posted 01-23-2002 10:48 AM
Dear 3T3L1,Actually, LTC and Stuart are correct - in a manner of speaking. "g" cannot be an acceleration, because acceleration is a change in motion, and "g" is a force that (sometimes) causes acceleration.
Let's look at the two concepts.
Acceleration
Acceleration is based on a speed change (usually measured in meters per second or m/sec) over time (measured in sec). If you start off at rest and increase your speed from zero to 9.8 m/sec the first second, to 19.6 m/sec the second second, to 29.4 m/sec third second, and so on, then each second your speed is increasing by 9.8 m/sec. Put another way, your speed is increasing 9.8 meters per second per second, or your acceleration is 9.8 m/sec/sec. (The reason I use 9.8 m/sec/sec for my acceleration example is that it's the approximate value of the acceleration caused by gravity on the Earth's surface.)
There are several basic formulas used to determine the average acceleration of an object if the acceleration is constant, and to determine the object's displacement (how far the object moves) under average acceleration. If the acceleration changes, you can still determine displacement and averages, but it requires calculus to do so.
Gravity
Gravity, from nonscientific terms, is seen as the reason the apple falls from the tree to the earth and the explanation for why we do not float off the face of the planet. From the scientific point of view, it is a bit more tangible and less mystical. Gravity, or gravitation, is the force of attraction between two objects because of their masses. The force of gravity increases with the masses, and thus gravity and mass have a direct relationship.
A force is usually described as a push or a pull exerted on an object by another. This push or pull, if it is strong enough, will accelerate the object significantly. Forces are measured in newtons, which is equivalent to kg*m/s, and that a one-Newton force is required to accelerate a one-kilogram object one meter per second.
According to Newton, any two masses will attract one another with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. This became known as his Universal Law of Gravitation. In equation form, the force of attraction (F) is equal to G (the gravitational proportionality constant equal to 6.67 x 10^-11 N * m ²/kg²) times the product of the masses (m1, m2) divided by the distance between them squared (r²).
Earth, as we all know, has a very large mass and thus our attraction to it is large. So large, in fact, that it appears that objects accelerate towards the earth at a rate of 9.8 m/s². Remember, this value, 9.8 m/s², is the acceleration due to gravity (but not gravity itself) and is seen as the letter "g" in equations. Because falling objects are falling due to the influence of gravity, "g" (gravity) can be substituted for "a" (acceleration) for equations involving falling objects.
But they're not the same thing! G is a force measured in newtons which can cause an object to accelerate, which acceleration is measured in m/sec/sec.
Another way to think of this is to consider that you can have "g" without attendant "a".
Question: A ball in your hand (on the surface of the Earth) is subject to a force of one "g". What is its acceleration (in m/sec/sec)?
Answer: zero, if you don't drop it! The "g" vector (gravity) is balanced by an opposing force vector caused by the muscles in your arm holding up the hand. You still have the "g" vector, but you have no "a".
This is the easiest way to show that "g" and "a" are not the same thing.
And that is what Stuart was talking about when he mentioned standing on the Earth's surface. You are still subjected to the Earth's gravity (or else you'd float away) -- but you're not accelerating (because the Earth's surface in in the way).
Regards,
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Duncan Kunz / duncankunz@home.com
Mesa AZ / 480-891-2525
[Edited 4 times, lastly by Duncan Kunz on 01-24-2002]