How much weight can the balloon lift?

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SUMMARY

The discussion centers on calculating the lifting capacity of a balloon filled with hot air versus cool air, focusing on the relationship between mass, density, and volume. Participants emphasize using the density formula to determine the mass of the air inside the balloon. The total mass lifted by the balloon is the sum of the mass of the empty balloon and any additional load. Key insights include the importance of understanding the densities involved and how they relate to the balloon's lifting ability.

PREREQUISITES
  • Understanding of the density formula: mass = density × volume
  • Basic knowledge of buoyancy principles
  • Familiarity with the concepts of hot air versus cool air densities
  • Ability to perform calculations involving mass and volume
NEXT STEPS
  • Research the effects of temperature on air density
  • Learn about buoyancy and Archimedes' principle
  • Explore practical applications of balloon physics in engineering
  • Study the relationship between pressure, volume, and temperature in gases (Ideal Gas Law)
USEFUL FOR

Students in physics, engineers working with buoyant systems, and anyone interested in the principles of aerodynamics and fluid mechanics.

Funny_N_Cool
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Homework Statement
A typical hot air balloon has a volume of 2801 cubic meters. The density of air outside the balloon is 1.17 kg/ cubic meter. The density of the hot air inside the balloon is 0.9 kg/ cubic meter. How much weight can the balloon lift?
Relevant Equations
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Keep adding mass to the balloon until the densities become equal.
 
@chemisttree Could you please demonstrate the solution?
 
How would you calculate the total mass of the balloon using the information provided?
 
I think the only formula to calculate the mass is the formula of density given this info.
 
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@chemisttree Is there another way to solve? please provide it explained.
 
Funny_N_Cool said:
I think the only formula to calculate the mass is the formula of density given this info.
You are given a volume and two different densities. What is the weight of the balloon filled with hot air versus cool air?
 
@berkeman Do you have any idea how to solve it?
 
Funny_N_Cool said:
@berkeman Do you have any idea how to solve it?
Given that the solution is utterly trivial, I'm quite confident that he can, but you are missing the point. The purpose of this forum is to help people learn how to solve problems, not to solve problems FOR them. You have been given sufficient hints, so think about it.
 
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  • #10
berkeman said:
You are given a volume and two different densities. What is the weight of the balloon filled with hot air versus cool air?
Funny_N_Cool said:
I think the only formula to calculate the mass is the formula of density given this info.
I misspoke. I should have said what is the mass of the air inside the balloon? The total mass lifted will be the mass of the empty balloon plus the added load. The sum of these is the total mass lifted. Any clearer?
 
  • #11
Funny_N_Cool said:
I think the only formula to calculate the mass is the formula of density given this info.
This is the correct direction to take.
 
  • #12
phinds said:
Given that the solution is utterly trivial, I'm quite confident that he can
Um, that's a compliment, right? Um... :wink:
 
  • #13
berkeman said:
Um, that's a compliment, right? Um... :wink:
Well, in a backhanded kind of way :smile:
 
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  • #14
What is the relationship between mass m, density ##\rho##, and Volume?
 

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