Hot air balloon - Archimedes Principle

[Attis]

Homework Statement

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.

Homework Equations

Archimedes Principle F0 = ρVg

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?

 

[ehild]

Homework Statement

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.

Homework Equations

Archimedes Principle F0 = ρVg

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?

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

 

[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.

 

[ehild]

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 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

 

[voko]

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.

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