Last time, faithful readers of this column, we introduced the units of mass, length, and time, using the metric system. Briefly you will recall that these are the gram, meter, and second. To get an idea of how big these things are, recall that a gram is about a one-fifth of a teaspoon of water, a meter is about the size of a 3 year old kid, and a second is the amount of time it takes for my 300MHZ Intel Pentium processor to perform 100 million instructions, or about how long it take for you heart to beat once. (Sorry)
This time, I would like to take some time to give you a feeling for these units. Their precise definitions are very abstract, and were covered in the previous article, but perhaps if we can relate them to everyday life, they will take on a new meaning. Why should we care? Well, using these kind of units is really the only way to get a real understanding of the world around us. Sure, everybody knows that what goes up must come down, but how fast does it come down? Everyone knows its a long way to Tipparery, but how far is it? Everyone knows that your life can change in the blink of an eye, but how long is that? Only by understanding and using units like the gram, meter, and second can we make sense out of questions like this. So onwards, gentle reader, and lets dive into the measurement of the mysterious world around us.
Let's start with mass. A gram is pretty small, so a lot of everyday things are measured in kilograms (1000 grams) rather than grams. A liter (or quart) of milk weighs about a kilogram. A (heavy) bowling ball weighs in at around 7 kilograms. A good sized football player runs around 100 kilograms, and a pickup truck is about 1000 kilograms. Jumping ahead, the mass of the earth is about 5.9x10^24 kilograms, and the mass of the sun is 1.99x10^30 kilograms (about 333,400 times heavier than the earth). At the other end of the scale, the mass of a single water molecule is about 18 2.988x10-26 kilograms. Given these points on the scale, it should be possible for you go look at the objects around you and have a reasonable idea of how much mass, in kilograms, they might contain. For example, your TV set is probably between 10 and 20 kilograms, your golf clubs are around 15 kilos, as is your head, and your gold Visa card is is around 10 grams.
Alright, enough about mass, lets tackle distance. A meter is roughly the distance from your toes to your waist. Ten meters is the distance from your 2nd story window to the ground below, and 100 meters is about how far you can run in 10 seconds, if you're pretty fast. It is also a little longer than a football field, for the sports minded among you. 1000 meters, or one kilometer, is a 15 minute beach walk, 10 kilometers is roughly the distance from the golden zone to El Centro, and 100 kilometers is an hours drive on the freeway. For reference, the circumference of the Earth is around 40,000 kilometers, and the distance of the Earth to the sun is about 150 million kilometers. With this as a basis, how many kilometers is it from Mazatlan to New York? How many meters to the top of the El Moro tower?
Finally, let's take our time and look at seconds. We probably all have a pretty good intuitive grasp of spans of time from seconds to years. In 100 years, or about one very long human lifespan, the rotation of the Earth slows down about 1 second. In 1000 years (roughly), we have gone from fighting the crusades in the middle east to fighting the Iraqis in the middle east. Isn't it nice that some things in life never change? 10,000 years is longer than all of recorded human history, and the first human appeared on the Earth roughly one million years ago. Current estimates of the age of the universe is somewhere between 10 and 20 billion years, that is somewhere between 100 and 200 thousand times longer than the dawn of the age of man. Going in the other direction, one tenth of a second is about twice as fast as the fastest human reaction time. One hundredth of a second a horse at full gallop can cover about 10 centimeters, or a tenth of a meter. At the further end of the time spectrum, in one millionth of a second a computer can add 2 or 3 numbers, and in one billionth of a second light can travel about a third of a meter. Finally, physics is considered "well known" for all times after 10^-43 seconds after the big bang, or one ten millionth of a billionth, billionth, billionth, billionth of a second.
As I mentioned last time, these are the 3 main fundamental units, but there are many other important units derived from these fundamental ones that we use everyday. One of these is the kilowatt-hour, which we pay (plenty) for every month when we get our electric bill. But what is it. We know it has something to do with energy, but what? First we need to take a step back and examine the newton, which is a unit of force. If you hold a one kilogram mass in your hand (about a liter of milk) you are applying about 10 newtons of force to keep it from falling to ground. Remove your hand (and the force it is supplying) and the carton of milk will accelerate towards the floor at 9.0 meters per second per second and go splat. Now even though if you hold this carton in your hand for an hour, you are not really using any energy, you are only supplying a force. Energy is expended when you move an object against a force for a certain distance. Thus if you lift the carton of milk one meter off the ground, you will have expended 9.8 newton-meters of energy. Saying newton-meters gets to be tedious very quickly, so physicists call it a joule. Thus lift a liter of milk to your waist and you've used up roughly 10 joules of energy. If you did this once every second, you would be generating ten watts of power, you see the watt, a unit of power, is one joule per second. Okay, we're getting close now. Instead of lifting up one milk carton per second, lift up one hundred milk cartons per second, and you're generating one kilowatt of power. Do this for an hour, and besides getting pretty tired, you will have used up one kilowatt-hour of energy, or 3.6 million joules. For that amount of energy you pay about a nickel. Maybe it's not such a bad deal.
I can't quit without somehow incorporating the title of this piece. I'm sorry to say I've deceived you though, gentle reader, for a horse(power) is not a unit of force, but a unit of power. It is supposed to be the amount of power that a horse can generate, and its actual definition is the power it takes to raise 3,300 pounds 10 feet in one minute. This unit was created by James Watt in the late 18th century. These days a horse can only generate about 3/4 of a horsepower on a sustained basis. I guess they just don't make horses like they used to. In terms of watts, its about 746 watts, which is about how much power a microwave oven puts out when it heats up your hamburger. Just think about it, sitting there in your kitchen in a little box, all the power that Secretariat could generate to run across the finish line in the Kentucky derby. I hope it give you a new appreciation for that burger the next time you nuke one in microwave.
One last thing. My sincere best wishes to Mr Ed and his descendents. Adios.
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