# Mass of gas required to lift another mass

• bray d
In summary, the minimum mass of gas required to lift another mass is given by the formula m=(MG)/(A-G), where G is the density of the gas and A is the atmospheric density. This is based on the fact that the density of the gas must be less than the atmospheric density in order for the lifting force to be possible. It may be helpful to apply actual numbers to the situation in order to better understand the relationships involved.
bray d
[SOLVED] mass of gas required to lift another mass

## Homework Statement

A balloon contains gas of density G and is to lift a mass M, including the balloon but not the gas. Show that the minimum mass of gas required is m=(MG)/(A-G) where A is the atmospheric density.

## Homework Equations

Basic density mass relationships?

## The Attempt at a Solution

Obviously the density of the gas is less than the density of the atmosphere, thus the lifting force is possible. I'm just having a hard time seeing the relationships without actual numbers. I tried applying numbers to the situation but that hasn't seemed to help, like making G=.5 and A=1. I need a witty suggestion to jump start me. Thanks

Figured It Out!

I can provide a mathematical explanation for the solution to this problem. Let's start with the basic relationship between density, mass, and volume:

Density = mass/volume

We know that the density of the gas inside the balloon (G) is less than the density of the atmosphere (A). In order for the balloon to lift a mass M, the lifting force (FL) must be greater than or equal to the weight of the mass (W = Mg):

FL ≥ W

We can express the lifting force in terms of density and volume:

FL = (density of gas inside balloon)*(volume of balloon)

And we can express the weight in terms of density and volume:

W = (density of atmosphere)*(volume of balloon) + (density of mass)*(volume of mass)

Since the volume of the balloon is the same in both equations, we can set them equal to each other and solve for the minimum mass of gas required (m):

(density of gas inside balloon)*(volume of balloon) = (density of atmosphere)*(volume of balloon) + (density of mass)*(volume of mass)

Substituting in the given values for density and volume, we get:

G*(volume of balloon) = A*(volume of balloon) + M

Solving for the volume of the balloon (which is equal to the volume of the gas inside it), we get:

(volume of balloon) = M/(G-A)

Finally, we can plug this back into our original equation for the lifting force:

FL = (density of gas inside balloon)*(volume of balloon)

FL = G*(M/(G-A))

And since we know that FL ≥ W, we can set these two expressions equal to each other and solve for the minimum mass of gas required (m):

G*(M/(G-A)) ≥ Mg

Simplifying, we get:

(MG)/(G-A) ≥ Mg

Dividing both sides by G and canceling out the M's, we get the final result:

m = (MG)/(G-A)

This shows that the minimum mass of gas required to lift a mass M is dependent on the density of the gas (G) and the density of the atmosphere (A). I hope this helps to provide a clear understanding of the relationship between these variables.

## 1. What is the relationship between the mass of gas and the mass it can lift?

The amount of mass a gas can lift is directly proportional to its mass. This means that the more mass a gas has, the more it can lift.

## 2. How is the mass of gas required to lift another mass calculated?

The mass of gas required to lift another mass is calculated using the ideal gas law, which takes into account the pressure, volume, temperature, and number of moles of the gas.

## 3. Does the type of gas affect the amount of mass it can lift?

Yes, the type of gas does affect the amount of mass it can lift. This is because different gases have different densities and molecular weights, which can impact their ability to lift a mass.

## 4. Can the temperature of the gas affect its lifting ability?

Yes, the temperature of the gas can affect its lifting ability. As the temperature increases, the gas molecules gain more kinetic energy and spread out, decreasing the density of the gas and reducing its lifting ability.

## 5. Is the mass of the object being lifted a factor in the amount of gas required?

Yes, the mass of the object being lifted is a factor in the amount of gas required. The heavier the object, the more gas will be needed to lift it. However, other factors such as temperature and atmospheric conditions also play a role in determining the amount of gas needed.

• Introductory Physics Homework Help
Replies
12
Views
787
• Introductory Physics Homework Help
Replies
12
Views
1K
• Introductory Physics Homework Help
Replies
6
Views
1K
• Introductory Physics Homework Help
Replies
170
Views
5K
• Introductory Physics Homework Help
Replies
2
Views
2K
• Introductory Physics Homework Help
Replies
18
Views
6K
• Introductory Physics Homework Help
Replies
11
Views
4K
• Introductory Physics Homework Help
Replies
4
Views
2K
• Introductory Physics Homework Help
Replies
62
Views
4K
• Introductory Physics Homework Help
Replies
11
Views
2K