated. Because as stated, the answer is simply $m = \rho V$, where $\rho$ is the hot air density, by definition of density.

The answer that you think should be true is not a correct answer to a question about mass, simply because that answer gives some force.

4. Feb 26, 2014

### ehild

The total mass of the hot-air balloon was asked. It is not the mass of the air only, but includes both the balloon material and the cargo.

ehild

5. Feb 27, 2014

### voko

Then the answer is wrong. Just the air in the balloon is 375 kg.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Threads - balloon Archimedes Principle Date
Test Balloon on a planet Mar 7, 2018
Balloon (Pressure) Jan 27, 2018
Archimede's Principle-Hot air balloon floating Sep 17, 2008