Finding the maximum density of a balloon

[penzoate]

Homework Statement

A balloon is filled with helium at an atomospheric pressure. The skin of the balloon has a mass of 3.1 kg and the volume of the balloon is 18 m^3.

Homework Equations

What is the greatest weight of the balloon?

The Attempt at a Solution

In order to determine the maximum weight of the balloon, wouldn't you have to calculate the weight differences between the balloon and the air surrounding the balloon. Assuming this is the correct step,

18m^3*(density of air=1.293)*9.8-3.1*9.8=maximum weight
or
18m^3*(density of air=1.293+density of helium=.1786)-9.8*3.1=maximum weight
or
18m^3*(Density of air=1.293)*9.8-18m^3*(density of helium=.1786)*9.8-3.1*9.8=maximum weight

Which of these 3 calculations I attempted is correct

 

[berkeman]

You need to add the weight of the balloon skin, not subtract it. Other than that, your 3rd try looks correct to me.

 

[m2003]

?

It is not possible to determine the maximum weight of the balloon with the given information. While it is true that the weight of the balloon will be affected by the density of the air and the helium inside, there are other factors that need to be considered such as the elasticity of the balloon material and the temperature of the air and helium. These can all impact the maximum density of the balloon. In order to accurately determine the maximum density, a more comprehensive study would need to be conducted, taking into account all the variables and their potential effects on the weight of the balloon.

 

[kyle8921]

?

I would like to clarify that the density of helium is not a constant value and can vary depending on temperature and pressure. Therefore, the maximum density of a balloon cannot be determined solely by calculating the weight differences between the balloon and the surrounding air. Other factors such as the temperature and pressure inside the balloon, as well as the properties of the balloon material, also play a role in determining the maximum density.

To accurately determine the maximum density of a balloon, experiments would need to be conducted under controlled conditions to measure the weight and volume of the balloon at various levels of inflation. This data could then be used to plot a graph and determine the point at which the balloon reaches its maximum density.

It is also important to note that the term "maximum density" may be interpreted differently depending on the context. For example, the maximum density of a balloon may refer to the point at which it can hold the most weight without bursting, or it could refer to the point at which it can hold the most volume of helium. Therefore, a clear definition and context is necessary when discussing the maximum density of a balloon.