Convert linear density to area and volumetric density?

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Homework Help Overview

The discussion revolves around converting area density to linear and volumetric density, specifically in the context of a flat square surface. Participants are exploring the relationships between these different types of density based on given parameters.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the necessity of knowing the shape of the object to convert area density into linear and volumetric density. There is an attempt to derive formulas for mass and volumetric density based on area density and thickness.

Discussion Status

Some guidance has been provided regarding the relationships between the different densities, particularly how to express volumetric density in terms of area density and thickness. Multiple interpretations of linear density are being explored, particularly in relation to the geometry of the square surface.

Contextual Notes

Participants note that the thickness of the plate is a critical factor in determining volumetric density, and there is an emphasis on the specific geometry of the object being discussed.

silverdiesel
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if I am given a area density of 10^-4, I can get linear and volumetric density from that right? I just can't seem to figure it out.
 
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silverdiesel said:
if I am given a area density of 10^-4, I can get linear and volumetric density from that right? I just can't seem to figure it out.
Only if you know the shape of an object you are working on.
 
It is a square (not a cube, a flat square surface)
 
silverdiesel said:
It is a square (not a cube, a flat square surface)
Then the total mass of the object is

M = σA

The volume density is

ρ = M/V = σA/V = σA/(AT) = σ/T

where T is the thickness of the plate.

If you want the linear density, it is only constant in a direction parallel to one side of the plate. See if you can do that one.
 

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