Derivate the forumla for the acceleration due to gravity

[JohnDubYa]

Gawd, I miss Oklahoma. Are you a physics major at the University?

My allusion to GR was a jab at those that conjure GR to explain the most elementary physics.

 

[woodysooner]

good question, at the present I'll be a junior in chemical eng. and eng physics, but bout to give all that up and start over lol in Physics and Math.

if dad let's me, he runs the show sadly, but he shouldn't cause he don't pay for it the state and a lot of other do.

 

[JohnDubYa]

Take all the classes that Bruce Mason teaches. I had him as an undergraduate and he may be the best Prof I have ever had at any level. Doc Watson and Mike Morrison too.

 

[cepheid]

I'm a student and I'd just like to offer my two cents on this debate over terminology:

When we began our study of physics in high school, we began with kinemetics. Certain problems (involving freefall and later projectile motion) involved use of the physical quantity g, which I learned was the acceleration of objects in freefall. (Our physical model for falling objects always neglected air resistance, so I did not trouble myself over it). My teacher referred to this as the acceleration due to gravity, which made perfect sense to me, because it meant that gravity caused objects to accelerate at 9.81m/s^2. More precisely, when gravity was the sole force on an object, it's resulting acceleration would be g. I accepted this to be true, even though I had no idea how or why it was so, i.e. was was the nature of the graviational force and why did all objects under it's influence accelerate like so?

Later, when we studied dynamics, we attempted to determine how such 'action at a distance' was possible, and we were introduced to the notion of fields. From Newton's Universal Law of Gravitation, we derived the 'graviational field strength' at the Earth's surface to be g. I must admit to being mometarily confused. Why should these two quantities with totally different names be represented by the same symbol? I decided that the quanitites must actually be one and the same, and set about explaining it to myself. I asked myself the question: "Why is the acceleration of objects under the sole influence of Earth's gravity equal to the strength of the graviational field at the Earth's surface? The answer is simple: From the definition of a field, we see that the Earth's graviational field exerts a force of 9.81 Newtons on every kilogram of an object's mass. It therefore exerts a force of 9.81 Newtons on a 1kg object in freefall. Since the definition of a Newton is the force required to accelerate a 1kg object at 1 m/s^2, it stands to reason that our 1kg object in freefall will accelerate at 9.81 m/s^2, since 9.81 N of force are being exerted on every kilogram of mass. Therefore, the two quantities are one and the same: the acceleration of an object in freefall is equal to the strength of the gravitational field. I was sure this was true when I observed that

$$\frac{N}{kg} = \frac{m}{s^2}$$

In short, I sorted it out on my own and I really don't care whether you call g 'acceleration due to gravity' or 'gravitational field strength' since the fact that the two must have the same magnitude (and direction) at the Earth's surface is direct consequence of the Law of Gravitation and Newton's Second Law.