DENSITY AND VOLUME
Density and volume are simple topics, yet in order to work within any of the hard sciences, it is essential to understand these two types of measurement, as well as the fundamental quantity involved in conversions between them—mass. Measuring density makes it possible to distinguish between real gold and fake gold, and may also give an astronomer an important clue regarding the internal composition of a planet.
There are four fundamental standards by which most qualities in the physical world can be measured: length, mass, time, and electric current. The volume of a cube, for instance, is a unit of length cubed: the length is multiplied by the width and multiplied by the height. Width and height, however, are not distinct standards of measurement: they are simply versions of length, distinguished by their orientation. Whereas length is typically understood as a distance along an x -axis in one-dimensional space, width adds a second dimension, and height a third.
Of particular concern within this essay are length and mass, since volume is measured in terms of length, and density in terms of the ratio between mass and volume. Elsewhere in this book, the distinction between mass and weight has been presented numerous times from the standpoint of a person whose mass and weight are measured on Earth, and again on the Moon. Mass, of course, does not change, whereas weight does, due to the difference in gravitational force exerted by Earth as compared with that of its satellite, the Moon. But consider instead the role of the fundamental quality, mass, in determining this significantly less fundamental property of weight.
According to the second law of motion, weight is a force equal to mass multiplied by acceleration. Acceleration, in turn, is equal to change in velocity divided by change in time. Velocity, in turn, is equal to distance (a form of length) divided by time. If one were to express weight in terms of l, t, and m, with these representing, respectively, the fundamental properties of length, time, and mass, it would be expressed as
—clearly, a much more complicated formula than that of mass!