Buoyant force on a balloon is equal to the mass of air it displaces

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Discussion Overview

The discussion revolves around calculating the diameter of a spherical hydrogen-filled balloon necessary for it to lift off the ground, given specific conditions such as temperature and atmospheric pressure. The context is primarily homework-related, focusing on the application of gas laws and buoyancy principles.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant states that the buoyant force on the balloon equals the mass of air it displaces, linking this to the gravitational force acting on the balloon and its contents.
  • Another participant suggests calculating the volume required for sufficient buoyancy as a first step.
  • A participant expresses uncertainty about the formulas needed for the calculations, indicating a lack of familiarity with buoyancy concepts.
  • One reply clarifies that buoyancy can be calculated as the weight of the air displaced by the balloon.

Areas of Agreement / Disagreement

Participants generally agree on the principle that buoyancy relates to the mass of air displaced, but there is uncertainty regarding the specific calculations and formulas needed to solve the problem.

Contextual Notes

Participants have not yet established a clear methodology for solving the problem, and there is a lack of consensus on the necessary equations and concepts related to buoyancy.

chemguy12345
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Homework Statement



The buoyant force on a balloon is equal to the mass of air it displaces. The gravitational force on the balloon is equal to the sum of the masses of the balloon, the gas it contains, and the balloonist. If the balloon and balloonist together weight 175 kg, what would the diameter of a spherical hydrogen-filled balloon have to be in meters if the rig is to get off the ground at 22 degrees Celsius and 752 mmHg? (Take MM air= 29.0 g/mol)

Homework Equations



We're currently studying gases. So I'm thinking of finding mass of h2 gas and then the moles of H2, then the volume and plugging into V=(4/3)(Pi)(r^3) to find radius and then diameter. Relevant Equations --> V=nRT/P. (r=.0821 atm L/mol K), PV=nRT(ideal gas law)

The Attempt at a Solution


I don't know where to begin. The wording is confusing me. Help please
 
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You need to calculate first what volume will have buoyancy high enough.
 


What formula would I have to use? I'm not sure because we haven't learned anything about buoyancy yet. Thank you for helping
 


Buoyancy is physics, but you are told how to calculate it - it equals mass (I would say weight) of the air balloon displaces.
 

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