Upward Acceleration of a ballon...?

Question

The hot air inside the balloon has a density of 0.79 kg/m3, and the cool air outside the balloon has a density of 1.29 kg/m3.

(a) What is the algebraic expression for the upward acceleration ay of the balloon? Express your answer in terms of the density ρC of the cool air outside the balloon, the density ρH of the hot air inside the balloon, and the magnitude g of the acceleration due to gravity. Upward is the positive direction.
(b) What is the upward acceleration ay of the balloon?

Thanks...

Answer 1

a)
The upward acceleration will be due to the buoyant force on the balloon.

The force of buoyancy is equal to ρC * V * g , where V is the volume of the balloon

The downward force due to gravity is the weight of the balloon = ρH * V * g

This is divided by the mass of the balloon to give the acceleration (ρH * V)
So, the total upward acceleration =
(ρC * V * g - ρH * V * g)/(ρH * V)
So, the acceleration = (ρC - ρH)/ρH * g


b)
This is equal to (1.29-0.79)/0.79 * 9.8 = 6.202 m/s

Answer 2

Won't give you the exact answer (that would be unethical, right?) but here's the main idea:

You'll be using three main principles/equations:

1. The relationship between volume, mass and density.
2. The amount of buoyant force on an object.
3. Newton's 2nd law (F = m*a).

If you are unfamiliar with any of these, stop now and go crack open you books.

So here's the plan:

1. Write an equation for the balloon's volume, in terms of its mass and density; V = ??? (Use "Mh" for the balloon's mass, which you don't know, but no matter.)
2. Write an equation for the mass of cold air that the balloon displaces, in terms of the balloon's volume V, and the density of cold air. Mc = ???
3. Write an equation for the upward buoyant force, in terms of the mass of displaced cold air Mc, and gravity g. Fb = ???
4. Write an equation for the downward force (weight) of the balloon, in terms of its mass Mh, and gravity g. Fg = ???
5. Use Newton's 2nd law. For "F", use the net upward force (Fb - Fg); for "m" use the balloon's mass (Mh). For "a", just write "a".

If you know algebra, you should be able to combine all of the above equations to end up with an equation "a = ???", where the "???" is in terms of your known quantities (density of hot air & density of cold air), and gravity g.

Good luck!

Answer 3

Accurate answer to this question is far beyound
most university courses in physics.

Mass of the balloon is not the only thing which acclerates.
The air around the ballon will acclerate too.

People will tell you (well, they already did) that
the force of bouyancy acting on the ballon is equal to
F = g (density of air) * (volume).
This formula is for valid for _static buoyancy only,
and is not applicable in case of acclerating balloons.
That's why it is called hydrostatic buoyancy.

Answer 4

ρ = m/V

g = F/m = F/(ρC-ρH)*V

Oh, heck...I don't know.