Equilibrium and Force on Lower Hemisphere

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Homework Help Overview

The discussion revolves around the equilibrium of a sphere, specifically focusing on the forces acting on the lower hemisphere. Participants are examining the balance of forces in the vertical direction and the implications of the center of mass for both the whole sphere and the lower hemisphere.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the equilibrium conditions for the sphere and question the acceleration of the center of mass of the lower hemisphere. There is an exploration of the forces acting on the lower hemisphere, including the weight and the normal reaction from the floor.

Discussion Status

The discussion includes attempts to clarify the forces involved and the conditions for equilibrium. Some participants express agreement with the reasoning presented, while others continue to explore the implications of centripetal acceleration on the forces acting on the lower hemisphere.

Contextual Notes

Participants are working under the assumption that the sphere is in equilibrium and are considering the effects of acceleration on the center of mass of the lower hemisphere. There is a focus on the relationship between the forces and the geometry of the sphere.

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Homework Statement



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Homework Equations

The Attempt at a Solution



Using the fact that the sphere is in equilibrium in the 'y' direction , the force exerted by the floor N = 2mg .

Now , if I consider the lower hemisphere then , vertical force exerted by top hemisphere + weight of lower hemisphere = Normal reaction from the floor .

This means , vertical force exerted by top hemisphere on lower = mg

Should this be the total force exerted on the lower hemisphere ?

Thanks
 

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Yes, the sphere as a whole is "in equilibrium in the y direction" since the center of mass of the sphere has no acceleration.

However, does the center of mass of the lower hemisphere have any acceleration?
 
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TSny said:
However, does the center of mass of the lower hemisphere have any acceleration?

It has centripetal acceleration ω2r ( r=3R/8) directed towards the center of the sphere i.e in +y direction (upwards)

Taking + y to be upwards , 2mg - mg +R = mω2r , gives R = 5mg/8 downwards i.e option A)

Is that ok ??
 
Vibhor said:
It has centripetal acceleration ω2r ( r=3R/8) directed towards the center of the sphere i.e in +y direction (upwards)

Taking + y to be upwards , 2mg - mg +R = mω2r , gives R = 5mg/8 downwards i.e option A)

Is that ok ??
Yes, I believe that's all correct.
 
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TSny said:
Yes, I believe that's all correct.

Thank you :smile:
 
Last edited:

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