At 11:04 PM 11/24/98 EST, you wrote: >how can i use the law of gravitation or normal gravitational force in everyday life?? i need it like tomorrow please try to send it quick thanx >
Heh..... all I can say is that you are one lucky (insert word here)/person ..... I would be asleep if it wasn't for some stupid party that's making too much noise....
Anyway, to your question: Wow.... this has to be one of the hardest questions I have ever recieved, so this is the best I can do in such a short notice:
Personally, the only use that I have had for it other than tests are to show off my intelligence on it, but that isn't what you are looking for, right?
Okay, I just thought of something.... but in order for me to explain this, I'll need to talk about Newton to make it clear.
I guess you can say that in Newton's Law of Gravitational Force is:
F=Gm(1)m(2)/r^2
(For a better picture, go here, http://www.mines.edu/fs_home/tboyd/GP311/MODULES/GRAV/NOTES/graveq1.gif) Which really means that mass #1 and mass #2 are at "r" distance away, what's the force of attraction in between them?
(Please don't feel like I am insulting your intelligence, I do not know how old you are, or grade, or any knowledge in this field, so I am assuming that you know nothing.)
Think of it this way, you have two spheres hanging, let's say two Christmas ornaments (hey, it's what's on my mind ^_^) hanging on a tree about 10 centimeters apart. Each ornament weighs 1 kg (yeah, I know it's a lot, but just for the sake of easy numbers). Now, we assign each ornament as M#1 and M#2. Plug it into the formula. 'G' is the gravitational constant of 6.67 x 10^-11.
SO, it'll be:
F= (6.672 x 10-11)(1)(1)/(.1)^2
F= 6.67 x 10^-9
The answer would be that the two ornaments are attracting each other with the force of 6.67 x 10^-9 Newtons.
(If you don't understand scientific notation (the "x 10^??" part), just e-mail me again, or ask someone.)
What the Newton Gravitational Formula just did was to solve for the attraction of two things in matter. This explains why Earth orbits around the sun, because of such huge masses. And the distance has a factor too, the closer the distance, the more it is attracted to another.
As for the Gaussian theorems:
Copied from my page:
(http://www.geocities.com/RainForest/Vines/2977/gauss/formulae/14.html)
Gauss' Law of Normal Gravitational Force
The surface integral of the normal component of the gravitational force on a particle of unit mass, taken over any closed surface is equal to (4 pi G) times the total mass enclosed by the surface.
Now, a surface integral, meaning it probably has to do with non-Euclidean Geometry (as opposed to Plane Geometry). (The stuff that you have learned in elementary school is planar geometry. y'know, where the sums of the angles in a triangle are equal to 180 degrees? Well, that doesn't apply in non-Euclidean geometry. Think of it this way, if you drew on a sheet of paper, a triangle, the angles would add up to 180 degrees, right? Well, what if you did that on a curved surface? Like if you choosed three cities on the globe, and made a triangle of the three points, the triangle would no longer seem like a triangle that you are used to, because it's no longer on a flat surface. So, the angles wouldn't add up to 180, in fact, it can be anything! It's different, it depends on the situation.
The 'normal component' and 'particle unit mass' can be ANYTHING! As long as it is tangible. Like those Christmas ornaments I used before.
Okay, it also mentions "Closed surface," back to the globe idea. The earth is 'closed' for the most part, don't you think so? It's not like it has a hole like a doughnut, right? (Well, that is technically still a closed surface, but that goes into complicated Calculus, and I don't think that neither of us want to go into that!)
Now, that I dissected it, now we put it together!
What it is saying, what is the force that the Earth has directly on you. You, the 'normal component' and 'partical unit mass' is on the 'closed surface' (Earth)! So, we'll take your mass... let's say it's 50kg. Now, we multiply it all together.
(pi is equal to 3.14, another constant)
50 * 4 * 3.14 * (6.67 x 10^-11)
This all equals up to: 4.19 x 10^-8
(I'm not quite sure, but I think that's how it goes)
Okay, onto the other one!
(http://www.geocities.com/RainForest/Vines/2977/gauss/formulae/13.html)
Gauss' Law for Gravitation
The total gravitational flux passing out from a closed surface is, in rationalized units, equal to the negative of the total mass enclosed within the surface, or to (-4 pi) times the total mass enclosed in the more usual case of unrationalized units.
Flux... I hate this word, but in a nutshell, think of it as constant change, a wave on an ocean, just flowing..... in this case, gravitional flux is 'flowing' out of the closed surface (I'll use Earth as the example, again).
Let's take the 'rational units' case, because it is much easier, but if you want me to explain the 'unrationalized units' just e-mail me again. This e-mail's being much too long as is...
Rationalized units, think of it as being able to be counted, easily measured.
Okay, a total mass in a closed surface. Think of it this way, you know those things you get from a vending machine? Little toys, like rings, or other trinklets? They come inside one of those clear bubble containers, but there's also air inside of it. The toy inside is the 'total mass' and the 'enclosed surface' is the bubble container. Because the toy is a mass, you want to see how much gravitational power on it's own.
In Newton's Law, it had one mass in relative to another mass, in other words, in comparison with another mass.
But this law tell's how much the item by itself has on its own. So, let's say the toy is 1 kg, it's gravitational flux would be -1. Simple enough? In this case, the size of the closed surface, or bubble, doesn't matter. It usually does, but in cases as flux, magnetic flux, or in this case, gravitational flux, it doesn't.
Well, that's it! Just as a side note, notice how everything is in SI or metric units? The other units might work in some cases, but it is guaranteed to always work in SI units. Constants, like "G" are in SI units, so unless you want to convert it, I suggest to stay with the SI units.
Okay, this took me a LONG time, and sleep too (the party stopped when I got to the end of Newton...), so I hope you do good on your report! (Heh, signing the guestbook wouldn't hurt either.... if I can type all this, you can certainly type a few measly words...)
Additional Follow-up:
Sorry, I just realized I didn't completely answer your question... With these formulas, you can find out what I just told you what you could. But also with it, you can find out many various forms of other things. The Gaussian formulae are often used for atoms and such, not so much with Earth (but I figured it would be easier to explain it in that fashion, otherwise I would have to bring in a bit of Chemistry).
If you also want to, you can also make little prank jokes about it... like 'attraction' like the 'gossip' types. heh heh. Of course, they'll all think you're a wierd, but that's okay, right? :o) If you're an overwieght person, you can just say that you are more 'attractive' person... or something like that.... *shrug*
But more or less, there really isn't much use for it unless you are into this field or are using it to show off about it. But now that you understand the formulae, maybe you can use your own imagination to figure out uses for it!
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