FBD of Hot Air Balloon and Buoyancy

[zeralda21]

Homework Statement

I want to find all acting forces on a hot air balloon rising form the ground. Volume and mass of balloon are given.

Homework Equations

F=mg
F_{b}=ρVg

The Attempt at a Solution

Here is my free-body diagram;

There are three acting forces:
1) F_1 = mg Which is the gravitational forces acting on the balloon itself(m is mass of the balloon)

2) F_2 = p_{balloon}Vg Which is the gravitational force of the air inside the balloon.

3) F_3 = p_{air}Vg Which is the gravitational force of the air outside of the balloon.

F_1 and F_2 are downward(negative y-direction) so F_3 must be an upward force. But I don't understand that. Say that you are pushing down an object into a fluid, then there is an upward force(buoyancy). And in this case we are lifting an object through a fluid, should not the buoyancy force be pushing down?? In that case, which force is forcing the balloon to rise?

 

[zeralda21]

Or maybe it is this way;

F_1 and F_2 are forces we want to lift and hence are upward and F_3 is in the opposite(negative direction). But that still does not explain which force that lifts F_1 and F_2...

 

[gneill]

Investigate Archemedes' Principle. If you do a web search you will turn up lots of resources. Include the string "free body diagram" or "FBD" to narrow things down.

 

[zeralda21]

Investigate Archemedes' Principle. If you do a web search you will turn up lots of resources. Include the string "free body diagram" or "FBD" to narrow things down.

Does not that mean that there should be a buoyancy force even when the balloon isn't rising(at rest at the ground)? In that case the density(or should we say temperature) of the air inside is the obviously the same as outside and

ƩF: N+ρ_{air}Vg-ρ_{balloon}Vg-mg=0

since ρ_{air}Vg=ρ_{balloon}Vg and N=mg

Correct analysis?

 

[gneill]

Something can be at rest at ground level either by having weight that presses it to the ground, or because it is neutrally buoyant. In the latter case, the density of the gas in the balloon can be less than that of the external air so that buoyancy just balances the weight of the balloon.