Fundamental quantities are numbers that we need to describe the world around us, which we cannot express in terms of "simpler," more basic quantities. I’ll give a few examples.
My weight is not a fundamental quantity, because it depends on how much stuff makes up my body. A good approximation to my weight is just the sum of the weights of all of the protons, neutrons, and electrons which make me up. If I could count those, I could calculate my weight in terms of the masses of the proton, the neutron, and the electron (and I’d need the local strength of gravity to get my weight once I know my mass). The mass of a proton is more fundamental, although we know now that protons are made up of smaller pieces (quarks and gluons). People are actively trying to refine calculations of the proton mass in terms of the stuff inside a proton and their interactions.
The electron does not appear to have any pieces inside of it, and so as far as we know, the electron mass and the electron’s charge are fundamental quantities. The strength of gravity, which scales with Newton’s gravitational constant, is also a fundamental quantity. The speed of light is a fundamental quantity (although these days the speed of light really is used as a definition of how long a meter is). Planck’s constant, which governs how big atoms are and how much energy photons have at given wavelengths, is a fundamental quantity.
We strive as physicists to have as few fundamental quantities around as possible. Being able to calculate other necessary quantities in terms of those few we don’t know how to compute means we understand more about nature.
(see also http://van.physics.illinois.edu/qa/listing.php?id=19474)
Tensile stress is just the amount of force per unit area when an object is pulled on opposite sides. Tensile strain is the amount the object changes shape in response to this stress (objects will stretch when pulled). Strain doesn’t have any dimensions because it represents fractional changes in the length. If the strain is 10%, then all pieces of the object getting pulled on lengthen in one direction by 10%.
(republished on 07/12/06)