TGM Matter: Mass, Density, Force, and Pressure

From time to space, we have already learned two of the three units that give TGM its name. "T" is the Tim, the basic unit of time; from which we derive the Grafut, the basic unit of distance. Now, it is time to proceed to the third, the "M"; and to learn it, we must consider mass.

Mass

We've already discussed volume; that is, the amount of space that an object takes up. But considering matter gives us another aspect to think about. Volume may be the amount of space; but what is the amount of matter? That is, what is the unit for the amount of stuff, physical stuff, that an object contains?

That amount of matter, of physical stuff, is called an object's mass. It can be hard to devise a unit of mass, and consequently for centuries---until very recently in human history---volume was the preferred unit. It's easy to measure how much volume a thing has; measuring how much matter is in it is a different story. To understand the difference, think of a bowl full of popcorn and a bowl full of syrup; both have the same volume (that is, they take up the same amount of space), but much of the popcorn's volume is just air, so there's much less matter, or mass, there. However, by choosing a substance as a baseline we can devise a unit for such measurements. Traditionally, that unit has been water, at once the most useful and the most abundant of all fluids. And so we have the TGM unit of mass, which is the amount of matter contained in one Volm of pure, air-free water under a pressure of one standard atmosphere at the temperature of maximum density:

Just a tiny bit less than fifty-seven (48) pounds, and a little less than twenty-six (22) kilograms. This unit is large compared to basic mass units in other systems, but it still carries a number of advantages over either pounds or kilograms:

1. It maintains a 1:1 ratio between basic units, which is not true for pounds, and is only partly true in for kilograms. (Though kilograms are technically the basic unit of mass in SI, they carry a prefix meaning "thousand," which thus fudges up the entire vaunted SI system of prefixes. Indeed, in prior versions of the metric system the gram was, indeed, the basic unit of mass; but then it had to be paired up with the centimeter as the basic unit of length, because SI units are so comically mismatched.)
2. It's still a convenient size in the abstract; it and basic uncial fractions of it are perfect for sizing the everday items of human life.
3. Its multiples and fractions remain close to units which are commonly used in both systems. E.g., the biciaMaz is about six and a third ounces, or one hundred and thirty grams, a good size for measuring smaller masses. For example, a can of food might have a standard size of two biciaMaz (2 ₂Mz = 10;7E83 ounces = 25E;0486 g). The triciaMaz makes a good unit for spices and such, totally a bit over half an ounce (0;63EX oz). For large things, the megaton is 1;0E56 septquaMaz (⁷Mz). (The megaton is 1,000.0 times the metric ton.)

The overall impression given is that the Maz is an eminently useful and convenient unit, despite (or perhaps because of) its relative size.

Density

Volume is the amount of space an object occupies; mass is the amount of matter an object contains; density is how tightly packed a given mass is in a given volume. In TGM, we call it the Denz:

Due to both mass units being defined in terms of the density of water, the Denz is quite close to an even number of kilograms per cubic meter. The difference is due to the fact that TGM is a modern system, while SI metric is an old one constructed prior to exact measurement instruments existing. When metric was developed in the 1790s, a clear understanding of the variations in density in an object depending on temperature was not clearly understood. By the time TGM was developed, in the 1960s-1980s, this was clearly understood; so the Denz is more exactly based on the density of water. (This strange off-by-a-little error also explains why the old liter isn't really equal to a cubic decimeter, and therefore why it was deprecated by SI.)

Force and Weight

Newton's Second Law of Motion tells us that force equals mass times acceleration; in TGM terms, it equals Maz times Gee, or Maz times Grafut per Tim squared:

This means that the Mag is the force required to accelerate a mass of one Maz by one Gee; put another way, it is the force exerted by Earth's gravity on an object of one Maz. Thus an object's mass in Maz is equal to the force of gravity on it in Gee, assuming it's on Earth.

This brings us to the usual confusion between mass and weight. Mass, as we've discussed, is the amount of matter a thing contains; weight is how hard gravity is pulling on that thing. Weight, in other words, is a force. The two are not the same thing. For this reason, both the customary-imperial and the SI metric systems tend to bifurcate into two systems: one based on mass, and the other based on weight. So, for example, one often hears about someone weighing so many kilograms, which is clearly incorrect; more properly, a person masses a given number of kilograms, but weighs a certain number of newtons (newtons = kg*m/s², the SI unit of force). However, newtons are rather small for this purpose; so we develop the kilogram-force (kgf) (and, in customary-imperial, the pounds-force, or lbf) to describe the force of gravity pulling on an object which masses one kilograms. This needlessly splits the force systems into two sets (newtons and kilograms-force), a problem that TGM avoids entirely.

If you're on Earth, then your weight in Mags is equal to your mass in Maz. It's that simple. (There are very minor variations in this due to the variations in the pull of gravity; but for most purposes this equation holds.) One need only distinguish between the two off of Earth, in those situations in which it is easy to remember to do so. This is a huge advantage for TGM that metric and customary-imperial simply miss.

For the record, the Mag is equal to about 21;X38X kgf and 49;0154 lbf. But it is good to know that this whole needless mess will be done away with when TGM is widely used.

Pressure and Stress

Along with force comes force per unit area. In other words, it's all well and good to think of force being exerted on objects; but as a practical matter, force is often not exerted simply on objects, but on surfaces. Force per unit area is called pressure.

We often refer to "lbf/in²" (read "pounds-force per square inch") as "psi," or "pounds per square inch," but this abbreviation isn't systematic. The SI unit for pressure is the newton per square meter, or pascal (Pa). The pascal is a tiny unit; people frequently work in kilopascals rather than the unit itself. Indeed, standard atmospheric pressure is 4X779 pascals, in decimal 101,325 pascals; this is commonly voiced as simply "101.325 kilopascals," when pascals are used. More comonly, the "bar," which is X⁵ pascals, is the unit actually employed.

This SI "standard atmosphere" is, roughly, the average atmospheric pressure at the latitude of Paris at sea level. It's easy to see that there's nothing particularly special about Paris, other than the fact that SI metric was devised there; and in reality atmospheric pressure varies considerably, even around sea level, based on many thing, not least of which is temperature. The SI standard atmosphere is 2X;E237 Prem.

This is extremely close to simply 2E Pm; indeed, it's so close that simply making 2E Pm the TGM standard atmosphere is well within the reasonable values for atmospheric pressure at sea level. So TGM defines an auxiliary unit in terms of the Prem which represents its own standard atmospheric pressure.

Those are millimeters and inches of mercury, of course, as measured on old-style barometers. In TGM terms, though, the Atmoz is simply 2E Prem.

(For reference purposes, the Atmoz is equal to 1;0033 SI standard atmospheres.)

What is the utility of making the TGM standard atmosphere equal to 2E Pm?

1. There is great value in having the standard atmospheric pressure be equal to a simple, round number of the normal pressure units which conform to the rest of the system according to a 1:1 ratio. TGM does this.
2. 2E (thirty-five in decimal) is an extremely convenient number; a shockingly large number of fractions of the Atmoz are even, or very short uncial fractions, in Prem. 1--X all come to whole numbers or one or two uncial places; 10, of course, comes to 2;E Pm; 12--14, 16--20, 23, 24, 26, and 28 all comes to three uncial places or less. This extreme divisibility is shown in the table below.

So much for the units of mass, force, and stress. We now proceed to those units that depend upon these units, particularly those of force. These are units of work; of energy; of heat; and of power.