Confusion of circle and sphere for physics problems

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Homework Help Overview

The discussion revolves around a physics problem involving the application of pressure on a surface area, specifically comparing the use of a circle's area versus a sphere's surface area in calculations. Participants are exploring the implications of these geometric considerations in the context of atmospheric pressure and force calculations.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the original poster's attempt to calculate force using the surface area of a sphere and the resulting confusion when the answer did not match expectations. There is a suggestion to consider using the area of a circle instead, which led to a correct answer. Questions arise regarding the appropriateness of using a circle versus a sphere in this context.

Discussion Status

The discussion is ongoing, with participants providing insights into the nature of pressure and its application to different surface areas. Some guidance has been offered regarding the need to consider the direction of forces and the concept of projected area, indicating a productive exploration of the topic.

Contextual Notes

Participants are grappling with the implications of using different geometric shapes in their calculations and the assumptions related to the direction of forces acting on the surfaces involved.

zabachi
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Homework Statement



The problem is attached

Homework Equations



P=F/A

The Attempt at a Solution



I did the question like this (got wrong answer though):

Surface area of sphere=4∏r2=4×∏×0.252
Atmospheric pressure=1.01×105

Force=1.01×105×4×∏×0.252≈80000N
Actual answer 20000N

So my friend said something about using a circle instead? I tried it and indeed got the right answer. So why do we use a circle's area instead of sphere.
 

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Check the value of radius.
 
i Changed the radius but the answer still reamins the same as i did the question previously itself
 
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object.

The force is not completely perpendicular to the whole surface of hemisphere.
 
You have to resolve the pressure force acting on each element of area of one of the hemispheres into the component in the direction that the rope is pulling. This is equivalent to using the projected area of the hemisphere times the atmospheric pressure.
 

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