Solving a Balloon Mass Calculation: Find Minimum Gas Mass Needed

Click For Summary

Homework Help Overview

The problem involves calculating the minimum mass of gas required for a balloon to lift a given mass, incorporating concepts from fluid dynamics and buoyancy. The original poster presents a formula relating the mass of gas to the atmospheric density and the density of the gas.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of Archimedes' principle and the relationship between buoyancy force and the mass of gas. There are attempts to rearrange equations and apply fluid motion principles, but some express confusion about reaching the desired equation.

Discussion Status

The discussion includes various attempts to clarify the relationships between the forces involved and the variables in the problem. Some participants have provided insights into the necessary equations, while others are still grappling with the calculations and expressing a need for further assistance.

Contextual Notes

There is mention of specific variables such as the density of gas and atmospheric density, as well as the need to consider the buoyancy force in relation to the total mass being lifted. The original poster indicates a connection to a related question, suggesting constraints on the problem's context.

etothey
Messages
22
Reaction score
0

Homework Statement



A balloon contains gas of density pg and is to lift a mass M, including the balloon but not the gas. Show that the minimum mass of gas required is m= Mp / (pa - pg). Where pa is Atmospheric density

Homework Equations



I assume fluid motion so
P= Po + p*h*g
Also archimedes principle Vair=Vgas could come in handy?


The Attempt at a Solution



I managed to rearrange into mpa-mpg = Mpg and then i am so stuck.

Help is needed so I can solve a question that is related to this!
 
Physics news on Phys.org
Hi
Buoyancy force has to be , at least

F_B=Mg+M_{gas}g

where Mgas is the mass of the gas in the balloon. If V is the volume occupied
by the gas and if \rho_g is the density of the gas,

M_{gas} = \rho_g V

Now apply Archimedes principle
 
IssacNewton said:
Hi
Buoyancy force has to be , at least

F_B=Mg+M_{gas}g

where Mgas is the mass of the gas in the balloon. If V is the volume occupied
by the gas and if \rho_g is the density of the gas,

M_{gas} = \rho_g V

Now apply Archimedes principle

I keep walking around in a circle. I convert Fb into mass atmosphere times gravity, i convert that into mass of gas times density of atmosphere over density off gas times gravity. I cancel gravity on both sides but still don't manage to get the equation needed.
 
Managed to solve it. Thanks!
 

Similar threads

  • · Replies 12 ·
Replies
12
Views
2K
Replies
11
Views
5K
Replies
8
Views
2K
Replies
170
Views
8K
  • · Replies 84 ·
3
Replies
84
Views
8K
  • · Replies 3 ·
Replies
3
Views
8K
  • · Replies 2 ·
Replies
2
Views
3K
Replies
18
Views
8K
  • · Replies 62 ·
3
Replies
62
Views
5K
Replies
6
Views
8K