How Is the Initial Upward Acceleration of a Weather Balloon Calculated?

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Homework Help Overview

The discussion revolves around calculating the initial upward acceleration of a weather balloon, modeled as a sphere with a specified radius and mass. Participants explore the principles of buoyancy and forces acting on the balloon when released from sea level.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to calculate the volume of the balloon and apply the principles of buoyancy and density to find the acceleration. They express uncertainty about their approach and seek clarification on their reasoning.
  • Another participant shares their experience with a similar problem, mentioning a method of manipulating equations to find acceleration.
  • One participant notes they arrived at a numerical answer for acceleration and discusses a subsequent question regarding terminal velocity.

Discussion Status

The discussion includes various attempts to understand the problem and apply relevant equations. Some participants have shared their methods and results, while others are still seeking guidance on specific steps and concepts. There is no explicit consensus on the correct approach, but multiple lines of reasoning are being explored.

Contextual Notes

Participants are working with assumptions about the balloon's shape and properties, and there may be constraints related to the homework guidelines that influence their approaches.

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Homework Statement



assume the balloon is a spherical shape whose radius is 2.5m and total mass of 15 kg

a) what is the initial upward acceleration of the balloon when it is released from sea level


Homework Equations





The Attempt at a Solution



i know the volume of a sphere is =4/3 (pi)r3
so can calculate the volume
i know the density of the balloon is

p=m/v
and that the buoyancy is going to be greater than the weight
i reaaranged the equation and substituted m=pv into fb=ma

to get fb=pva

but i don't think this is the right way to do it
where am i going wrong and how do i finish the equation?

cheers
 
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i had a similar problem i solved for the force then the volume and manipulated the equation to read a=f/pv i got a reasonable answer
 
ye i got the answer in the end. the acceleration comes out as about 42 m/s^2 but the next part of the question was to find where it reaches terminal velocity and it reaches it at 3m/s^2
 

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