Dimensions Definition and 1000 Threads

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...

Hello, Let's start with a cellular decomposition of 3-space, a "foam". A foam can be represented by its dual graph: cells and faces are dual to vertices and links. What about the opposite? It is clear that one can construct graphs for which no dual foam exists: take a large foam and...

1. Is it possible to calculate the capacitance of a system where the top plate has the dimension d1 and the bottom plate has a dimension d2 and d1<<d2. Now, the difference between the plates are t. Is it possible to calculate the capacitance of this system where the dielectric is oil? 2. In...

Okay, thanks Hikaru and K2 for your help on the accelerated drag problem. Now I have another drag related problem I wonder if you you help me with. Say a car is put in a wind tunnel and is measured to have the following attributes: Frontal Area: Ax Side Area (Right): Ay Frontal Coefficient of...

Is a curve (Say 'S') 1d or 2d? I ask this question because for so long i was under the impression that it was 2d, since we need a 2d cartesian plane to draw and describe a curve. But then i read in a popular book that it was 1D, which is hard to believe. so which is it?

Why do we call them 3 dimensions when all that they are, are just the ability of movement in space? Physical movement cannot be restrained in any vector. It takes place in a 3 dimensional dimension. Thus 1 dimension is physical movement in space and the second dimension is time. Within the 1st...

Homework Statement Let v = 1 / kt v = m/s k = 1/m t = s v = dx/dt so dx = dt / kt integrating, x = ln (kt)/k + C However the argument of a logarithm is dimensionless. But an integration is a perfectly normal thing to do. So how come this integration results in a...

Homework Statement How do you find the volume of three dimensions. 2.52x4.57x5.61 Homework Equations The Attempt at a Solution All you have to do is multiply the three right So the answer would be 64.607004? Thanks

I've been reading all about dimensions and started theorising myself , can there be something like -1D? The theory I came up is this: The Minus Dimensions don't have an object (it doesn't exist), but it's form is created by the location, which is other specific positive D objects. For...

How do you derive the hypervolume/hypersurface of the unit ball in n dimensions? I thought it'd be trivial but oh well. I'm guessing switch to n-D spherical coordinates? Is there an argument which doesn't involve explicitly calculating too many things? :x

I have a rectangular sheet of given dimensions say L wide and H high. Out of each point some variable field is flowing through given by rules as follows: Consider the top left corner of the sheet, the field is perpendicular at that point. As one moves from top left corner to the top right...

According to string theory, are strings Planck length in 1 dimension and 0 in all other dimensions? Or more than Planck length in 1 dimension and exactly Planck length in all other dimensions? Or something else? Thanks.

Hi, I was thinking about Knot Theory for a while and started thinking about higher dimensionalities. Could the knots we know so well (knots in 3d space) be undone if allowed to be manipulated through a fourth spatial dimension? Could they be made topologically equivalent to the unknot? And if...

Greetings. My question comes in two parts. Part one - In most "low-level - made for t.v." explanations of the extra dimensional space they describe these extra dimensions as "curled-up". If I were to visualize the extra dimensions of string theory would it be better to think of these extra...

I wonder why it took me so long to ask this question. But it's better late than never. Space has 3 dimensions. I have read numerous books where there are creatures who live in 1-D space, there're also hypothetical creatures who live in a 2-D space. But I don't remember reading a book where...

Homework Statement three distiguishable spin 1/2 particles interact via H = \lamda ( S_1 \cdot S_2 + S_2 \cdot S_3 + S_3 \cdot S_1 ) a) What is the demension of the hilbert space? b) Express H in terms of J^2 where J = S_1 + S_2 + S_3 c) I then need to find the energy and...

Homework Statement Three students push a box. Michael pushes with a force of 200 N at 0 degree. Shannon exerts a force of 150 N at 30 degrees, and Adam pushes with 175 N at 145 degrees. What is the magnitude of the net force? Homework Equations Some trig nothing special The Attempt...

Do you know of any papers about spin in dimensions>4? It seems that there are two independent spins in 4+1 dimensions, since you can replace spatial dimension 1 with 2 and 3 with 4, each pair not messing with the other. I found only one paper on arxiv: <http://arxiv.org/abs/0908.2484> on 5D...

Homework Statement One object is traveling in the x direction at 0.935c and another is traveling at 0.98c in the z direction. Determine the overall velocity of the second object from the point of view of the first object. Homework Equations v'x=(vx-v)/(1-vx*(v/c^2)) The Attempt at a...

the top and bottom margins of a poster are 2cm and the side margins are each 4cm. If the area of printed material on the poster is fixed at 382 square centimeters, find the dimensions of the poster with the smallest area. so the area l*w = 382 and the perimiter = 2(l-4)+2(w-8) but if i...

A radioactive nucleus of mass 5 × 10–26 kg is at rest and emits two neutrons, each of mass 1.6 × 10–27 kg, at right angles to each other. If both have speeds of 360 m s–1, calculate the recoil speed of the nucleus. I named calculated the neutrons and named them p1 and p2. Since p1 = p2...

My best guess is this fits in algebra, I've been scratching my head with this for a while. I have a three dimensional array representing points of certain objects in a game. int [5,5,5] currentLocs I want to be able to rotate these 3d points around the center in any direction by 90...

Homework Statement Find the dimensions of the following linear spaces. a. the real linear space C^3 Homework Equations n/a The Attempt at a Solution So I'm not really sure what C means. I know it's the smooth functions and I think raised to the 3rd power means it the functions...

Hello :smile: I was hoping someone could help me with this mechanics problem. Homework Statement A particle of 2kg mass moves in three dimensions under the action of a force \underline{F}=6\underline{i}-6t^2 \underline{j}+(4-2t)\underline{k}. At t=0, it is at rest with position...

Homework Statement Homework Equations Moment of Inertia equation: I=(1/12)bh^3 Stress and Strain equations: Sigma= -(M*c)/I Tao = (V*Q)/(I*t) The Attempt at a Solution I know I need to use shear and moment diagrams to find the max moment so I can use the Stress diagram to...