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/sci/ - Science & Math


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6729178 No.6729178 [Reply] [Original]

Answering physics questions!

>> No.6729208

>>6729178
why are physics students so bad at getting laid they didn't even show up on the chart?

>> No.6729209

Dear Mr Science-

Say I have an object free falling in a gravitational field. Does the path of the center of mass follow the same path that a "point mass" of equal mass would follow?

>> No.6729212

>>6729208
>he thinks real life is like his cartoons
This place is 18+.

>> No.6729218
File: 62 KB, 1094x386, time average power.jpg [View same] [iqdb] [saucenao] [google]
6729218

how the fuck do I handle the big N in the time average power equation? I understand that for energy you see if it converges, but i dont understand what that other variable means in the power equation or how to handle it

see pic

>> No.6729222

>>6729178
I've heard that there have been attempts at axiomatizing physics. Could you provide more information on this?

>> No.6729226

Why is my physics grad friend so seemingly miserable?

>> No.6729235

>>6729209
Yes. The force on a body in a gravitational field is proportional to its mass, and so is the acceleration, so the mass of the body itself cancels.

>>6729218
I'm not entirely sure what you are asking, or what the math on your scanned sheet means. Why did you set x = 1? Why did you write E = infinity?

>>6729222
This is a really broad question. The fundamental underlying axiom of physics is the scientific method, but I am assuming this is not what you are asking. Are you asking about which axioms of mathematics best represent the mathematics that the natural universe obeys? Or are you asking what the "furthest back" we can take physics is, before we have to just accept certain facts as axioms?

>> No.6729237

>>6729226
>>6729226
I don't know, people are miserable for all kinds of reasons. Maybe their advisor is a bastard, maybe they don't really enjoy physics.

But probably it has nothing to do with physics, and there's something else at play. Maybe they are ill, they are having family trouble, or they feel lonely, inadequate, or bored. Why don't you ask your friend and see what they say?

>> No.6729239

>>6729235
the series is divergent for the given signal meaning that it has infinite energy

disregard the physics then. if someone wrote a summation to N starting with n=-N how do you process that shit? Plug in N or something?

>> No.6729240

>>6729235
Sorry, my response to >>6729209 didn't really make sense the way I meant it to. What I meant to say is that the force on a body in a gravitational field is proportional to its mass, and force is mass times acceleration. Setting the force <span class="math">F = ma[/spoiler] equal to <span class="math">F = mg[/spoiler], where <span class="math">g[/spoiler] is the gravitational field strength, the mass terms cancel.

>> No.6729244

>>6729237

He's always complaining about his department. Maybe being a physics grad student is a terrible gig until you get some kind of big break for your career?

>> No.6729245

>>6729239
Divergence is not the same as infinity. For no <span class="math">n[/spoiler] is <span class="math"> \sin (n \pi / 4) [/spoiler] going to be infinity.

What you want to do regarding the second equation is observe that <span class="math">sin(-x) = -sin(x)[/spoiler], so each negative term will cancel with each positive term in that summation. The only term left will be the <span class="math">n = 0[/spoiler] term, which will be divided by <span class="math">2N+1[/spoiler], so the limit is 0.

>> No.6729250

>>6729244
No, lots of physics grad students are happy. I had a great time in grad school, and so did lots of my cohort, whether they ultimately went into industry, academia, finance, whatever. There were a few people who were totally miserable, and a couple people who didn't hate or love it but just were there to get through it, but that's the case anywhere you go.

>> No.6729258

>>6729245
but thats wrong. if the energy for a signal is infinity the power will be a real positive number and vice versa. your thread a shit

>> No.6729263

>>6729258
I don't know what the physics problem is that you are talking about. I am just looking at the math on that page, and it is wrong. The limit as n goes to infinity of <span class="math"> sin(n \pi / 4) [/spoiler] is not infinity. Can you explain what the problem you are working on is?

>> No.6729274

>>6729263
there should be an absolute value sign around the expression hence no negative values to cancel out

>> No.6729276

>>6729274
and a summation. who ever wrote the answer key i am referencing is asleep on the job

>> No.6729277

I'm utterly confused about what this question means, even after seeing the answers others have given. I'm not even sure what exactly is being asked here. This showed up on my first exam on Friday.

au.answers.yahoo.com/question/index?qid=20121203225405AAlUeXO

>> No.6729286

>>6729274
I still can't really provide input unless you explain the problem. Why are you summing values of the sines of multiples of <span class="math">\pi/4[/spoiler]?

I did overlook the absolute value sign, which changes my result slightly for the limit on the bottom. For every 8 values of n you are picking up <span class="math">2 + 2 \sqrt{2}[/spoiler] in the sum. So you can rewrite it as <span class="math"> \lim_{\rightarrow \infty} \frac{(2N+1)(2 + 2\sqrt{2})}{8(2N+1)} = (1 + \sqrt{2})/4 = 0.604[/spoiler]

>> No.6729288

>>6729277
>au.answers.yahoo.com/question/index?qid=20121203225405AAlUeXO
Can you post the figures referenced in the problem?

Also, I'd rather not do peoples' homework for them.

>> No.6729295

>>6729288
Nvm, I found an answer I get while looking for a copy of the figures. Since my non-homework is out of the way, here's a different question:

How do dimensions beyond the third relate (if at all) to imaginary numbers?

>> No.6729300
File: 38 KB, 1227x284, Capture.jpg [View same] [iqdb] [saucenao] [google]
6729300

>>6729286
thanks for offering input, all i really need to know is how to handle the "N" variable in the summation sign. that is what is tripping me up.

The equation for energy is shown in the pic. It runs from negative inf to inf. Cool I get that. The power equation shown involves summing from n = -N to n = N. I do not know how to move forward because I don't understand plugging in a variable into another variable when trying to find out how it converges. I've googled all kinds of shit to find out how to do it. If you could point me in the right direction with a link or explain it im set for this assignment.

>> No.6729303

what do you think would be a better plasma-facing material for a tokamak type fusion reactor, beryllium, tungsten, carbon

>> No.6729307

>>6729300
I see. Well it's pretty much what I said. The first infinite sum gives you infinity, as you found. The second one can be found by observing that every 8 values of n contribute <span class="math">2 + 2 \sqrt{2}[/spoiler] to the sum, so (not in general, but within the limit as N goes to infinity) you can rewrite <span class="math">\sum_{n=-N}{N} | \sin (n \pi / 4) | = (2 + 2\sqrt{2}) (2N + 1) / 8 [/spoiler].

>> No.6729309

What kind of a role do you see physics playing in finance?

>> No.6729316

>>6729309
bout 3fiddy k

>> No.6729321

>>6729307
That sum should be typeset as <span class="math">\sum_{n = -N}^{N}[/spoiler].

>>6729295
They don't. There are two ways that imaginary numbers come into geometry in physics. One is the use of geometry to describe complex numbers, using the complex plane. This is a way of representing an imaginary number <span class="math"> z = a + bi[/spoiler] as an x-y pair <span class="math">(a, b) [/spoiler] of the real and imaginary parts. Representing complex numbers in this way yields many beautiful and non trivial results that are invaluable for certain computations.

The other relationship is when complex numbers are used to represent geometry. The distance between two points in Euclidean space is the sum of squares of the differences in their cartesian coordinates, or for a 4D space, <span class="math"> d^2 = x_1^2 + x_2^2 + x_3^2 + x_4^2[/spoiler]. But we live in what is called a Minkowski space, and the fourth coordinate, time, actually contributes negatively to distance in spacetime: <span class="math"> d^2 = x^2 + y^2 + z^2 - t^2[/spoiler]. One thing that is entirely non physical and unrelated to math is to do a coordinate substitution <span class="math"> \tau = it [/spoiler], which makes the distance equation look more like Euclidean space: <span class="math"> d^2 = x^2 + y^2 + z^2 + \tau^2[/spoiler]. This can occasionally simplify calculations, but before any usable results are obtained you have to substitute back in the real <span class="math">t[/spoiler] coordinate.

>> No.6729325

>>6729307
t-thanks... but I am retarded and do not understand what the big N means.

is big N the upper and lower limits of time as specified in the problem? pls anon

>> No.6729327

>>6729240
Thanks, but I'm not sure if you are answering what I intended to ask. Suppose you have an irregularly shaped object, falling in a gravitational field. Perhaps it is turning over and over as it falls. The center of mass of the object traces out some path. Is this the same path as a very small spherical object of equal mass would take given the same initial condition?

>> No.6729331

>>6729303
I'm not a fusion engineer, so I can't really claim to know about what material properties are required in tokamaks. If the plasma-facing material is meant to absorb neutrons and radiate heat into a steam generator, I guess it would need to have a high neutron interaction cross section. If cooling is adequate I doubt that the temperature would be that much of a problem, so I'd go with beryllium?

>>6729309
Frankly there's not a lot of physics in finance, but research in physics has yielded and continues to yield results in nonlinear dynamics, chaos, probability, computer science, and other applied-math topics that are highly applicable to the study of finance.

>> No.6729335

Thought of this problem a couple days ago, but couldn't figure it out:

Suppose you have a thin, stiff, horizontal metal rod of length <span class="math">L[/spoiler] and cross-sectional density <span class="math">\delta(x)[/spoiler], so the total mass of the rod is <span class="math"> m= \int_0^L \delta(x) \,dx[/spoiler]. Suppose the rod is resting on <span class="math">n[/spoiler] pins at locations
<span class="math">0\le p_1< p_2<\dots<p_n\le L[/spoiler]. Let <span class="math">g[/spoiler] be the acceleration of gravity. What is the downward force <span class="math">F_n[/spoiler] that the rod exerts on the <span class="math">n[/spoiler]-th pin?

>> No.6729336

>>6729325
This is the definition of an infinite sum. Any time you see sum to infinity written, you aren't actually plugging in infinity to n, you are taking the limit of value of the nth partial sum as n goes to infinity. Big N is just the outer limit of your sum, and is being used to explicitly write the infinite sum as the limit by which it is actually calculated.

>>6729327
Oh, I see. For a body under no external forces, any rotation is about the center of mass, so you actually won't see any wobbling about happening at all. However, this is thrown out the window if your gravitational field varies on the size scale of the object- if the field is stronger at the left end than the right end, you have a torque and essentially a different system of forces compared to if you had a point mass.

Ultimately this boils down to the fact that a point mass is a completely adequate approximation for a free falling body, if and only if the gravitation field varies slowly compared to the dimensions of the body.

>> No.6729339

>>6729178
I have a question, if you sent a rocket to Europa, wouldn't it make the atmosphere explode since it's mostly oxygen?

>> No.6729343

>>6729339
the atmosphere would have to have something for the oxygen to react to release energy resulting in an explosion. oxygen doesnt just release energy by it's self. its got to have something to reach a lower energy state through an exothermic process

>> No.6729344

>>6729335
This is a tough question. The answer is going to be a big system of equations with terms like <span class="math"> \int_{p_i}^{p_{i+1}} x \delta(x) dx [/spoiler], constrained by the balancing of torques. I could try and work it out, but it might take a little to get everything right. I'll get back to you.

>> No.6729345

>>6729336
>Oh, I see. For a body under no external forces,...

Thank you! This is exactly what I wanted to know. I was interested in the case where the object is small relative to the varying force of gravity.

>> No.6729346

>>6729335
I think the system is unsolveable for more than two pins
Try some statics methods
<span class="math"> \Sum F = 0 [/spoiler]
<span class="math"> \Sum M = 0 [/spoiler]
Each give 1 equation, so two equations and n unknowns

>> No.6729348

>>6729339
Oxygen itself doesn't just flame or explode. It is highly reactive with other chemicals in the environment. Oxygen is fairly stable on Europa due to the lack of anything for it to react with, whether it is exposed to heat or not.

>> No.6729355

>>6729344
Thanks! I asked the falling body question too. I figured the sum of the forces should equal g*M, where M=\int_0^L \delta(x) dx. I thought I must consider the torques as well, but couldn't decide what fulcrum(s) to use.

I was putting up shelves in my garage and wondered how much weight each bracket would bear given some load. They were rated at 40 pounds. Turned out to be more difficult than I thought it would be.

>> No.6729365

>>6729346
>>6729344
>>6729335

OK, here is my analysis. You get the following equations:

<span class="math"> \sum_{i = 1}^N F_i = mg [/spoiler]

<span class="math"> g \int_0^{p_1} x \delta(x) dx = g \int_0^{p_1} x \delta(x) dx - \sum_{i = 2}^N F_i [/spoiler]

<span class="math"> g \int_{p_N}^L x \delta(x) dx = g \int_0^{p_N} x \delta(x) dx - \sum_{i = 1}^{N-1} F_i [/spoiler]

and then for j = 2, 3, 4 ... N-1:
<span class="math"> g \int_0^{p_j} x \delta(x) dx - \sum{i = 1}{j-1} F_i = g \int_{p_j}^{p_N} x \delta(x) dx - \sum_{i = j+1}^{N} F_i [/spoiler]

From here it's just computation.

>> No.6729366

>>6729365
Fucked up that last typesetting:

<span class="math"> g \int_0^{p_j} x \delta(x) dx - \sum_{i = 1}^{j-1} F_i = g \int_{p_j}^L x \delta(x) dx - \sum_{i = j+1}^N F_i [/spoiler]

>> No.6729376

>>6729366
Oh balls, the sums should all be sums of <span class="math"> F_i (p_j - p_i) [/spoiler], not just <span class="math">F_i[/spoiler].

So you understand what I did, I just balanced the torques about each pin. So the torque from gravity acting on the beam, which is the integral term on each side of each equation, minus the torques from each other pin, which is the sum of forces-times-distances-from-central-pin that I wrote above, should be equal on either side. The first equation comes from the fact that they have to all add up to the total mass.

>> No.6729378

Question: what is the interaction between two strong magnetic beams coming into contact?

magnetic fields projected as beams intersecting.

>> No.6729380

>>6729376
Goddammit, I keep seeing small errors, that's what I get for copying and pasting.

Final results:

Force balancing:
<span class="math">\sum_{i = 1}{N} F_i = mg[/spoiler]

Torque balancing, end cases:
<span class="math"> g \int_0^{p_1} x \delta(x) dx = g \int_{p_1}^L x \delta(x) dx - \sum{i = 2}{N} F_i |p_1 - p_i| [/spoiler]

<span class="math"> g \int_0^{p_N} x \delta(x) dx - \sum{i = 1}{N-1} F_i |p_N - p_i| = g \int_{p_N}^L x \delta(x) dx [/spoiler]

Torque balancing for pins j = 2, 3, 4, ... N-1:
g \int_0^{p_j} x \delta(x) dx - \sum{i = 1}{j-1} F_i |p_j - p_i| = g \int_{p_j}^L x \delta(x) dx - \sum{i = j+1}{N}F_i |p_j - p_i|}

>> No.6729381

>>6729346
Oh, surely it must be solvable. Don't engineers do this sort of thing all the time? Bridge and supports...

>> No.6729385

>>6729380
Seriously, fuck this TeX in the tiny reply box. You get what I'm saying, yes?

>>6729378
A magnetic beam isn't really a thing. Generally opposing fields cause repulsion, aligned fields cause attraction.

>> No.6729386

>>6729381
Of course it's solvable, but whether we can write an analytically exact expression for it entirely depends on what <span class="math">\delta(x)[/spoiler] is.

>> No.6729388

>>6729380
Thanks again! I'll try to follow what you've done. Then I'll be able to finish putting up those shelves. :)

>> No.6729403
File: 1.22 MB, 1830x1799, IMG_0047.jpg [View same] [iqdb] [saucenao] [google]
6729403

>>6729388
I just wrote it out by hand.

>> No.6729411 [DELETED] 

>>6729380
g\int_0^{p_1}x\delta(x)dx=g\int_{p_1}^L x\delta(x)dx-\sum_{i=2}^N (p_i-p_1)F_i

g\int_{p_N}^L x\delta(x)dx=g\int_{0}^{p_N} x\delta(x)dx-\sum_{i=1}^{N-1} (p_N-p_i)F_i

g \int_0^{p_j} x \delta(x) dx - \sum_{i = 1}^{j-1}(p_j - p_i)F_i = g \int_{p_j}^L x \delta(x) dx - \sum_{i = j+1}^{N}(p_i - p_j)F_i

>> No.6729414 [DELETED] 

>>6729403
Tried tex...

<span class="math">
g\int_0^{p_1}x\delta(x)dx=g\int_{p_1}^L x\delta(x)dx-\sum_{i=2}^N (p_i-p_1)F_i

g\int_{p_N}^L x\delta(x)dx=g\int_{0}^{p_N} x\delta(x)dx-\sum_{i=1}^{N-1} (p_N-p_i)F_i

g \int_0^{p_j} x \delta(x) dx - \sum_{i = 1}^{j-1}(p_j - p_i)F_i = g \int_{p_j}^L x \delta(x) dx - \sum_{i = j+1}^{N}(p_i - p_j)F_i
[/spoiler]

>> No.6729422

>>6729403
<span class="math">
g\int_0^{p_1}x\delta(x)dx=g\int_{p_1}^L x\delta(x)dx-\sum_{i=2}^N (p_i-p_1)F_i
[/spoiler]

<span class="math">
g\int_{p_N}^L x\delta(x)dx=g\int_{0}^{p_N} x\delta(x)dx-\sum_{i=1}^{N-1} (p_N-p_i)F_i
[/spoiler]

<span class="math">
g \int_0^{p_j} x \delta(x) dx - \sum_{i = 1}^{j-1}(p_j - p_i)F_i = g \int_{p_j}^L x \delta(x) dx - \sum_{i = j+1}^{N}(p_i - p_j)F_i[/spoiler]

>> No.6729426

>>6729381
I'm a MechE is why I mention it.
It's not solvable by statics 1 methods. (at least not to my memory)
We had systems that had more pins in statics 2 (3- and 4- point bending), but then the beam would be allowed to move
>>6729386
I like your solution and it seems promising, but I think you should do some simple solutions.
<span class="math"> \delta(x) = \lambda [/spoiler]
For 3 evenly distributed pins and then for 4.

>> No.6729429

>>6729426
*would be allowed to bend
problems were still static is statics ii

>> No.6729440

>>6729426
Well, you can see what it will be. Considering that we are punching in <span class="math">p_i[/spoiler] and <span class="math">\delta(x)[/spoiler], the integrals are just constants, as are the terms <span class="math">p_j - p_i[/spoiler]. So each equation is just a linear equation in <span class="math"> F_i [/spoiler]. We have N linear equations for the N variables <span class="math">F_i[/spoiler]. Solving is simple.

>> No.6729444

>>6729440
Looks like N+1 equations and N unknowns. One may be redundant.

>> No.6729446

>>6729444
Yeah, the force balancing equation is redundant and may be omitted.

>> No.6729464

If my dick is 15cm long, and I charge into a woman with 3atm of dick pressurization, how hard will her orgasm be?

>> No.6729466

>>6729464
8

>> No.6729619

Can you explain to me how to solve this by separation? Dx + e^(3x) dy = 0

>> No.6729628

>>6729619
Dx = e^3x dy
x' = e^3x ?

>> No.6729629

>>6729619
Well, you don't need to use separation to solve that equation, just multiply by e^(-3x), write dy = dy/dx dx, and integrate with respect to dx.

>> No.6729630

>>6729212
I take it that you haven't seen the charts.

>> No.6730467 [DELETED] 

>>6729403
Hey Mr Science... are you still around? Looking at terms such as

<span class="math">g \int_0^{p_j} x \delta(x)\,dx<span class="math">

I'm now wondering if these should be

g \int_0^{p_j} (p_j-x) \delta(x)\,dx

because it's supposed to be the torque around the j-th pin due to the mass of the rod, i.e. the pin is the fulcrum.[/spoiler][/spoiler]

>> No.6730468

>>6729403
Hey Mr. Science-
Looking at terms you have like
<span class="math">g \int_0^{p_j} x \delta(x)\,dx [/spoiler] I'm now wondering if these should be <span class="math">g \int_0^{p_j} (p_j-x) \delta(x)\,dx[/spoiler] because it's supposed to be the torque around the j-th pin due to the mass of the rod, i.e. the j-th pin is the fulcrum.

>> No.6730479

>>6729178
How does gravity work? Is it related to the attraction between oppposite charges?

The Earth orbits the Sun because of the velocity perpendicular to the pull of the Sun. Where did that velocity come from?

>> No.6730642

>>6730479
Not related to opposite charges just the presence of mass. The velocity relative to the sun originated during the formation of our solar system when you first have gas collapse into a star and then a protoplanetary disk.

>> No.6731527

>>6729178
please answer
>>6723022

>> No.6731547
File: 4 KB, 120x120, avatar5302_28.jpg [View same] [iqdb] [saucenao] [google]
6731547

how does the linear congruential method work as a random number generator? I'm trying to understand this modulo operation but either i'm retarded or i'm retarded

>> No.6731552

>>6731547
>I'm trying to understand this modulo operation but either i'm retarded or i'm retarded
it divides a number by another number then gets the remainder

>> No.6731556

>>6731552

ok, i have this example in the book:

3 mod 7 = 3

I really don't see how to get that result

>> No.6731561

is it correct, that the earth had to make a full revolution in about 10 minutes in order to compensate all of it's gravitational force at the equator?

>> No.6731565

>>6731556
how many times fits 7 into 3? 0 times! and what is the difference between 0 and 3? 3!

>> No.6731568

When will we have Alcubierre drives?

>> No.6731570

>>6731568
never

>> No.6731571
File: 15 KB, 447x444, 5138266+_cb2d6da46d20d43ae647fb664fef5dcb.jpg [View same] [iqdb] [saucenao] [google]
6731571

>>6731565

fuck man i've been trying to understand that for the last 30 minutes

thanks bro

>> No.6731577

>>6731571
hey, i forgot something: you're not interested in the difference between 0 and 3, but in 7*0 and 3

so e.g.:
9 mod 7
-> 7 fits 1 time in 9
-> abs(7*1-9) = 2

>> No.6731584

>>6731577

oh i see, i understood you wrong before then

>> No.6731734

>>6729178
I'm trying to learn thermodynamics. Is the P-V energy of a simple system consisting of a gas in a container part of its internal energy?

>> No.6731793

>>6730468
paging Mr. Science.

>> No.6731839

>>6729178
Who are you?

>> No.6732118

>>6731839
just search image on google. not hard to find out.

>> No.6732144

Monkey hate math.

Make monkey button to make machine go?
Make monkey button to make machine go!

>> No.6732283

>>6729403
So I'm thinking this isn't sufficient to determine the forces. If what you mean is this: <span class="math"> g
\int_0^{p_j} (p_j-x) \delta(x) \,dx + \sum_{i = 1}^{j-1}(p_j - p_i)F_i = g \int_{p_j}^L (x-p_j) \delta(x)\, dx + \sum_{i = j+1}^{N}(p_i - p_j)F_i
[/spoiler], then re-arranging we see this is equivalent to <span class="math"> g \int_0^{p_j} (p_j-x) \delta(x)\, dx + g \int_{p_j}^L (p_j-x) \delta(x) dx
= \sum_{i = 1}^{j-1}(p_i - p_j)F_i + \sum_{i = j+1}^{N}(p_i - p_j)F_i [/spoiler] or <span class="math"> g \int_0^{L} (p_j-x) \delta(x) dx = \sum_{i =
1}^{N}(p_i - p_j)F_i [/spoiler]. But this equation will be satisfied by any set of <span class="math">F_i[/spoiler] that
satisfy <span class="math"> g \int_0^{L} \delta(x) dx = -\sum_{i = 1}^{N} F_i [/spoiler] and <span class="math"> g \int_0^{L} x
\delta(x) dx = -\sum_{i = 1}^{N} p_i F_i [/spoiler]. That is, the <span class="math">F_i[/spoiler] need only have the
opposite total force and center of force to the rod. That's only two linear conditions, which will only yield unique <span class="math">F_i[/spoiler] when <span class="math">N=2[/spoiler].

>> No.6732286
File: 20 KB, 660x239, chan29.gif [View same] [iqdb] [saucenao] [google]
6732286

>>6732283
blah. pic related.

>> No.6733655

>>6729466
:^)

>> No.6733707

What is a time paradox?

>> No.6734208

anyone here? i need help with a problem. you can laugh at how basic it is and how stupid i am

>> No.6734244
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6734244

>>6729178
Why is my dick so small?

Did gravity do this to me?