Finding the maximum density of a balloon

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In summary, to determine the maximum weight of a balloon filled with helium at atmospheric pressure, you need to calculate the weight difference between the balloon and the air surrounding it. Adding the weight of the balloon skin to the weight of the air and subtracting the weight of the helium will give the correct calculation.

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

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

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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.

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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.

What is the maximum density of a balloon?

The maximum density of a balloon depends on several factors, such as the material it is made of, the amount of air or gas inside, and the temperature and pressure of the surrounding environment. In general, the maximum density occurs when the balloon is filled with the maximum amount of air or gas it can hold.

How is the maximum density of a balloon determined?

The maximum density of a balloon can be determined through various methods, such as measuring the mass and volume of the balloon, or by using mathematical equations that take into account the properties of the material and the gas inside. Experimentation and calculations are usually involved in determining the maximum density of a balloon.

What factors affect the maximum density of a balloon?

The maximum density of a balloon can be affected by several factors, including the material of the balloon, the amount and type of gas or air inside, the temperature and pressure of the surrounding environment, and the size and shape of the balloon. These factors can all impact the overall density of the balloon and influence its maximum density.

Why is finding the maximum density of a balloon important?

Finding the maximum density of a balloon is important for various reasons. It can help determine the maximum weight a balloon can lift, the maximum pressure it can withstand before bursting, and the overall stability and performance of the balloon. Understanding the maximum density can also aid in the design and construction of balloons for different purposes, such as hot air balloons, weather balloons, and helium balloons for parties.

Is there a limit to the maximum density of a balloon?

The maximum density of a balloon is limited by the properties of the material it is made of, the gas or air inside, and the laws of physics. However, with advances in materials and technology, the maximum density of a balloon can be continually improved and may vary depending on the specific purpose and design of the balloon.