Posted July 22, 2001
Welcome back to Mostly Mozart. The kind of radio show you can't hear on any other radio station but KCR. That's right, you're listening to CJLY fm 93.5 in Nelson. Today is Thursday or Sunday, 2 or 3 o'clock, and that means it's time to listen to some Mozart and hear Tom Clegg do things that were never meant to be done on the radio. Mostly Mozart is sponsored by Comfort and Joy, a unique children's store.
I'd like to start off by thanking all the people who have given me questions and suggestions for what to discuss on the show. Whether or not I actually address your questions, at least it shows that people are listening. Sometimes even paying attention. A few months ago, when I was talking about salt water being heavier than fresh water, someone phoned the studio to point out that I was wrong. After all, a pound of fresh water is just as heavy as a pound of salt water. I think in the end we agreed that it would have been more correct to say that salt water is more dense rather than more heavy. Of course, I accused the caller of playing a word game, because if A being heavier than B means that a pound of A is heavier than a pound of B, then there is no legitimate use of the word "heavier."
Language is always a bit of a slippery eel when it comes to hair-splitters like me and the disgruntled listener. If I tell you that the Empire State building is heavier than my refrigerator, that means that if you put them on a set of balance scales, the Empire State building would tip them, so to speak. If you put your gold watch and my aluminum car on a balance scale, my car wins. But that doesn't make aluminum heavier than gold. When I say gold is heavier than aluminum, or when I compare any two substances, as opposed to objects -- the only thing I can possibly mean is that a given volume of gold is heavier than the same volume of aluminum. If there's any confusion, of course, I can always fall back on the word density. But really, what did you think I meant? What's heavier, a ton of feathers or a ton of iron? Well, that depends on which one is on the moon and which one is on the earth. It also depends on whether "ton" is spelled "t-o-n" or "t-o-n-n-e", because they measure different things.
I'll go on about that in a few minutes, but first I'd like to break for some music; and also to mention that I really like that sort of phone call because if you call to pick apart my choice of words, then it means you're not only listening but paying attention. And that means you are fully enjoying the benefit of non-commercial radio: you can actually pay attention, and be rewarded. With something other than an inexplicable urge to buy tickets to
Monster Truck Madness, this Thursday to Sunday at the Rideau Carleton Raceway highway 17 past Stittsville, DON'T MISS IT!
Welcome back, you're listening to Mostly Mozart on CJLY fm 93.5 in Nelson. Comfort and Joy is happy to sponsor Mostly Mozart. Today's topic is weight, and here it goes. The wait is over.
Sorry. I won't say that again.
Usually, the most confusing part about weight is that people say weight when they really mean mass. Weight is a measure of force, so in the metric system it's given in Newtons. Specifically, the weight of an object is the net gravitational force acting on it. That's why you weigh less when you're on the moon. This fact is well known to most people, even those who have never even been on the moon. The moon exerts less gravitational force than the earth. Why? Because it's less massive than the Earth.
Mass is a measure of how much matter is in an object. Where weight is an extrinsic quality, mass is intrinsic. Mass measures a property of an object, while weight measures an external force acting on the object. You're just as massive on the moon as you are on the Earth, because you're still made of the same stuff. You have less weight, because there's less gravitational force acting on you.
So, are you heavier on Earth than you are on the moon? That depends on whether "heavy" refers to mass or weight. Usually, "heavy" refers to weight. When you lift a box, you're pulling against the gravitational force, so when you call it heavy, you're talking about weight. It might be more correct to say "weighty" but that seems to have taken on other, more literary, meanings. In any case, if you want to be clear that you're talking about mass, you can say "massive". That's right kids, "massive" doesn't mean big, it means lots of mass.
Things with lots of mass, like the Earth, come with gravitational fields. Anything inside the gravitational field -- which is everything in the universe because the field extends indefinitely in all directions -- everything feels a force toward the Earth. Distant objects feel a lot less than nearby objects. More massive objects feel more. In fact, you might have heard that F=GMm/r2. If you double your mass, you feel twice as much gravity, so you double your weight. That's small m. If you double the mass of the Earth, or move to a planet that's twice as massive as the Earth, then you double your weight again. If you double big G, well, you can't change big G. It's the gravitational constant and the rules of physics say you're not allowed to change constants. If you double your distance from the planet, then you divide your weight by 4. Which brings you right back where you were. Gravity wise, anyway. You're twice as massive yourself, and you're on some other planet twice as massive as the Earth, and you're twice as far away from it as you used to be, but at least you are the same weight. So you'll probably feel right at home.
Now, if you were really paying attention, you noticed something that doesn't quite work. Right now, you're probably sitting less than 30 feet from the surface of the earth. If you find a taller building and get 60 feet away from the earth, you will not feel 1/4 as heavy as you do right now. And that brings me to the interesting fact I want to leave you with.
If you're on the outside of a solid homogeneous sphere, which is a half-decent approximation of the Earth's structure, the gravitational force you feel is exactly the same as it would be if the entire mass of the Earth were concentrated at a point in the centre.
An even better approximation of the Earth's structure is a bunch of concentric spherical layers, each of which is symmetrical all the way around. That same rule applies to each layer: from outside, then gravity feels exactly the same as it would if the mass were concentrated at a point in the centre.
So when you double your distance from the Earth, gravitationally speaking, you have to double your distance from the centre of the earth, not the surface. That requires more effort than finding a tall building. In fact, climbing buildings makes so little difference that you don't even have to adjust your spring scales when you move from the 12th storey to the 23rd storey.
Oh, and one final final thought:
Suppose you're inside a spherical shell, the same size and mass as the Earth, but hollow inside. What do you suppose the gravity feels like? Which direction does it pull from, and how strong is it compared to the gravity you're used to when you're on the outside?
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