/sci/ - Science & Math

>>5782236
Bumping.

Yes, as the force of gravity is taken as acting from the centre of mass of the object.

The equation is F = G* (M1*M2/r^2), by the way. Where M1 and M2 are the masses of the two objects.

>>5782236
>Is the formula (g = GM/r^2)for calculating the acceleration due to gravity applicable for non-spherical objects?
you need to integrate over the cube using that formula for every point.
maybe this will help.
>https://dl.dropboxusercontent.com/u/46685978/1206.3857v1.pdf

>>5782236
You could convert cartesian coordinates to spherical coordinates..

rho = sqrt(x^2 + y^2 + z^2)
theta = atan2(y, x)
phi = atan2(z, sqrt(x^2 + y^2))

And use the spherical formula.

It would be like an Earth with 8 really tall mountains.

>>5782295
No, that simplification only works for a spherically symmetric object.

>>5782295
No, that simplification only works for a spherically symmetric object.
In general you need to do >>5782298

>>5782236
No, but you can just enclose the cube in a sphere of the same mass and then it is.

how do you know the earth isnt already square?

>>5782964

/sci/ gold here goize xD xD xD

>>5782236
>if the formula for calculating the acceleration due to gravity appicable for non-special objects?

No. That formula only works for a sphere. It is derived from simplifying the integral form of Gauss's law for gravity, given the spherical symmetry.

To calculate the gravity equation at a point in a "cube" you would need to start at Gauss's law for gravity, and modify accordingly. It is going be a whole lot more complicated though.

http://en.wikipedia.org/wiki/Gauss's_law_for_gravity

Any other questions?

>>5782295
>>5782298
>>5782300
How the fuck did you guys get it all wrong?

>>5785084
\THREAD

>>5785088

What's wrong with >>5782298 ?

You'd need to do a vector integral, but that's easily done.

>>5785084
>>5785088
>>5785089
Cool samefag bro.

A differential, point mass is indistinguishable from a sphere.

>>5785098
>a differenital point mass.....

Ok, way to state the fucking obvious and add nothing to the conversation. You gonna list some random unrelated theorems next?

>>5785098
i thinking this is correct since every object has a center of mass and that center can be considered a point which would be indistinguishable from a center mass point inside a sphere

>>5785106
>state the obvious
>list random unrelated theorems

If it was obvious to you, you wouldn't be upset right now about someone stealing your thunder.

>>5785111
Yes. The g = G*M/r^2 equation is exact for point masses. Perform an integral. dg = G*dM/r^2

>>5785106
>>5785111
my sides

>>5785098
A sphere isn't a contractible space.

>>5785092
I hadn't read it, but I just skimmed it now.
Damm that is some really sloppy messy shit.
Why the fuck would anyone try to do it that way? Do you just want to waste time?

You also get a really fucking fault notion of what is really going on. Goddam that is some high level faggotry right there.

Leave it to an engineer to fuck up a very basic problem.

>>5785127
How would you do it?

>>5785084
Of course it applies to a cube.

Honestly people I may be in grad school now but I could have answered this question when I was 13.

The fact that you know about Gauss's Law but don't know the most fundamental fucking thing about gravity really scares the shit out of me.
How do you people go through school? You just apply equations to specific situations without actually knowing where the logic comes from?

Any two particles attract each other with a force of:
<span class="math">F_{G}=G\frac{Mm}{r^{2}}[/spoiler]
along the radial direction joining the two particles.

Of course it applies to a cube, it applies to every geometry. Just integrate over the cube.

>>5785088
>How the fuck did you guys get it all wrong?
what the fuck? the one was actually correct you dumbfuck.

>>5785151
The one link looks like is was written by a grade schooler. It is pretty pathetic, and goes about the whole thing is some ass-backwards manner. It is pretty sad.

>>5785160
Again, please explain a better way.

>>5785153
0/1000

Really shitty engineer is obvious

>>5785160

and yet isnt not wrong.

nice damage control btw.

>>5785182
so you are saying you cant just integrate?

>>5782236
gmr^-2 is obviously an integral of something. if you have a cube, you need to reintegrate accordingly.. but, you could obviously treat chunks of the earth as d-sized spherelets and integrate the integral into a cube.

>>5785182
You're either a troll.

Or you genuinely don't know what you're talking about.

>>5785185
He's an idiot don't listen to him.

You're going to take the word of some guy who just says "0/1000" without pointing out a single flaw or contributing anything, over the guy who explained that the equation is a fundamental law of physics?

>>5785153
But is doesn't apply to a cube you retarded hick!

>Is the formula (g = GM/r^2) for calculating the acceleration due to gravity applicable for non-spherical objects?

FUCK NO. That formula is only directly applicable to point masses, or some spherical objects. For a cube you will get a different formual for g, and for _whatever the fuck_ you will get another different formula for g.

No one is arguing the validity of newtons law of universal gravitation you dumb prick. No one is arguing about any of the shit you are trying to point out!

There is a huge difference in what OP is asking, and the question you seem to think he asked. Learn to read and stop being a fag and go to bed kid!

GMr^-2 applies to POINT MASSES. It works outside a sphere because the field is equivalent to a point mass at the center. Therefore for ANY other shape you just have to integrate over every point. The integral would be ridiculous though

>>5785220
Nobody is saying that g = GM/r^2 is applicable to a cube.

Everyone has said that if you use its differential form, you can integrate over the cube to find g.

It applies to every geometry as long as you integrate over the region of that object.

You are pulled towards center of the cube, the middle of the square on any of the sides of cube is closest to the center of mass you'll get.

>>5785245
>You are pulled towards center of the cube
only at a couple of points; in general you wouldnt be

>>5785254
You would be pulled towards the center of the cube at all points. The only thing that changes is the magnitude of the force.

See >>5782298 's paper

>>5785262
>If we look at the changing direction of the field as we move across a face, then we observe that the field vector only points towards the center of the cube at the center of each face, at the corners, and at the center of each edge, which could also be deduced by symmetry arguments, refer Fig. 2.

>>5785181
>better way

Use actual physics and understand what is going on to simplify shit, instead of this pointlessly complicated engineering circle jerk method.

They initially use "F" and "g" from universal gravitaion between point masses, then get "cube V" from integration of this. Then get "cube g" from differentation of "cube V". WHAT THE FUCK? This is some really sloppy circular nonsense shit. It is needlessly complicated.

>Lets integrate them immediatly differentiate?!

Goddamm...that is some A+ faggotry. There is NO FUCKING NEED to break everything down to point particles and then build a cube! Just start off with a "cube g"! Derive is equation directly from basic fucking physics (Gauss's law for gravity)! The math is alot simplier.

Goddamit that paper is retarded. It is like a little kid trying to explain everything through newtonian mechanics, instead of lagragian shit. Or like the biologist who "discovered" basic calculus.

You can tell he was nothing more than a lowly dumb engineer undergrad.

>>5785263
fuck me sideways.

>>5785236
But that is what OP is asking

>>5785283
And the "Actual physics" way is?

Seriously. I defy you to find any way other than using gauss' law for gravity and integrating over a cube.

>>5785283
Go away EK, you don't know what you're talking about.

>>5785288
>implying the "actual physics way" isn't to use gauss's law for gravity

>implying you can't read the post?

The easiest thing to do this is to integrate the gravitational flux over the surface, you don't actually need to integrate over the volume.

This is really basic undergrad physics here. It involves actually understanding what is "going on" as opposed to this ad-hoc "pluging and chuggin" nonsense you do.

That is the problem with the paper and engineers in general. You may get some of the right answers some time, but you actually have no fucking idea what you are doing. You end up making the dumbest mistakes, and taking the very very very very very very very long way to arrive at anything.

>>5785283
You are mistaken.

I don't think anyone would disagree that integrating over the cube is definitely not the best way to do it, and ya it is sloppy.

But I seriously fucking hope you don't become a teacher and tell students that Newton's Law of gravitation equation can't apply to a cube.

We are speaking from the point of view of the fundamental physics, and saying yes it can be done this way, and it is more instructional to tell someone unfamiliar with physics to think of the cube as a bunch of individual particles, explain how those particles interact gravitationally (classically) and they will understand.

Going into all this Gauss's Law bullshit isn't helping him anymore than saying integrate over a cube is. The difference is that saying to integrate over the cube gives them a better idea of what is physically happening (classically).

But you're clearly one of those people who can't distinguish between intuitively understanding what is physically happening and the mathematical method of solving a problem.
To you they are probably the same thing and that's why you will never contribute to physics in any way remotely comparable to that guy in your pic.

>>5785300
EK doesnt know calc.

>>5785286
OP asked if it applies.
You guys are assuming he meant to ask "does it _directly_ apply"

If you can use it to solve the problem then it sure as hell applies.
Who said OP was asking if he can just plug numbers in and get an answer?

>>5785314
Your point is to cater to dumb people?

>>5785320
0/100

You can't be that retarded.

>>5785314
0/100

So many trolls?

>>5785316
Not the same guy, but quit with the engineering insults.
You sound like an idiot.

I am in a physics PhD program and I disagree with you.
It sounds more like you are just trying to show off that you learned Gauss's Law or something. Are you proud of yourself?

There is no "official" way to solve the problem. If you integrate over the cube and find a solution it's just as valid as using Gauss's Law (albeit much more difficult), but it still works.

"Why don't we just start kids off by learning Lagrangian and Hamiltonian dynamics? It's easier than doing it the way kids first learn it in school.
Lol they are such engineers"
^^ your logic

>>5785314
Did you confused /sci/ with /liberal art/?

>>5785316
How are you going to integrate a quantity that you don't know?

Integrating the flux over the surface is going to give you the mass. You're looking for the magnitude of the gravitational field at any arbitrary point.

>>5785323
see
>>5785335

>>5785335
>what about the kids

Sorry, I keep forgetting how /sci/ is all about "the kids"

ITT: WE GOTTA CATER TO THE KIDS!!!!

>>5785341
also see
>>5785335

seriously guys, you are so fucking smart. You are all geniuses bravo!

Is that what you want to hear? Get over your fucking egos.

It doesn't matter if you solve a problem in the most absolutely retarded way possible
IF IT WORKS THEN IT'S STILL A SOLUTION.
My goodness the level of stupidity in this thread is astounding.

>>5785345
>>thinks an answer is wrong if you don't solve it "the best way"

>>5785283
>>5785286
>>5785316
>>5785341
>>5785345
stop posting faggy image macros.

who feels more gravity?

>>5785356
Hurr durr. Gravity is a constant. Moron

>>5785356
Guy on the left.
the vectors of the guy on the right cancel out in most directions.

>>5785316
omg you know Stokes theorem, you're the smartest /sci/ poster ever.

>>5785358
that would only be true on an infinite plane. This plane is finite and therefore g is not constant.

>>5785364
Seriously?

>>5785361
>>5785364
these

>>5785368
100% serious right now.

you would find yourself walking tilted to side because of difference of gravitational pull

>>5785314
>integrating over the cube is definitely not the best way to do it
What's the better way then?

you guys are fuckin missing the most obvious answer

what is gravitation accelerational?

9.81m/s^2 obviously

on a cube you just havce that much gravity 'downwards' relative to wherever you 'are'

let me clear some air here
F = G* (M1*M2/r^2) is the formula used to compute the force between two point objects .

Now we apply this to earth by replacing the centre of mass with the equiavalent mass of the earth . this method allows us compute forces between two distant bodies

Will this apply on a cube , maybe and maybe not . If you are calculating the force between this mega cube and a distant object this will work quite well . But using it to calculate gravity is wrong the gravity will not be uniform on the surface of such a body since from different points on this cube the mass of the cube is in different orientations . Calculating the dynamics of such a system will cause dizziness and nausea and you are much better modelling this in a supercomputer .

Do i have the money to get a supercomputer.
NO
Do I have that much time to do calculation myself
NO
Is it over 9000
probably

>>5785339
>can't do basic vector calculus

You seperate it out into parts dumbass. A vector part and a scalar part, you solve for the scalar part. You calculate the vector part.

You exploit the symmetery of the cube, and only need to integrate over 1/4 of one of the faces, as opposed to the retarded engineering method of integrating over the entire volume for sheer dumbfuckeries sake.

I would explain more and actually do it for you. But everyone keeps kelling me to "remeber the kids". So Sorry. I guess /sci/ is just for highschool bullshit.

>>5785349
Better?

orbital rotation of earth would not occur properly

atmosphere would not sustain itself

measurement of time would not berelative anymore and that would be a huge headache

>>5785384
The question is NOT what is the best way to solve it?

The question is can it be solved with g=GM/r^2

and the answer is YES.. Period.

/thread

>>5785383
>implying you can't do the calculation in about 10 minutes

It is a pretty trivial problem kid

>>5785397
>implying that is what OP asked

Why can't you read?

>>5785393
>orbital rotation of earth would not occur properly
yes
>atmosphere would not sustain itself
not the case that only depends on g , depending on how big the g is the thickness of atmosphere will vary on the cube but that is no reason for the atmosphere to not exist
>measurement of time would not berelative anymore and that would be a huge headache
assuming the non regual rotation of the planet yes but seasons will still exist

>>5785398
I DARE THEE , GO ON AND DO IT

>>5785384
Yea, you can't find the scalar part without integrating over the volume of the cube using the differential form of gauss' law.

Sure, we know the total flux, but that flux is not evenly distributed, so now you have to find a flux function. How do you do that? Well, the only way is to look at the differential masses that make up the whole. Congrats, now you're stuck doing two integration problems rather than one.

I don't think you can do what you say you can. Care to enlighten me?

Calculate the gravitational field at the corner of a uniform density cube whose side is 1 meter long, and whose mass is 1 kilogram.

>>5785403
It is you dipshit

Even if that's not what he intended to ask.
He did ask if it can be applied.

You can apply the equation to the problem.

There is no way you can possibly be dumb enough to think that's wrong. Either way I'll consider our conversation over because you either just realized your a moron, or you actually think that using an equation to solve a problem is not applying the equation to the problem, and if that's what you think then you are hopeless.

>>5785404
NO! THINK OF THE KIDS! WE NEED TO DUMB DOWN EVERYTHING!

>>5785406
This is not the board for science talk.
Think of the kids.

>>5785409
You are clearly inventing arguments in your head that don't exist in this thread.

>>5785406
If it's at the corner it's just the same as if it was on a sphere of course

http://news.discovery.com/space/what-if-earth-was-a-cube-110815.htm

http://possiblywrong.wordpress.com/2011/09/09/if-the-earth-were-a-cube/

>>5785416
science plz go

>>5785413
...but that's wrong.

>>5785384
you mean integrate 1/3 of its surface right?

>>5785416
>inventing

Sounds like science talk? GTFO!

>>5785426
I'm pretty sure the avatarfag doesn't have a clue how to do it. She probably took freshman E&M last semester or something, and thinks that because they did so many exercises using Gauss's law, it's the right way to solve all problems.

>mfw 90 thread where people do
>lol engineers
>wtf retards
>implying
>marcos
>lelelelelele
>argue what OP is asking
>mfw i lost my face half way trough.

Seriously the autism burns my soul, either agree to a solution or at least answer the OP, who is most likely gone at this point but keep your flaming fagotry in check.

>>5785441
...what makes you think avatar fag is a girl?

Could it be because it's EK?

Could it be because you're avatar fag?

Because in both cases, the poster wouldn't be a girl.

>>5785366
obviously you're not

>>5785446
Everyone on /sci/ is a girl. After all:
http://www.youtube.com/watch?v=g032MPrSjFA

>>5785182
>>5785316
>>5785325
>>5785328
>>5785336
>>5785341
>>5785345
>>5785384
>>5785392
>>5785415
And another physics thread ruined by a ban evading shitposter. *sigh*

When will he stop?

>>5785476
EK is not a girl?

>>5785481
That's not EK.

>>5785476
EK is not a girl?

>>5785484
That's not EK.

>>5785485
Who is it then?

>>5785486
A mentally ill person who used to go by the name of "physics guy". He has been derailing physics threads with insane shitposting and flaming for more than year.

>>5785488
What kind of mental disorder do you think he has?

>>5785485
EK is already pretty much fixed, she doesn't shitpost anymore whenever she eats her meds.

Somebody should just make a computer model of it and see what happens. It would seem like a better way of doing this than arguing and posting insult macros.

Perhaps this will be of interest to you:
http://www.askamathematician.com/2011/05/q-what-would-earth-be-like-to-us-if-it-were-a-cube-instead-of-spherical-is-this-even-possible/

>>5785605
Of what? The gravitational field? We already have an explicit calculation of that: >>5782298