What a fun question! The Greek mathematician Archimedes is said to have faced a similar problem when he was asked by King Hiero II to determine whether or not the king's new crown had been made with pure gold, as requested. Of course, the easiest course of action would be to melt the crown down to a less irregular shape and compare its mass to its volume, but Archimedes couldn't do that with something as valuable as a crown! He considered the problem at length and, while in the bath one night, Archimedes noticed the change in the water level in the tub as he got in, and he had an idea. The crown, once fully submerged, would displace an amount of water equal to its own volume, so he could calculate its density by dividing its mass by the volume of the water displaced and compare that density to pure gold.
If you don't mind, I'm going to assume for the sake of simplicity that we're discussing an object small enough for measurement on a household scale. In order to determine the density of your object, you will need the following:
-your object (of course)
-a scale (the more precise, the better)
-any sort of device for volumetric measurement (e.g. measuring cups, a liter bottle or empty gallon container)
-a large container (I recommend a bucket or a mixing bowl... something large enough to hold your object and a significant quantity of liquid)
First you need to find the mass of your object. If it is small enough, I recommend a postage scale, or a trade scale (the kind with which you'd weigh fruits or vegetables at the grocery store). If you have access to either of these, finding the object's mass should be as easy as placing it on the scale and choosing convenient units. Grams or kilograms would be best.
If you have only a bathroom scale, you can first weigh yourself, then weigh yourself holding the object. Try to be as accurate as possible with your measurements, and then subtract the former from the latter to find the mass of the object. This process is commonly referred to as "taring."
Now we need to find the volume of the object. If you're lucky enough to have a container with volumes marked on it, you can simply fill said container with just enough water to submerge the object. Measure the volume of the water without the object in it, then carefully and completely
submerge the object and note the new volume of the liquid, taking care not to throw your data off with the addition of any foreign objects to the system (for instance, don't use your hand to push the object down and then measure the volume with your fingers in the water). Once more, tare the two values -- subtract the former from the latter -- to find the volume of your object.
If you don't have a marked container, the procedure will be a little bit different. Submerge the object in the water (this time, the initial volume of the water in the container is irrelevant) following the same guidelines outlined above, then mark the volume the water reaches and remove the object. Use your smaller device to measure out the volume of water it takes to exactly meet that mark. The volume of water you use will be equal to the volume of your object.
Assuming you've worked carefully through the above instructions, finding a relatively accurate approximation of the object's density should be a piece of cake from here. The average density ρ
will be given by the expression ρ = m/V
, where m
denotes its mass and V
its volume. You may now divide your measurements accordingly to find this density. Depending upon the units of the household scale/container you used, it may be necessary to do some conversion to get your object's density in the standard, meaningful units of kilograms per cubic meter, kg/m3
. Here are some helpful conversion tables...
Remember that this density is probably not uniform. Most objects will have internal regions of greater and lesser density -- what you've computed is just an average.
Hope that helps!
(published on 03/03/2011)