What is the solution to the Center of Mass problem?

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Homework Help Overview

The discussion revolves around determining the center of mass for a composite shape, specifically a cube divided into slabs. Participants are exploring the coordinates of the center of mass along different axes, particularly focusing on the x, y, and z coordinates.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the assumption that the center of mass aligns with the geometric center of the shape. There is an exploration of how to calculate the y and z coordinates, with some participants attempting to find the x coordinate and questioning why it might differ for the slabs.

Discussion Status

The conversation includes attempts to clarify the relationship between the geometric center and the center of mass, with some participants suggesting that symmetry or calculations could be used to prove their points. There is a recognition of differing interpretations regarding the x coordinate, particularly in relation to its sign.

Contextual Notes

Participants note that the homework platform indicated an error in the x coordinate calculation, leading to a discussion about the implications of negative values in this context.

Riman643
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Homework Statement
The figure shows a composite slab with dimensions d1 = 11.6 cm, d2 = 3.30 cm, and d3 = 14.0 cm. Half the slab consists of aluminum (density = 2.70 g/cm3) and half consists of iron (density = 7.85 g/cm3). What are (a) the x coordinate, (b) the y coordinate, and (c) the z coordinate of the slab's center of mass?
Relevant Equations
Weighted Average
I was able to find the y and z axis. To find the x-axis I was assuming they would be the same for both of the slab parts and since the center of mass is the middle of the cube it should be halfway between 14.0 cm, which is 7.0cm. I can't think of any other reason why it would not be.
 

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Are you saying that the centre of mass is the geometric centre of the shape?
 
PeroK said:
Are you saying that the centre of mass is the geometric centre of the shape?

No the center of mass is not the center of the shape. I know the z coordinate is the same for both. I found the y value by taking the weighted average of the two components of the slab. I just cannot figure out what the x coordinate is. I can't think why it wouldn't be the same for both.
 
Riman643 said:
No the center of mass is not the center of the shape. I know the z coordinate is the same for both. I found the y value by taking the weighted average of the two components of the slab. I just cannot figure out what the x coordinate is. I can't think why it wouldn't be the same for both.

Okay, although I'm not sure why there would be any doubt. You could prove it using symmetry or calculation.
 
Haha, I figured out my problem. The homework website was showing 7 as wrong because it is on the negative x-axis making it -7 as the right answer.
 

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