Dimensions Definition and 1000 Threads

Hi, in my physics book (serway) they say "dimensions can be treated as algebraic quantities" but I don't understand this very well. If I sum meters I get meters, if I multiply meters I think I get meters^2 because the area of a rectangle is b.h. But if, for instance, I multiply seconds.seconds...

Can anybody tell me the known dimensions and how they are proved? I still can't understand how time is proved.

Homework Statement Water from a garden hose that is pointed 25 degrees above the horizontallands directly on a sunbather lying on the ground 4.4 m away in the horizontal direction. If the hose is held 1.4 m above the ground, at what speed does ithe water leave the nozzle? Homework...

Homework Statement A magnetic field has these components: x: B = 0.056 T y: B = 0.046 T The particle has a charge of +6.5e-5 C, has a velocity of 2.6e3 m/s, and is moving along the z axis. Questions: 1: What's the magnitude of the net magnetic force on the particle? 2: What's...

What are the properties of SO(4) group? , How this acts as a rotator in 4 dimensions?, What are the elements of Rotation matrix in a specific dimension among four dimensions?

What do electromagnetic waves look like in 3 dimensions? In my textbooks etc. they are always represented as the standard sine wave. But what about actual 3 dimensions? Are there waves with smaller wavelengths than gamma waves?

Scientists and mathematicians speak of extra dimensions that are "curled up" so small that it is impossible to detect them, but what exactly would an extra dimension look like:confused:? I realize that these extra dimensions have been detected mathematically, but the entire concept of something...

Hey, first I want to say my English & Math aren't the best yet, so ill be glad to explain myself again if I'll need to :smile: I hope this question belongs to this section. I want to ask, is there today a way to do calculations about vectors above fractal dimension? (and I would like to...

Apparently, when one calculates a length in flat space-time, one must add the lengths in the three spatial dimensions, and subtract... square root(-1)ct, my first question is... is there some sort of physical significance to a dimension being imaginary or is this simply a mathematical trick so...

I'm confused about the 6 extra curled up dimensions in that they are always portrayed like this: http://people.cs.uchicago.edu/~mbw/astro18200/calabi-yau-grid-small.jpg" But according to that picture it seems there are multiple "extra" dimensions, and that if you move to a different location...

Hi everybody, I have a quite simple question (in my opinion) but my background is quite poor about three dimensions physics. I need to express two velocity vectors, v1 and v2, in three dimensions polar coordinates, which means using polar and azimuthal angles. The two polar angles represent...

are there any introductory books on the theory behind gravitons and extra dimensions and also the experimental tests that could be done?

Would I be correct in thinking of time as the measure in length of a single point. If we take into account one second of this measure of time, would a photon be the longest and the shortest a cesium atom? Would I be correct in thinking of space as the measure in length between two points...

Homework Statement As picture attached .We need to find the dimensions of all the parts that are Pin(A),Jaw(B and C), NUt (D) , Handle (E) .The jaw B is fixed and C is free to move towards B.There is a force T=1779.261 N on Jaw C.Secondly there is a human force involved in turning the handle...

Homework Statement Explain why, using this outline for creating the cylinder, the volume of the cylinder is fixed for an A4 piece of paper (30x21) Homework Equations h=30-4R I really don't know how to approach this question, i know it has something to do with the radius and the height...

Hello everyone, I almost done with all the homework from my calculus class, but I got stuck on one problem, only one problem, but very difficult to understand. I would really appreciated if someone helps me with it. I don't even know how to start it : / here it goes... " Your neighbors...

Homework Statement Point A (2i +j 2k) Point B (3i +2j +5k) Point C (4i +5j -2k) the point d is such that abcd in that order is a parallelogram. Find position Vector D Homework Equations The Attempt at a Solution ok so i start of like this but I am getting the wrong...

Let's say you know x1, x2 and y1=y(x1), y2=y(x2) and gradients dy/dx at x1 and dy/dx at x2. That's 4 knowns. Thus, you can uniquely define the parameters in a cubic curve y=a+bx+cx^2+dx^3, which has 4 unknowns, that interpolate the function between x1 and x2. The interpolated cubic spline...

Hi, This might sound a very basic question to most of you all. But could you kindly give me some information on what eactly is a Metric Tensor and what is its significance in the higher dimension study? (Wiki or Google info seemed too cryptic. Thus...I ask you) Thank You

The 4 dimensions are the 3 spatial and the one time but is there any order for which these can be listed? Also is it possible that the sub-atomic particles exist on another dimesion (such as photons, neutrinos, and etc.)? And this is why we have such a challenging problem understanding the...

I can't quite remember where I got this idea, but once my brain remembered one point about higher dimensions(that of how each higher dimension, at least in terms of the first three dimensions, is at 90 degrees from one another. Well, actually how can you say the first dimension is 90 degrees...

Homework Statement A box with a square base and open top must have a volume of 32,000cm^3. Find the dimensions of the box that minimize the amont of material used. Homework Equations Sa(surface area)=4xy+x^2 Volume=x^2y The Attempt at a Solution I want to minimize Sa I am pretty sure so how...

WHY there is no scalar equation for a line in three dimensions ? :confused:

Say you have the function f(x)=log(x). If x had dimensions of metres, say, then you can't have x=2m or whatever because dimensions can't be put into the equation to give log(2m). What about if you have x1=4m and x2=2m and put log(4m)-log(2m) Each term doesn't exist by itself, but using...

How many degrees of freedom has Riemann Tensor in general D dimensions and how it can be calculated?

I humbly ask if someone can please help me dissect this problem. The problem is worded verbatim and I explained how I initially approached it. Please help. Homework Statement Two crickets, Chirpy and Milada, jump from the top of a vertical cliff. Chirpy jumps horizontally and reaches the...

Hi, this is my first post. Congratulations to a very interesting forum. The issue, I want to bring up, has probably been discussed already, but hopefully at least not in exactly the same way. I have read the book "Road to Reality" from Roger Penrose, which by the way I found quite interesting...

The attached image file shows the extra dimensions might come from overlapping planes with different energy value. In this model the extra dimensions are very small at the point where they intersect at the parent universe event horizon at the Plank Level (10 Minue 39). This idea suggest the...

Hey Everyone, I've just signed up for this forum because I'm currently taking a correspondence course and there's one problem in particular that I'm having problems with and there isn't really anybody I can ask. Can anybody here help me with this? Two spacecraft s from...

I have a question for you, well actually two. If we measure speed using light, then would light not only be a wave/particle but time as well? Now supposing that above question was right would time be the fourth dimension then, which is time if I can remember correctly?

Sorry for opening up the discussion again, but I joined late. anantchowdhary's question is an extremely valid one, even though most commentators claimed to not understand the question. A photon has a wavefunction. The standard interpretation is the wavefunction gives the probability that...

Does a photon have spatial dimensions.Also do two photons having different energy occupy the same volume? Thnx

i would like to ask a question about what does quantities and dimension mean in this sentence is it possible for two quantities to have the same dimensions but different units? thanks a lot in advance

Homework Statement Two spacecraft s have linked in space and are coasting with their engines off, heading directly towards Mars. The spacecraft s are thrust apart by large springs. Spacecraft 1 with mass of 1.9 x 10^4 kg, then has a velocity of 3.5 x 10^3 km/h at 5.1 degrees to its original...

I was doing some math problems involving surface area and maximum dimensions and then I wondered: Suppose you are given the surface area of a rectangular box but none of its dimensions. Is it possible to find the best dimensions (x,y,z) that would give the maximum volume of the box? I was...

1) Why is it that a sphere is a 2-dimensional object even though we need 3-dimensions to actually *draw* the sphere. 2) If the Cartesian plane is a 2-dimensional *space*, then the number-line should be a 1-dimensional *space*, right? (not sure if space is the appropriate term here) 3) Would a...

This should be possible with table top experiments rather than LHC scale experiments:abstract: Electromagnetic radiation decays with 1/r in three dimensional space, while the non radiating Coulomb field decays faster with 1/r^2. The general expressions for any dimension are 1/r^{(d-1)/2} for...

A rectangular catalyst panel must provide 500cm2 effective area, and requires installation margins of 5cm on the longer sides and 7cm on the shorter sides. What panel dimensions minimize the total area? (1) Formulate a penalty function, identitfying all constraints(active and...

Hi, I am having problems with a particular question it says: Two 30kg children, each with a speed of 4.0m/s, are sliding on a frictionless frozen pond when they collide and stick together because they have Velcro straps on their jackets. The two children then collide and stick to a 75kg man...

[FONT="Lucida Console"][SIZE="5"]Frendz , here is a problem of motion in 2 dimensions. I simply stuck in basics . A man wants to cross a river 100mt long He has a velocity of 10m/s in still water and river has a velocity of 20m/s. What angle should he make with flow of river so that...

Hello, I was interested in learning more about the possibility that there are several dimensions of space that we cannot physically detect. These spatial dimensions are permeable to radiation to different degrees of permeability. So for example, gravity, being the weakest of the 4 forces we...

When analyzing/studying thermochemistry or any system with gases, i.e., combustion, fusion, fuel cells, often time in the literature the system is derived or modeled as being zero-dimensional or quasi-one dimensional. Can anyone provide a good explanation as to the differences between 0, 1...

Hello, folks - this is my first post here. I am hoping some of you will be kind enough to help me understand something I have struggled with for a long time. A brief background: My lifelong interest in science fiction led me to start reading about relativity and quantum physics around 20...

I just finished learning the fundamental theorem of curves in 3 dimensions. As a reminder, this is the theorem that states that a continuous, C infinity, unit speed curve in 3d is uniquely determined by its curvature and torsion (up to actions by SE(3), that is rotations and translations)...

A barge with mass 1.50 X 10^5 kg is proceeding downriver at 6.2 m/s in heavy fog when it collides with a barge heading directly across the river (see the poorly drawn image, in link)http://img.photobucket.com/albums/v638/ravenatic20/untitled4.jpg ... The second barge has mass 2.78 X 10^5 kg and...

I am working on a lab assignment that is having us figure out an unknown force based on various given forces. All the 2-D problems I could do easily. Unfortunately, the last problem has thrown me for a loop as it deals with an actual setup in the lab room with forces in all 3 directions. Here...

OK, I've been trying to get problems like these where you are given the angle (but not the velocity) of the direction in which a projectile is fired. I have tried as many ways as i could conceive using kinematics, but i keep getting stuck. If anyone could just give me an idea how to go about...

Sponge Bob Square Pants makes an open-topped box from a 30-cm by 30-cm piece of cardboard by cutting out equal squares from the corners and folding up the flaps to make the sides. What are the dimensions of each square, to the nearest hundredth of a centimetre, so that the volume of the...

5. As a science fair project, you want to launch an 800g model rocket straight up and hit a horizontally moving targer as it passes 30 m above the launch point. the rockey engine provides a constant thrust of 15.0N. The target is approaching at a speed of 15m/s. At what horizontal distance...

A box has dimensions that are linear factors of (x^3-7x^2+14x-8) cubic centimetres. What dimensions give a volume of 12 cm cubed? I started it off by moving 12 to the left side giving the equation: x^3-7x^2+14x-20=0 then from then I don't know...If I substitute 5, the equation is...