George,
A clarification. There is a difference between the force of pull exerted by the Gravitational Constant and the acceleration of a falling body that results from the pull of the gravitational constant.
The force of the Gc is a universal constant. The Gravitational Constant, denoted Gc, is an empirical physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal gravitational constant. The rate of acceleration of a falling body resulting from the pull exerted by the Gc changes, depending on the medium the object is falling through. Ergo, as a 'body' is falling through air the resistance gradually increases, progressively reducing the rate of acceleration until "limiting velocity" is reached. In a true vacuum the rate of acceleration would not decrease. However the Gc would remain constant in each case.
The rate of acceleration resulting from the pull of the Gc at sea level is 32.174 feet per second/second ... until the limiting velocity is reached, where the force of resistance equals the Gc acting upon the body. To be absolutely precise, I should have said that the Gravitational Constant is 32.174 lbm-ft/lbf-sec2, which results in the acceleration rate of a falling body of 32.174 feet per second/second at sea level.
So, just for clarification:
"It is easy to verify that, when air resistence is negligable, all objects accelerate towards the earth at the same rate. The 'reason' is that the gravitational force on an object is proportional to its inertial mass. According to Newton's second law, in order to calculate the acceleration of an object caused by gravity, we must take the gravitational force on that object and divide by the inertial mass. Thus, the inertial mass of the object cancels out of the resulting expression for the acceleration. In fact the acceleration of any object at the Earth's surface is determined by the distance of the object form the center of the Earth, Newton's constant (Gc) and the mass of the Earth:
Acceleration = Gc multiplied the Mass of the Earth divided by the Radius of the earth squared
If you put the value of Newton's constant, the radius of the Earth ( 6 x 106 meters) and the mass of the Earth ( 6 x 1024kg) into the above expression you will get approximately 9.8m/s2, which is the rate at which all objects accelerate downwards at the surface of the Earth (at the level of the earth's surface).
Although the magnitude of the acceleration due to gravity, g, is the same everywhere on the Earth's surface, its direction changes depending on where you are. It is a vector that always points towards the center of the Earth, so, for example, it is in the opposite direction at the North Pole than at the South Pole. This effect is not very relevant to us because the Earth is so big. If we move from one end of the room to another, or even one end of the city to another, we are only moving across a very small fraction of the total circumference of the Earth, so the direction of the gravitational acceleration changes very little. Our notion of ``down'' only changes significantly when we travel very large distances. However, if you happen to be near a very massive, but small object, such as a black hole, the fact that gravitational acceleration changes direction depending on your location becomes very significant indeed: it gives rise to so-called tidal gravitational forces that can tear a spaceship apart in microseconds.
Note that the rate at which objects accelerates towards the Earth changes with distance. We don't notice this because we are already so far from the center of the Earth (6 thousand kilometers) that we would have to move vertically a large distance to cause a significant change: for example, to decrease the acceleration due to gravity by half down to 4.9 m/s2 we would have to go out into space about 1500 km above the Earth's surface."
Gc is a constant. The rate of acceleration resulting from the Gc changes with a number of factors. Nonetheless, the Gc always remains constant. Hope that clears everything up.
I was trying to keep the explination(s) as simple as I could - as some folks think I tend to make explinations too complex - but any time I'm less than absolutely precise there's always someone looking to point it out. That's good. Keeps us all on our toes! 
Ed
Topic: arrow physics 2 (Read 5133 times)
