Dimensions Definition and 1000 Threads

Homework Statement Let W1 and W2 be subspaces of a finite-dimensional vector space V. Determine necessary and sufficient conditions on W1 and W2 so that dim(W_1 \cap W_2)=dim(W_1)Homework Equations Replacement Theorem The Attempt at a Solution To clarify on the question: is the problem asking...

Homework Statement [PLAIN]http://img406.imageshack.us/img406/3756/fmp1.jpg How do I calculate the magnitude of the sum of these 3 vectors? Also, how do I find the angles the sum of the vectors make with each axis? F1 = 260N F2 = 75N F3 = 60N Homework Equations F = F1 + F2 + F3The Attempt at a...

Homework Statement The top and bottom margins of a poster are each 6 cm and the side margins are each 4 cm. If the area of printed material on the poster is fixed at 384 cm2, find the dimensions of the poster with the smallest area. Homework Equations Area of a rectangle is length...

Is it just me, or are dimensions supposed to simply add another coordinate, i.e., I can move 1m in x, y or z direction and be 1m away from where I started, are the dimensions in string theory based on this concept or do I not understand what a dimension is? The most confusing part is how these...

Homework Statement Two important quantities associated with air are the pressure and density. How can the pressure and density be combined to produce dimensions of speed? Look up the pressure and density of air at sea level and use your equation to estimate the speed of sound. Is your answer...

Would I be right in supposing that the function of coordinates is to allow one to find an object that one knows to exist in relation to another which one also knows exists? And if said coordinates do an acurate job then these coordinates are said to be correct until such time as...

I've read that string theory requires 11 dimensions, our 3 spatial dimensions, time, and then 7 more dimensions that only exist at sub-nuclear distances. They are described as tightly wound up dimensions, much smaller than a proton. I don't understand this picture. Mathematically, we can...

I am trying to solve something of an inverse problem for inertia, and having a real tough time with it. Any suggestions would be helpful. For a rectangular prism the mass and moments of inertia are: m = rho*A*B*C Ixx = m/12*(B^2 + C^2) Iyy = m/12*(A^2 + C^2) Izz = m/12*(A^2 + B^2)...

Brilliant forum, wish i'd spent time browsing it years ago. In my layman's "understanding" of string theory six dimensions are compactified and usually presumed to be of very small size. My questions are: 1. Is there any mathematical or (better still) physical reason why this space does...

hi, I have a very simple question: why is there really a need for more than 4 spacetime dimensions? are there any concepts for which 4 dimensions are not sufficient? thank you!

I have a few questions on non-critical string theory... terminology: 1: Are "Gepner models" a subset of non-critical string theory? technical: 2: Given a set of spectrum, are there ways to construct a non-critical string theory with enough symmetries so that the CFT becomes minimal and...

Homework Statement Hello everyone, i have been stuck on this question on the Physics year 12 Nelsons textbook, and it is pissing me off because I've been working so hard on it and i can not get it. It is in the chapter of Movement in one and two dimensions. The question is: A person...

Search for Microscopic Black Hole Signatures at the Large Hadron Collider Authors: CMS Collaboration http://arxiv.org/abs/1012.3375 (BTW, slashdot is running this as a falsification of string theory, based on a jokey summary on the Not Even Wrong blog. Not Even Wrong has posted an update...

Homework Statement A and B are trains on perpendicular tracks, radiating from the origin of a coordinate system S. Train A is moving along the positive Y axis at a velocity of 0.8c, and train B is moving along the positive X axis also at a velocity of 0.8c. All velocites are measures with...

Homework Statement An object moves clockwise with decreasing speed around an oval track. There are velocity vectors at two points (G and H). G has a greater speed than H. Is the angle between the acceleration and velocity vector of G greater than, less than, or equal to 90 degrees...

Can dimensions exist that are not space dimensions nor time dimensions? I was just curious.

Homework Statement This question is from a correspondence course I'm taking: Two spacecraft from different nations have linked in space and are coasting with their engines off, heading directly toward Mars. The spacecraft s are thrust apart by large springs. Spacecraft 1, with a mass of...

Homework Statement Jim moves a 2kg brick along the ceiling by applying a force at an angle of 24.6 degrees. If the brick moves with no acceleration and the coefficient of kinetic friction between the brick and the ceiling is 0.467, what is the magnitude of the applied force? Homework...

I am not sure under which rubric questions about string theory or M-theory should go. Anyway, since this question concerns sizes down to the Planck distance, I suppose it should go here. The question is two fold: in such a case as the 6 extra spatial dimensions of string theory, how does...

I am wondering if anyone here conversant with information theory could tell me what the difference is in potential information content between 3 dimensions and 4 dimensions.

dimensions of the one-dimensional wave function? is it [si]=L-1/2?

Homework Statement [PLAIN]http://img515.imageshack.us/img515/5139/physicsproblem.jpg Homework Equations in the image The Attempt at a Solution I don't know if i placed the angles theta1 and theta2 correctly in the diagram..I feel like this is incorrect, since the value i...

Is there a possibility that there are infinite dimensions in our universe.M theory predicts that there are 11 dimensions,but why not more?

Homework Statement Attached Homework Equations 5.104 mentioned in the problem is Also attached The Attempt at a Solution Suppose the mass is moved to (x,y), the distance from the mass to the left spring is denoted by A, the distance from the mass to the right spring is denoted...

So a particle of mass M is moving in one dimension given by: x(t) = (alpha)t^2 + (beta)t + (gamma) where alpha, beta, gamma are non zero constants. What are the dimensions of the alpha, beta, gamma? Either the answer is staring right at my face or my physics is rusty :/

Homework Statement A basketball star covers 2.40 m horizontally in a jump to dunk the ball (see figure). His motion through space can be modeled precisely as that of a particle at his center of mass. His center of mass is at elevation 1.02 m when he leaves the floor. It reaches a maximum...

Homework Statement Consider a two-dimensional function φ = φ(x,t) that satisfies the relativistic wave equation given by: https://adgiiq.blu.livefilestore.com/y1pe5tdBVr0r62krIiWV_PQ42r1jrzQpWKz24xRgNe138phEqCNyZJKFXhBXqqL4YCvYeAsgVQtJJwovzjL0mKiNXyd6p1zHvkx/equation.jpg?psid=1...

In superstring theory there is a 10 dimensional space-time with 6 compactified spatial dimensions in Calabi-Yau manifolds and 4 expanded dimensions with three being space and one temporal. Now with m-theory there is one more dimension so does that mean there are 7 compactified dimensions (I know...

dimensions of our world... we know our world is three dimensional, that's length, width, height. Then Einstein came along and said don't forgot time as another dimension. now we have a four dimensional world = length, width, height, time those who said there are more dimensions, what are...

Hello all, I already have the answer to my question, but what I would like to know is why. My question is: why in the question below is the plane 111 used to find ao and not another plane? An ordered compound of NiAl has a cubic structure with one formula unit/cell. One Al atom at...

How Gravitational force differs in different dimensions. what it would be for four dimensions, two dimensions and one dimension. Give me the formula of Gravitational force in n dimension space. If it is described well (complete derivation) in other web site, send me the link.

I would like to show that (cxb).a = (axc).b in Rn where x denotes the cross product and . denotes the dot product. Since the cross product is only defined in R1, R3, and R7, my inclination is to prove the above equation in cases (case one being a,b,c are vectors in R1, etc). However, this...

Homework Statement Ship A is located 4.8 km north and 3.0 km east of ship B. Ship A has a velocity of 22 km/h toward the south and ship B has a velocity of 40 km/h in a direction 37° north of east. (a) What is the velocity of A relative to B (Express your answer in terms of the unit vectors i...

Homework Statement With the diagram and the data answer the question: What is the magnitude of A + B? http://i995.photobucket.com/albums/af79/huybinhs/w.gif DATA: theta1 = 33.7 deg, theta2 = 141.9 deg , A = 3.6cm, B =8.3cm. Homework Equations This is an example of vector...

Homework Statement The "Solar Sail I" experimental spacecraft is launched from the international space station with an initial velocity of 12 m/sec in a direction that makes a 120 angle with respect to the direction of radiation coming from the sun. Measurements show that an acceleration of...

I know of the gravitational analogy. The bending of spacetime due to a mass is analogous to a ball placed on a sheet, other balls in the region will be "attracted" towards each other. My question is, if we have to simplify our 3 spatial dimensions to 2 dimensions for the analogy, does that...

Hi, I'm having a bit of a hard time stumbling over the concepts of the following problem: Homework Statement In Electrostatics: How do you modify the div and curl of the electric field from 3D to 2D? What are the 2D and 1D versions of Coulomb's Law? Homework Equations In 3D (sorry, no latex...

I think because the number 3 is still pretty low it isn't so suspicious to people, but imagine we lived in some universe with, say, 186 dimensions (that miraculously supported intelligent life, so there's someone to ask the question - I know about the anthropic principle). Wouldn't we have asked...

simple question which probably has a complex answer, if given the dimensions and composition or a permanent magnet ie if the magnet is a cube 10mm x 10mm N35 Neodymium where would one find the equation to calculate the range at which the magnet extended

Homework Statement Which one of the quantities below has dimensions equal to [ML/T2]? Homework Equations a. mv b. mv2 c. mv2/r d. mvr e. mv2/r2 The Attempt at a Solution I know that ML/T2 is for calculating force for circular motion (I believe) Therefore after breaking it...

Homework Statement An artillery shell is fired with initial velocity of 300 m/s at 55 degrees above the horizontal. TO clear an avalanche, it explodes on a mountainside 42 secs after firing. What are the x- and y- coordinates of the shell where it explodes, relative to its firing point...

Hi, I've been reading quite a few popular science books (Michio Kaku, Stephen Hawking) where the specific example for us to visualise how a 4D creature would interact with us is portrayed through us interacting with 2D "flatlanders". The specific example is how we would lift a 2D flatlander of...

My friend is programming a curling application for the Android. He needs a way of calculating the results of perfectly elastic collisions in 2 dimensions with perfectly round objects (curling stones in this case, naturally). I know what the basic formula for the conservation of momentum is for...

The density of the material of a rectangular block is determined by measuring the mass and linear dimensions of the block. The table shows the results obtained, together with their uncertainties. mass = (25.0 ± 0.1)g length = (5.00 ± 0.01) cm breadth = (2.00 ± 0.01) cm height =...

could you apply this to humans who are 3 dimensions and discover a 4 dimensions?

Homework Statement A projectile is being launched from ground level with no air resistance. You want to avoid having it enter a temperature inversion layer in the atmosphere a height h above the ground.(a) What is the maximum launch speed you could give this projectile if you shot it straight...

Homework Statement Prove Rank A + dim Nul A^T = m where A is in R^(mxn) Homework Equations The Attempt at a Solution I honestly can't figure out where to go with this. I know that Rank A + dim Nul A = n, but I don't know if there is a relationship between the two.

Homework Statement A radioactive nucleus at rest decays into a second nucleus, an electron and a neutrino.The electron and neutrino are emitted at right angles and have momenta of 9.3x10^23kg*m/s and 5.40x10^23kg*m/s, respectively. What are the magnitude and direction of the momentum of the...

Homework Statement Billiard ball A of mass mA= 0.400kg moving with speed vA=1.80m/s strikes ball B initially at erst, of mass mB=0.500kg.As a result of the collision,ball A is deflected off at an angle of 30.0degrees with a speed v'A=1.10m/s. Taking the x-axis as the original direction of...

Homework Statement Do the following limits exist? State any relevant ideas. a) limit as (x,y) -> (0,0) of (xy)/(x2 - y2) b) limit as (x,y) -> (0,0) of (x2)/(3x4 + y2) c) limit as (x,y) -> (0,0) of sin(2x)/y The Attempt at a Solution I don't really know where to start; I can't...