Where is the Center of Mass in a Solid Hemisphere?

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Homework Help Overview

The discussion revolves around determining the location of the center of mass for a solid hemisphere of uniform density with a specified radius R. Participants are examining various potential answers and reasoning through the implications of mass distribution within the hemisphere.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Some participants are questioning the validity of certain answer choices, particularly A, E, and C, while others are exploring the implications of mass distribution in relation to the center of mass. There is a discussion about the significance of the range provided in the answer choices and its relation to the actual location of the center of mass.

Discussion Status

The conversation is ongoing, with participants actively engaging in reasoning about the center of mass and its relation to mass distribution. Some guidance has been offered regarding the interpretation of the range of answers, but no consensus has been reached on the exact location of the center of mass.

Contextual Notes

Participants are navigating assumptions about mass distribution and the implications of the center of mass being located at various points along the z-axis. There is an emphasis on avoiding direct answers and encouraging independent problem-solving.

Westin
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Homework Statement


Consider a solid hemisphere of uniform density with radius R. Where is the center of mass?

z=0
0
char3C.png
z
char3C.png
R
char3D.png
2
z=R
char3D.png
2
R
char3D.png
2
char3C.png
z
char3C.png
r
z=R

Image is provided.

Homework Equations

None

The Attempt at a Solution



Answer A and E do not seem logical. I thought it was answer C from my eyes. Center of mass is the average of the masses factored by their distances from a reference point. I didn't think the answer could range like B and D do.[/B]
 

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Westin said:

Homework Equations

None
Really? No equation for the center of mass?

Westin said:
Answer A and E do not seem logical. I thought it was answer C from my eyes. Center of mass is the average of the masses factored by their distances from a reference point. I didn't think the answer could range like B and D do.
Do you understand that the range is there to keep you from having to calculate the exact value? It doesn't mean that the center of mass can be anywhere within that range.
 
If the center of mass were precisely at R/2, there will be more mass below than above that point. Hence, it must be somewhere between R/2 and...
 
NTW said:
If the center of mass were precisely at R/2, there will be more mass below than above that point.
I don't understand what you mean.
 
DrClaude said:
I don't understand what you mean.
To make a mental experiment: If I imagine a given point on the Z axis, precisely at R/2, and also imagine the hemisphere as formed by a very large, but finite number of particles, the number of particles with z-coordinates lower than R/2 will be larger than the number of particles with z-coordinates higher than R/2. Hence, in order to reach a 50% partition in the values of the z-coordinates, that point must be placed somewhere between 0 and R/2.
 
NTW said:
If I imagine a given point on the Z axis, precisely at R/2
Ok, but that's not the same as saying "if the center of mass were precisely at R/2."

Also, please to not give direct answers in the homework forums. The poster has to do the work.
 

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