What is 2D Density? Understanding Mass, Volume, and Area in Relation to Density

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    2d Density Units
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Discussion Overview

The discussion revolves around the concept of density, specifically exploring the relationship between mass, volume, area, and a potential term for mass per unit area. Participants examine how this concept applies in various contexts, including practical examples like paint coverage and theoretical applications in astrobiology.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant defines density as mass divided by volume and questions the analogous concept of mass divided by area.
  • Another participant suggests that there may not be a widely recognized name for mass per unit area.
  • It is proposed that if the weight for one square meter is known, the thickness of the paint can be inferred.
  • Some participants propose the term "areal density" for mass per unit area.
  • Another participant mentions "density per unit thickness" and notes its relevance only when thickness is constant.
  • One participant states that "area density" is the commonly used term, while also mentioning an incorrect term "mass spread rate."
  • In astronomy, the term "surface density" is introduced, though its universal applicability is questioned.
  • A participant shares a practical application of area density in the context of designing a light sail for interstellar travel, discussing its implications on mass and acceleration.
  • The participant provides a link to a calculator related to area density and its application in their project.

Areas of Agreement / Disagreement

Participants express differing views on the terminology for mass per unit area, with suggestions including "areal density," "area density," and "surface density." There is no consensus on a single term, and the discussion remains open regarding the best terminology and its implications.

Contextual Notes

Some limitations include the dependence on the assumption of constant thickness for the proposed terms and the varying applicability of these concepts across different fields, such as physics and astronomy.

tony873004
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density is (mass / volume). But what is (mass / area)?

For example, if I wanted to know the mass of how much water would fill a jar, it would be mass = (volume of jar * density of water) = cubic length * (mass / cubic length.)

But imagine I knew how much a square meter of paint weighed, even if I did not know the thickness of a coat of paint. If I wanted to know the mass of how much paint it would take to cover a wall 10x10 meter wall, it would be mass = (area of wall * ??) = squared length * (mass / squared length).

mass / cubed length = density
mass / squared length = ??

Is there such a term?
 
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I don't believe there's a name for the quantity.

- Warren
 
If you know how much it weights for one square meter, then you know the thickness of your paint.
 
If you want a name, go with "areal density".
 
density per unit thickness? [M/L2]

I'd imagine it only has meaning where the thickness is known to be constant, not really a very natural phenomenon at macroscopic scales
 
"Area density" is the term used for this quantity. Sometimes it's (incorrectly) called "mass spread rate." Do a google of "area density" for plenty of examples.
 
Thanks, everyone for you answers. And thanks, Chi, that's exactly what I was looking for.
 
In astronomy, it's often called "surface density", though I'm sure that term isn't universal.
 
Thanks, ST. For my purposes, I think "area density" is the more proper term. As a challenge to our Astrobiology class, we were asked to consider whether or not a light sail might be a good idea for accelerating an interstellar spacecraft towards Alpha Centauri. The goal is to reach 10% the speed of light.

The area density of the sail seems to be very critical. For example, a mylar emergency camping blanket 56x84 inches and weighing 10 ounces, with an advertised reflectivity of 90%, has an area density of 0.093 kg/m2. This is WAY too heavy to accelerate even a 1 kilogram nano-bot to even solar escape velocity, let alone 10%c, even starting the journey from the surface of the Sun for maximum flux. But sails made of ficticious materials 1/1,000,000 the area density of an emergency mylar blanket can do the trick as long as they are HUGE (kilometers in diameter).

Here's a link to a calculator I made using my new knowledge of area density just to make the formula prettier. For small velocities (<~500 km/s) the answers it gives are a bit high as it ignores gravity. But for higher velocities where gravity becomes neglible, the answers are in nice agreement with my numerical model.

http://orbitsimulator.com/gravity/articles/sailformula.html

Sorry for getting a little off-topic, but I thought I'd show everyone why I needed to know this.
 

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