• Question: How do you calculate density?

    Asked by anon-252499 on 30 Apr 2020.
    • Photo: anon

      anon answered on 30 Apr 2020:

      Like everyone else, I imagine 🙂
      We take the mass and divide by the volume.
      But pretty often it gets more complicated, because the density is not uniform – like if the body is made from a mix of several materials. If you just divide mass by the volume you will get an average density. To have exact density at each point in the volume – a density distribution – we have to know how the body looks inside. This can be measured by a number of ways and is very important for planetary sciences – we want to know what is inside a planet, a comet, an asteroid, so we can understand how it was formed, and what properties we can expect if we want to, say, land on it.

    • Photo: Susan Cartwright

      Susan Cartwright answered on 30 Apr 2020:

      The simplest answer is that density is mass over volume. For example, if you have a cube of wood 10 cm on a side, and you weigh the cube and find that it weighs 750 g, then the density of your wood is (750 g)/(10 x 10 x 10 cubic centimetres) or 0.75 g/cm^3 (750 kg/m^3 in SI units).

      This will always give you the average density of any object. It gets more complicated if your material is not uniform, and you want to know how the density varies at different places. You could chop your object into little pieces, and calculate the density of each little piece separately, but that is not very practical if the object is somethig valuable, like an antique statue, or something not capable of being diced, like a mountain. There are various ways you can tackle that kind of problem: for example, finding its centre of gravity (the point where you can balance it) is helpful – if you have a rod whose density increases from one end to the other, for example, the balance point will be closer to the heavy end. It is also useful to find the force needed to set it rotating about different axes.

      One of my colleagues has an interesting approach. He measures the number of cosmic ray muons (an elementary particle similar to, but much heavier than, the electron) that get through the object. The denser the material, the more efficiently it absorbs muons, so the fewer muons you get out. This can be used to find holes in apparently solid objects, e.g. hidden chambers in pyramids, or to gauge hw full the magma chamber under a volcano is. Airport security scanners use X-rays in the same way, to look for items of unexpected density in your suitcase – and of course medical X-rays image your bones by the same method (bines are denser than flesh).

    • Photo: James Smallcombe

      James Smallcombe answered on 1 May 2020:

      Density of an object is the ratio of it’s mass to its volume. However determining volume can be particularly tricky for a complex shape. The famous Greek Archimedes discovered a trick that he could use the amount of water displaced (pushed out) when he put an object in a container of water and use this to tell him the volume, in order to calculated density.

    • Photo: Paula Koelemeijer

      Paula Koelemeijer answered on 1 May 2020:

      It is one question to ask how you calculate it (mass divided by volume), but another question is how do you find out the density of something! For example, we try to find out the density variations within the Earth, which is not that easy! Some information comes from gravity measurements made using satellites. Other insights come from seismology, as the seismic waves that travel through the Earth are also sensitive to density. For planetary scientists, density variations are important, as they are the drivers of flow within the Earth.

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