Calculating Maximum Load Capacity of a Hydrogen-Filled Balloon

[anyone1979]

Help with a problem:

A spherical, hydrogen-filled balloon has a radius of 12 m.
The mass of the balloon plastic and support cables is 196 kg.
What is the mass of the maximum load the balloon can carry?
(Density of hydrogen = 0.09 kg/m^3; density of air = 1.25 kg/m^3)



I do not know where the radius of the balloon ties in but this is what I have so far.

V = mass/density = (196 kg)/(0.09 kg/m^3) = 2.2 x 10^3 m^3

mass of displaced air = (2.2 x 10^3 m^3) x (1.25 kg/m^3) = 2.9 x 10^3 kg

weight of displaced air = (2.9 x 10 ^3 kg) x (9.8 m/s^2) = 28420 N

maximum load the balloon can carry = (28420 N) / (9.8 m/s^2) = 2900 kg


Is that about right, or do I need to include the area?
If I need to include the area of the balloon, how do I do that?

 

[Shooting Star]

Help with a problem:

A spherical, hydrogen-filled balloon has a radius of 12 m.
The mass of the balloon plastic and support cables is 196 kg.
What is the mass of the maximum load the balloon can carry?
(Density of hydrogen = 0.09 kg/m^3; density of air = 1.25 kg/m^3)

I do not know where the radius of the balloon ties in but this is what I have so far.

V = mass/density = (196 kg)/(0.09 kg/m^3) = 2.2 x 10^3 m^3

1. Before moving on to the next questions, tell us whose volume is this V?

2. Do you feel that the volume of the Hydrogen gas itself has anything to do with the max load?

3. Please write Archimedes' Principle along with these so that we can proceed further.

 

[anyone1979]

Thanks for the reply. Archimedes' principle states: When a body is completely or partially immeresed in a fluid, the fluid exerts an upward force on the body equal to the weight of the fluid displaced by the body.

When a balloon floats in equilibrium in air, it's weight (including the gas inside it) must be the same as the weight of the air displaced by the balloon.

To answer you second question, I think so. To move upward, it should be the (mass of the displaced air) * (gravity).

To move downward, it should be the (mass of the hydrogen) * (gravity) right?

so, If these balance, then we find the max load the buoyant force can support.

 

[Shooting Star]

If you understand all this, why did you write > V = mass/density = (196 kg)/(0.09 kg/m^3) = 2.2 x 10^3 m^3 <?

The vol of the balloon is given via the radius. Vol of air displaced is known, and so the buoyant force is known. The mass of the balloon plastic etc and the H gas is known.

> so, If these balance, then we find the max load the buoyant force can support.

These won't balance. The buoyant force will be more. What do you think the answer should be?

 

[anyone1979]

Where will the mass of the balloon plastic etc.. tie in?

if ... V = (4 pi / 3)(radius^3) = 7.24 * 10^3 m^3 Then...

mass of displaced air = (7.24 * 10^3 m^3) * (1.25 kg/m^3) = 9.1 * 10^3 kg

weight of displaced air = (9.1 * 10 ^3 kg) * (9.8 m/s^2) = 89180 N

I am a little confused now...

 

[Shooting Star]

Where will the mass of the balloon plastic etc.. tie in?

if ... V = (4 pi / 3)(radius^3) = 7.24 * 10^3 m^3 Then...

mass of displaced air = (7.24 * 10^3 m^3) * (1.25 kg/m^3) = 9.1 * 10^3 kg

weight of displaced air = (9.1 * 10 ^3 kg) * (9.8 m/s^2) = 89180 N

B = Buoyant force = 89180 N, acting upward. (Already found.)

W = weight of H gas + 196 kg(plastic, rope etc) = weight of balloon, acting downward (Find it.)

MAx load it can carry now = B-W.

(Please check your arithmetic before replying.)

 

[anyone1979]

Thanks for clearing that up. I just got to add the 196 kg.

Weight of balloon = density of hydrogen * V * gravity + 196

then the buoyant force minus the weight of the balloon will give me the max load.