Dimensions Definition and 1000 Threads

Homework Statement The water in a river flows uniformly at a constant speed of 2.50 m/s between parallel banks 80.0 m apart. You are to deliver a package across the river, but you can swim only at 1.50 m/s. (c) If you choose to minimize the distance downstream that the river carries you, in...

I attached an image with problem and the associated illustration. I don't know what the relevant equations are for this problem. Each and every time I read the problem I keep drawing a right triangle to represent the velocity components. The problem says the river is flowing east at 5km/h. I...

Looking at Munkres "Analysis on Manifolds", it says for $A\subset R^n, f: A \rightarrow R^m$ suppose that $A$ contains a neighborhood of $a$. Then $f$ is differentiable at $a$ if there exists an $n$ by $m$ matrix $B$ such that, $\frac{f(a+h)-f(a)-Bh}{\left| h \right|}\rightarrow 0$ as...

Why do physicist presenting extra dimensions with 2d creature experiencing 3d space with object falling through 2d dimension. And that, that 2d creature can see only a slice of the 3d dimension. If time == space that means that 2d creature also experiences time because objects are moving...

I’d like to know if anyone has formulas for calculating the spring constant (k) of coil springs, from their physical dimensions. I bought a coil spring, suspended a 0.6 kg mass to it, observed its oscillation period at very close to 0.6 seconds, and so believed the spring constant “k” to be...

Hello all! I've got this problem I'm trying to do, but I'm not sure what the best way to approach it is. It's obvious that there can only be 2 dimensions, because there's only two linearly independent vectors in the span. However, what would be a good way of using the inequalities to prove...

Homework Statement A titanium disk (with ##E=107 ~GPa##, Poisson's ratio, ##v=0.34##) precisely ##l_0=8~mm## thick by ##d_0=30~mm## diameter is used as a cover plate in a mechanical loading device. If a ##P=20~kN## load is applied to the disk, calculate the resulting dimensions, ##l_{01}## and...

Suppose I have a velocity field V^a which looks like < \partial x / \partial t , \partial y / \partial t , \partial z / \partial t > and I use the metric tensor to change it into a covector field V_a = g_{ab}V^a. Does it then represent the same quantity or < \partial t / \partial...

Homework Statement A bomb initially at rest is exploded into three pieces on a smooth, horizontal surface. Two pieces fly off at a 60° angle to each other, a 2.0 kg piece at 20 m/s and a 3.0 kg piece at 12 m/s. The third piece flies off at 30 m/s with an unknown direction. Determine the...

Does dimensions and time have the same meaning in the Quantum world? Maybe that explain weird things as the spooky action at distance. What evidence are about the real existence of a 3 geometry dimensions world at quantum level? Maybe even time have a different meaning in the quantum world.

The second Randall-Sundrum model was based on a large as opposed to compactified dimension. Has the possible existence of large higher dimensions been eliminated and what evidence rules them out?

Homework Statement C is the directed curve forming the triangle (0, 0, 0) to (0, 1, 1) to (1, 1, 1) to (0, 0, 0). Let F=(x,xy,xz) Find ∫F·ds. Homework EquationsThe Attempt at a Solution My intial instinct was to check if it was conservative. Upon calculating: ∇xF=(0,-z,y) I concluded that...

What I did: x = Emily's garden's width x+4 = Emily's garden's length y= Sarah's garden's width 18 = Sarah's garden's length y=x+4(as stated in problem) x/x+4 = y/18(as the two gardens are similar) Which means that x/x+4 = x+4/18 Now I can't seem to find x

what are the dimensions of the double slits in comparison to the electron? what keeps the electron from decaying outside the environment of an atom long enough to run the experiment? how are the electrons detected before and after the slits?

Homework Statement One component of a magnetic field has a magnitude of 0.0431 T and points along the +x axis, while the other component has a magnitude of 0.0686 T and points along the -y axis. A particle carrying a charge of +1.70 × 10-5 C is moving along the +z axis at a speed of 4.24 × 103...

hi i want to design michelson interferometer device for measuring small distance movement i am using laser diode with a wavelength 635 nm and power 3 mw can anyone tell me how can i decide the dimensions (from source to beam splitter , for beam splitter to fixed mirror , from beam splitter to...

I once took notes from a website, and now I cannot find the reference anymore, so I am attempting to reconstruct it, and am sure that I have it all wrong (or that the website did, or both). Hence, I would be grateful for corrections. My apologies for not being able to provide the link. The...

Homework Statement I am looking for references for the scalar field theory in one-space, one-time dimension defined by: $$\mathcal{L}=-\frac{1}{2}(\partial_{\mu}\phi)^2-\frac{1}{2}m_{2,0}^2\phi^2-\frac{1}{4!}m_{4,0}^2\phi^4-\frac{1}{6!}m_{6,0}^2\phi^6$$ That explains why the only divergences...

Do string theory’s compactified dimensions have a predicted physical interpretation? Do they for example represent the space/planes/domains in which a string ‘lives’? That is, the local permissible evolution space of a given string?IH

I Had been given an assignment on electronic properties of materials in reduced dimension as mentioned above so I have been given another option to choose whether it to be a theoretical approach or experimental approach which one should I choose.

Hi. If you have seen the above image which shows a parabola then you can also see that there is a colored portion of the parabola that have solution in "another dimension" - the "another dimension" can give me new numbers to form a solution of a function like f(x) = x2 + 1. 1. Is this "another...

Radial and angular nodes are simply a region where the wavefunction is zero. But speaking about their dimensions, do they have any thickness or are they just an infinitesimal point in space without dimensions? Thanks a lot!

The question originates from what is often said in accounts of superstring theory, that (perhaps) 7 space dimensions might be curled up into such a tiny scale as to become undetectable. So the question came up, if dimensions might be curled up or extended into different scales, say "very tight"...

While resolving a problem in mechanics I discovered a beautiful and easy way for finding out what the rotation matrices in 3 dimensions are! And I'm surprised that I do not find this method anywhere on the internet! Would it be because it's not technically correct? Anyways, here it is: It's all...

Does Hyugens principle apply in three dimensions ? If a surface wave (for simplicity an ocean wave) is propagating along the x-axis we know that this wave ray is a point source for wavelets on the y-axis but what about the z axis? If this diagram was 3d would we see a spherical wave front...

Why do we see the dimensions of our universe as 3 dimensions of space and time instead of space, time, and matter? (Or another variation)

Homework Statement I have an empty cylinder with an external diameter of (23.0 ± 0.5) mm, an internal diameter of (22.5 ± 0.5) mm and a height of (60.0 ± 0.5) mm. I need to calculate its volume with its uncertainty/error. Homework Equations The Attempt at a Solution I do it like this...

Homework Statement I define the gamma matrices in this following representation: \begin{align*} \gamma^{0}=\begin{pmatrix} \,\,0 & \mathbb{1}_{2}\,\,\\ \,\,\mathbb{1}_{2} & 0\,\, \end{pmatrix},\qquad \gamma^{i}=\begin{pmatrix} \,\,0 &\sigma^{i}\,\,\\ \,\,-\sigma^{i}...

I and my teacher argued whether a uniform circular motion in polar coordinates is considered to be a motion in one dimension or it's a motion in two dimensions.

Hello! Can someone recommend me some good readings about spinors in physics? I know some basics (i.e. how they work in Minkowski space for Dirac field), but I would like to understand more of the mathematical formalism behind them (how can you build them, in a general number of dimensions, how...

Homework Statement In a physics lab, 0.30 kg puck A, moving at 5.0 m/s [W], undergoes a collision with a 0.40 kg puck B, which is initially at rest. Puck A moves at 4.2 m/s [W 30 N] . Find the final velocity of puck B. Homework Equations Conservation of momentum Pythagorean theorum The...

In this topic https://physics.stackexchange.com/questions/129417/what-is-pseudo-tensor one answer was the next: The action of parity on a tensor or pseudotensor depends on the number of indices it has (i.e. its tensor rank): - Tensors of odd rank (e.g. vectors) reverse sign under parity. -...

Most QFT texts, such as Peskin&Schroeder and D. Tong's lecture notes, contain a mention that the renormalizability of an interacting theory requires the coupling constants to have correct dimensions, making scalar fields with ##\phi^5 , \phi^6, \dots## interactions uninteresting. Maybe there are...

I have couple questions related to dimension and general physics law 1- Can we apply physics law in lower/higher dimensions. In another words does physics law makes sense in 2D or in 7D. 2- Is it possible that a 2D particle contains charge ? 3- Is it possible a 2D "object" exist in 3D ?

I started this post on physics.stackexchange but it's too vague for that site, so here I am! :) I'm trying to really get the intuition of spacetime. This video explains how Minkoswki was the first to think that maybe our universe does not consist of a 3d space which evolves in time, but rather...

So in string theory at each point of Minkowski spacetime we might have a 3 dimensional compact complex Calabi–Yau manifold? We can have curved compact spaces without complex numbers I assume, what is interesting or special about complex compact spaces? Thanks!

I am trying to understand what time^2 and velocity^2 mean in terms of how to visualize them? This wasn't explained in Physics or Mechanics (Further Mathematics) in high school, unfortunately. It seems likely it relates to matrices, maybe? Appreciate any replies! :)

OK, so time is change of displacement. Speed is change of change of displacement. Acceleration is change of change of change of displacement (or of distance, sorry I'm not sure whether acceleration is a vector or a scalar). Then you get change of change of change of change etc. ad infinitum. It...

Hi there, so recently we had professor's assistant covering our class and he decided to talk about Fractal Dimensions. Maybe its just the concept or his explenation but we all left the class bewildered to say the least. Could someone clarify for me, how do we refer to the number of dimensions...

Consider a free real scalar field. The quadratic term in field of spacetime implies that a universe of these free particles is created, annihilated, recreated, and so on moment by moment. In this video Susskind explains the quadratic term in the Lagrangian youtu.be/D7yXoNAg3J8 (At minute...

Greg Bernhardt submitted a new PF Insights post Make Units Work for You Continue reading the Original PF Insights Post.

Is there an upper bound for the number of curled-up extra spatial dimensions and perhaps also temporal dimensions? I just wonder how many more theories with extra dimensions are possible... infinite?

http://imgur.com/cUNs2z7 In this book I found by chance on Google, the author claims that “solutions of the wave equation only take the form of functions (...) in one and three dimensions. In two dimensions solutions are more complex”. Then, at the end of the paragraph of interest (which I...

Homework Statement The object is falling vertically in a strange fluid, the magnitude of the air drag is best described by the following FD = bv+cv2 where v is the speed of the object and b and c are constants. A. What are the dimensions of b and c B. If the object has mass m find an algebraic...

I wonder if dimensions of space are real things, or just a way that humans describe space, rather like 'good' and 'evil' are just ways that humans describe behaviour, but good and evil are not themselves real. So just as good and evil are not real, perhaps dimensions are not real, and space...

Hello For the purpose of the experiment, I wonder what the maximum dimensions can have a transparent tube, I thought over a diameter of 30cm and a length of 1-1,5m and from what material should such a pipe be made. I would like to get a high vacuum (about 0,2-2Pa)

If the dimension of A and B are different, then how to express the dimension of A and B together? how to write?

Hi PF! I am using a template I've used a long time for presentations but after I updated my machine (and consequently latex) the output I now get is tall and thin, acceptable for papers but not for presentations. I tried messing with the dimensions on line 9 right under \documentclass, where it...

The volume of a rectangular prism can be represented by the polynomial V(x)=2x^2+9x^2+4x-15 a. The depth of the tank is (x-1) feet. The length is 13 feet. Assume the length is the greatest dimension. Which linear factor represents the 13 ft?This is probably a really easy question but I am so...

This may seem a very elementary question, but I don't believe it is; so I put it in the advanced section. I'm mathematically experienced, and this question has stumped Ph Ds. I haven't figured out why space is usually described in terms of only 3 spatial dimensions rather than six: x,y,z, Tx...