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How to Measure Density:

Practical experiment ideas for How to Measure the Density of an Object

It's all very well knowing the density of gold is 19.3* and the density of aluminium is 2.7* but how would you set up a practical experiment to measure the actual density of some physical object? For example, if you had a complex manifold or chassis off some equipment, of an artifact which was said to be gold but you wanted to make sure of it, how would you measure the density? Here's a practical method by which you can measure the density of an object:

To measure the density, what you usually do is to measure the mass of the object, and also measure the volume, and then divide mass by volume to get the density. Measuring the mass is relatively easy, as you put the object on a weighing scale and find the weight, and that gives a pretty good idea of the mass. (see mass and weight). Then, measuring the volume? That's a bit more tricky...

If the object is a metal cube 10cm x 10cm x 10cm, then the volume is easy to find. It's 10x10x10 = 1000 cubic centimetres. But most objects are not as easy as this. Suppose the object is some unusual shaped item, some odd piece of engineering equipment, etc. What you do then is to drop it in a bucket, fishtank, or other vessel containing water, and measure how the water level rises. For this, it's best to choose a bucket or tank that's got a simple shape and straight sides.

When immersed in the water, the object displaces its own volume of water. You multiply the rise in water level by the surface area of the water, and you then have the volume of water displaced, and that is the same as the volume of the object.

For example, supposing you want to measure the volume of an engine crankshaft which you've got on the table. If you drop it in a fishtank which is 1 metre x 1 metre, and the water level rises by 1cm (0.01m), then the volume of water displaced is 1 x 1 x 0.01 cubic metres = 0.01 cubic metres = 10 litres. Therefore the volume of the object is the same as 10 litres of water, which is 0.01 cubic metres (10,000 cubic centimetres).

Having found the mass and the volume, you just divide the mass by the volume and you get... the density of the object. (Make sure you use consistent units, and get the answer in some sensible density unit like kilogrammes per cubic metre). It's also a good idea to do a consistency check by making an intelligent guess at the volume of the object and then see if your experimental result is of the same order of magnitude.

Historically, kings of old were keen to prove their gold crowns were real gold and not some cheap substitute. One way to prove a solid gold crown is made entirely of real gold is to measure its density and see if it matches up with the density of gold. The nice thing about experiments like this is that it's possible to perform a test independently without having to just believe someone's word.

Another thing about measuring density: It would be nice if instead of all this faffing-about, you could just put stuff on a set of scales and measure if something's density is heftier than something else. Well, now you can. Zyra has devised a set of Density Scales which you can put things on a two-pan balance and find out which is denser, not which is heavier.

In astronomy, how is it possible to find out the density of a planet? If someone says "the planet Saturn is lighter than water", how do they know? You can't put a planet in water and on a weighing scale, especially in space. The method then is to find out the mass and the volume by other means. In the case of a planet, the volume is easy to find out, because it's round! four-thirds pi times the radius3 gives the volume. The mass is found by seeing how it moves. An elephant turns corners slower than a mouse, and motion gives an indication of mass. With planets, they are attracted by other planets, and the slower they respond the bigger their mass. The earth has a mass of about 5.972 x 1024 Kg and a volume of 4/3 x pi x 64000003 , which when you divide it out gives a density of about 5500Kg/m3 , which fits well with the theory that it's made of heavy things such as rock and iron. In contrast, the planet Saturn (density about 900Kg/m3) is made mainly of compressed gas.

* specific gravity. The specific gravity of gold is 19.3 and the specific gravity of aluminium is 2.7 , whereas the density of gold is 19,300 Kg/m3 and the density of aluminium is 2,700 Kg/m3

Note: Although it is possible to Measure the Weight of a Cat, the method described on this page should not be applied to Measure the Density of a Cat, as that would be ill-advised!