The Universe in Perspective

 

3: Measured Steps

 

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"Meters, liters, and Kelvins. Oh my!!" - paraphrasing Dorothy setting off to Oz.

 

 

Stylized SunMeasured Steps: Metric System Exposed


The system of measurement used in science, and in this book, is the Metric System. It is logical, clear, and easy to use. In this short(ish) chapter we summarize the basic metric units used in science, review metric prefixes and look at some relationships.

The Metric System is based on the number 10, or multiples thereof, and so has similarities to Scientific Notation, as will be seen in the metric prefix system.

 

The basic metric unit of Time is...the second, abbreviated “s” or “sec”.

 

The basic metric unit of Temperature is...degrees Celsius, abbreviated “°C”. There is also the very interesting Kelvin Scale temperature, abbreviated “K” (no, not “°K”). More on this temperature scale when we need it.

 

The basic metric unit of Mass is...the gram, abbreviated “g”. Notice I didn't say "unit of weight", more on that later.

 

The basic metric unit of Length is...the Meter, abbreviated “m”.

 

The basic metric unit of Volume is...is the Liter abbreviated “L” and/or “l”.

U.S.A and/or U.K. equivalents:

A degree Celsius is equal to 1.8 degrees Fahrenheit,

0 °C = 32 °F = freezing point of water.

100° °C = 212 °F = boiling point of water.

The gram is equal to about 2/1000 of a pound (0.0022 lb.) so 1000 g is 2.2 lb.

A meter is equal to 3.28 ft., it is about 9% longer than a yard.

4 Liters are about 1.05 gallons US, 0.88 gallons UK

Do you see now why scientists, from all countries, prefer the Metric System??

That’s it, those are the basic metric measures.

Now you may be thinking I have left quite a few metric measures out of this list, but not so. These are the base units and combined with metric prefixes all can be specified.


Metric Prefixes

Here is a of the most commonly used metric prefixes, a complete list can be found in the Reference section.


Metric Prefixes

Prefix

Symbol

Size

Tera-

T

1 trillion (1012)

Giga-

G

1 billion (109)

Mega-

M

1 million (106)

kilo

k

1 thousand (103)

centi-

c

1 hundredth (10-1)

milli-

m

1 thousandth (10-3)

micro

µ

1 millionth (10-6)

nano-

n

1 billionth (10-9)

pico-

p

1 trillionth (10-12)

 

Know these and you know immediately the size being referred to. For instance, if something has “milli-” in front of it you know one is talking about a thousandth of something. The prefixes can be mixed and matched with anything: microliter, micrometer, microgram. These prefixes are also used outside of the metric system like kilobytes and Megabytes.

Let’s re-visit the basic measures.

Temperature measure:

As already mentioned the Celsius scale uses the freezing and boiling points of water as the 0 and 100 marks (approximately, the exact temperatures have been changed to match the Kelvin scale). And I also mentioned that there is another widely used scale: the Kelvin Scale. Now why would scientists bother having two temperature scales? This will become apparent later in the book. But I'll give a clue here: 0 Kelvin is equal to -273.15 degrees Celsius. Strange! Or no?

BTW, the size of the Kelvin Scale degree and the Celsius Scale (also historically called the Centigrade Scale) degree are the same.

Mass measure:

I lied. The real base measure of mass in the Metric System is the kilogram. There are historical reasons for this and for centuries the kilogram is the mass of an object stored in a temperature controlled basement in Paris. Currently scientists are looking at various methods to re-define the kilogram using a Universal constant rather than a hunk of metal that can only be found in one city on one planet.

The gram is actually defined as 1 one thousandth of that mass. But the physics community recognizes two systems of measurement, one based on grams and one based on kilograms. So I bent the truth a little.

The gram is a small amount of mass, about the mass of 20 drops of water or 30 or so dry rice grains. More often used for everyday things, is the kilogram (kg) which equals 1000 g. A liter of water weighs very close to 1 kg.

However, not everything is an "everyday" thing and for talking about small amounts or small things it is not uncommon to use milligrams (mg) and micrograms (µg).

You may have noticed that I refer to this measurement category as "mass", not "weight". There is a subtle difference here that will be explained further in the Focus section of this chapter.

Fortunately, in the metric system, the units of mass and the units of weight are the same and both are in grams / kilograms. This is not true of systems using the pound (lb) which is a unit of weight. The unit of mass in those systems is the "slug" equal to 32.2 lb. Rest assured we will not be using slugs in this book! No way.

Length measure:

The meter is used for everyday measures in our personal lives, almost all (outside of the U.S.A. and a few small countries) are very personally familiar with it.

For longer distances the kilometer (km) is used which is, of course, equal to 1000 m (kilo-).

Interestingly, usages such as Megameter or Gigameter are rarely, if ever, used even though they are "legal" metric measure names.

In science, scientific notation is favoured for large lengths and distances and will be, usually, in either meters or kilometers. Astronomically there are other measures for length such as parsec, light year, and AU for example. We will talk about these measures later in the book.

For smaller lengths metric measures are used frequently. Most common is the centimeter (cm) and the millimeter (mm). The micrometer (µm) is used often by Biology microscopists since cells are easily measured in this length. And when talking about wavelengths of visible light and atom sizes the nanometer (nm) and picometer (pm) are used.

Volume measure:

As we've already mentioned the abbreviation of the basic metric measure of Volume, the liter, is L. However you will often see it written informally (particularly when hand written) as a small "l". A liter weighs very close to 1 kg. I believe everyone reading will be familiar with what amount a liter is since water and other beverages are consistently labeled with the metric volume, even in the U.S.A.

In the chemistry lab or at the pharmacists you often see things labeled in the milliliter (ml) volume range, 1 thousandth of a liter. A milliliter is about the same volume as 20 drops of water.

Another common measure of volume one sees is the cubic centimeter (cc or cm3). This is, as you would imagine, the volume contained in a cube that is 1 cm on each side.

But be advised, while the names are different the volume measure is exactly equal and the names are used interchangeably. That is to say 1 ml = 1 cc = 1 cm3.

People working in labs often work with even smaller volumes and can use "micro-pipettes" to measure volumes in the microliter (µl) range.

 

Now for some everyday comparisons of these measures.

A meter is covers distances in daily life like the length of couch, height of a ceiling, distances between houses. 1000 m (1 km) covers distances in your neighbourhood. 1000 km covers distances in countries or states. 106 km covers distances in the neighbourhood of our planet. 109 km covers distances within our solar system, while 1012 km (and beyond) covers distances to stars and galaxies.

What does an average person weigh? The internet says 75 kg for a man and 60 kg for a woman. I would say that if we also included the children of the World the 60 kg figure is more accurate. A healthy "average" horse weighs about 700 kg, equal to 12 of our "average" people.

A fully grown male African Elephant weighs about 7000 kg, or 10 horses, or 120 people.

The largest existing pyramid, Khufu in Giza, Egypt, consists of 2,300,000 blocks weighing an average of 2300 kg and so weighs in total about 5.4 × 109 kg, and is equivalent to about 771,000 Elephants.

How much does Mount Everest weigh? This of course is an approximation, it is not a complicated calculation but it is simplified, but estimates are in the range of 1.6 × 1014 kg. This is about 30,000 Khufu Pyramids, or 23 billion elephants, worth of mass.

Mars' smaller moon, Deimos, with an average diameter of 5 or 6 km weighs 1.8 × 1015 kg, about 11 Mount Everests.

Our moon, the Earth's moon, weighs 7.35 × 1022 kg, which is equivalent to 41,000 Deimos moons, 450,000 Mount Everests, 13.5 billion Khufu Pyramids.

Your average bathtub filled up would hold 250 L of water.

An Olympic-sized swimming pool (25 × 50 m, depth varying around 1 m) holds 2,500,000 L, about 10,000 bathtubs worth.

The volume of the great Pyramid of Khufu could hold 1000 of these swimming pools.

The Mediterranean Sea has a volume of about 3.75 × 1018 L, and so could hold 1.5 trillion Khufu's.

But we're getting ahead of ourselves here.

First a bit about mass vs. weight, and then on to discuss the Earth...

 


 


Focus: Mass is not a Weighty Matter

 

A 1 kg mass weighs 1 kg at the surface of the Earth.

Notice that I said "at the surface of the Earth". This is quite important. The Earth is large ("mass"ive) and so has a large gravitational field. Weight is nothing more than this gravitational attraction.

You've no doubt heard that something will weigh less on the Moon. The Moon is smaller (less "mass"ive) than the Earth and so has a lesser gravitational attraction and so things weigh less.

Our 1 kg mass, that weighs 1 kg on Earth, would weigh only about 17% of it's Earth weight (0.17 times, or 170 g).

Similarly if the kilogram were at the surface of Jupiter, a very massive planet with a strong gravitational pull, it would weigh about 2.3 times as much. At the surface of the Sun, a fantasy since anything that close to the Sun evaporates to it's constituent atoms due to the intense heat, our 1 kg would weigh 27.8 times as much.

If our kilogram were put deep in space away from planets and stars (and so away from any strong gravitational influence) it would literally weigh 0.0; that is, nothing.

However...no matter where our kilogram is located in the Universe, on Earth, the Moon, Jupiter, the Sun, or in deep space it will always have a mass of 1 kg. This is because "stuff" (anything composed of atoms) has mass. Weight is simply mass's reaction to a gravitational field, how strongly it is attracted, and hence accelerated, to the other mass in question. Since everything you touch, and you yourself, are made of "stuff" then everything you touch, and you yourself, have an invariant mass that goes with you wherever you go.

Your weight will vary depending on where you are in relation to planets, moons, and stars, but your mass will not...unless you overeat or go on a diet.

One way to think of mass is that it is resistant to being moved. Makes sense, the more stuff it has the more energy it takes to move it. A ping pong ball weighs (mass) little and is easy to move. A bowling ball is weighs (mass) much more and is consequently harder to move. Extending: a bulldozer is really hard to move.

Another way: If a 1 kg mass was dropped from shoulder height onto your toes it would most likely end in a broken toe. Compare that with a 1 g mass dropped similarly, one would barely feel it.

You may have heard how Galileo proved that everything on Earth falls at the same rate whether it is a huge boulder or a cannonball or a pea. Dropped from the same height they will hit the ground at the same time (neglecting air resistance). This is a characteristic of gravitational fields, they accelerate things at a particular speed. Stronger gravitational fields accelerate them more, weaker gravitational fields accelerate them less. This is weight.

So now we know the 1 kg mass and the 1 g mass hit your toe at the same speed. The difference in effect, then, is the mass. The faster something moves the more energy (here we will call it damage) it can do. There is a big difference in the damage a 1 kg mass will do vs. the 1 g mass. Consider how much more damage a 10 kg mass would do...ouch.

If you were to drop the 1 kg mass on your toe on the surface of the Moon, however, it wouldn't be so bad, maybe like a strong tap. The moon accelerates the 1 kg mass much more slowly.

But if you were in the orbit in a space station around the Earth the 1 kg mass would weigh nothing, as you all know I'm sure.

So it has no weight, but it is still a 1 kg mass.

So if you threw it at your toes such that it's acceleration by your throwing equaled that acceleration of the Earth's gravity, it would do the same amount of damage. No weight, yes. But damage anyway. That is mass.

Say you are in this space station and must put in a new refrigerator. It weighs nothing, literally. But in moving it into place you will find it resists being moved (another property of mass) and once you do have it moving it takes a fair amount of force to get it to stop moving...so keep your toes out of the way.

On to the Earth...

 

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