Dimension Definition and 881 Threads

Homework Statement Two cars C and D travel in the same direction on a long, straight section of a highway. During a particular time interval \Deltat0, car D is ahead of car C and speeding up while car C is slowing down. During the interval \Deltat0, it is observed that C gains on car D...

Homework Statement Useful background for this problem can be found in Multiple-Concept Example 2. On a spacecraft two engines fire for a time of 871 s. One gives the craft an acceleration in the x direction of ax = 6.00 m/s2, while the other produces an acceleration in the y direction of...

We know that the Hilbert space of wavefunctions can be spanned by the |x> basis which is a non-countable set of infinite basis kets. Now consider the case of a particle in a box. We say that the space can be spanned by the energy eigenkets of the hamiltonian (each eigenket corresponds to an...

Wow... I'm fried from doing this problem... Any help would be nice... A 1000kg weather rocket is launched straight up. The rocket motor provides a constant acceleration for 16s, then the motor stops. The rocket altitude 20s after launch is 5100m. You can ignore any effects of air...

What is a fourth dimension?? Is this time or any other space coordinate??

Homework Statement Suppose V1 (dim. n1) and V29dim. n2) are two vector subspaces such that any element in V1 is orthogonal to any element in V2.Show that the dimensionality of V1+V2 is n1+n2 Homework Equations The Attempt at a Solution The subspace V1 is spanned by n1 linearly...

Homework Statement Suppose the positon vector for a particle is given as a function of time by vector r(t) =x(t)i + y(t)j with x(t) =at + b and y(t) = ct2 + d, where a=1.00 m/s, b=1.00m, c=.125 m/s2, and d=1.00m. (a) Calculate the average velocity from t=2.00s to t=4.00s. (b) Determine...

A hot air balloon is ascending straight up at a constant speed of 8.80 m/s. When the balloon is 12.0 m above the ground, a gun fires a pellet straight up from ground level with an initial speed of 31.0 m/s. Along the paths of the balloon and the pellet, there are two places where each of them...

Homework Statement A truck covers 40.0m in 8.50s while smoothly slowing down to a final velocity of 2.8 m/s. a) Find the truck's original speed b) Find its acceleration Homework Equations a= [v-vo]/t-to Constant acceleration: v=vo + at x= xo + vot + (1/2)at2 Constant velocity...

Homework Statement A wrecking ball is hanging at rest from a crane when suddenly the cable breaks. The time it taktes for the ball to fall halfway to the ground is 1.2s. Find the time it takes for the ball to fall from rest all the way to the ground Homework Equations v=vo + at The...

Are the any thoughts on this paper (which I copied the first part of as a reference)? They seem to be saying the existence of a 4th spatial dimension would help resolve questions. But, I think I've read other places that speculation of this type is meaningless. Hierarchy Problem in the...

Homework Statement (1) A speed trap is set up with two pressure activated strips placed across a highway, 116 meters apart. A car is speeding along at 29.6 meters per second, while the speed limit is only 19.4 meters per second. At the instant the car activates the first strip, the driver...

Homework Statement The speed of a bullet as it travels down the barrel of a rifle toward the opening is given by v = (-5.95 multiplied by 107) t 2 + (2.45 multiplied by 105) t, where v is in meters per second and t is in seconds. The acceleration of the bullet just as it leaves the barrel is...

1. Two planes are each about to drop an empty fuel tank. At the moment of release each plane has the same speed of 135 m/s, and each tank is at the same height of 2.00 km above the ground. Although the speeds are the same, the velocities are different at the instant of release, because one plane...

1. In getting ready to slamdunk the ball, a basketball player starts from rest and sprints to a speed of 6.0m/s in 1.5seconds. Assuming that the player accelerates uniformly, determine the distance he runs 2. Vf=Vo+at, VF^2=Vo^2+2a(Delta x) 3. Vf= 0m/s+(6.0)(1.5)= 9 Delta X=...

i have a quetion for you Dr., I know this is a simple problem but my physics book is not very clear on how to figure out this answer to the question. "A stone dropped from the top of a cliff. it hits the ground below after 3.25s. how high is the Cliff?" *to figure this out do you not use this...

Why is the time dimension multiplied by c^2?

Homework Statement Determine whether the points lie on straight line A(2, 4, 2) B(3, 7, -2) C(1, 3, 3) Homework Equations The Attempt at a Solution I've looked up at the equation for lines in three dimension, and it appears to be x=x_0+at y=y_0+bt z=z_0+ct i tried to take the x y z for A and...

Does linear algebra go in this thread?? Anyway, Homework Statement Let n be an integer at least 1, and x1,...,xn be distinct points in R. For any integer m>=1, let P denote the vector space of polynomials of degree at most m. Define a linear transformation T:P->R^n by [f(x1)]...

In one dimensional electron gas in charge density wave phase, as I know , the density of electrons will be periodic. The order parameter of charge density wave is written as O_{CDW}(x)=\sum_s\psi_{L,s}^{\dagger}(x)\psi_{R,s}(x) For Luttinger model, the \psi is the Fermion annihilation field...

I am not a physicists, engineer or even a student of such, however, I am writing a book and so this leads me to research. Say traveling to another dimension is possible. Would the traveler lose his/her memory there, only to regain it upon return to the dimension they started from? What...

Let {\mathbb I} = {\mathbb R} \setminus {\mathbb Q} the set of the irrational numbers of the real line. What is the topological dimension of {\mathbb R}^2 \setminus {\mathbb I} \times {\mathbb I} ?

Does the multiplicity of zero of characteristic polynomial restrict from above the possible dimension of the corresponding eigenspace? For example if we have a 3x3 matrix A, and a characteristic polynomial \textrm{det}(\lambda - A)=\lambda^2(\lambda - 1) I can see that the eigenspace...

Let g be a complex Lie algebra, of dimension greater than one. Does there always exist a subalgebra of dimension dim(g)-1? If the claim is not true, is it true for some particular dimension? I can see that the claim is trivially true for dim(g)=2, but what about for example dim(g)=3? The...

Problem Consider a free particle moving in one dimension. The state functions for this particle are all elements of L^2. Show that the expectation of the momentum \langle p_x \rangle vanishes in any state that is purely real. Does this property hold for \langle H \rangle? Does it hold for...

Considering momentum to be in units of \rm kg^1 m^1 s^{-1}, is there any particular attribute associated with \rm kg^1 s^{-1} (other than "momentum per metre")? Or perhaps the inverse \rm s^{1} kg^{-1}? Just curious.

Report on "dimension on the governing equation.." help Ciao all, I am sorry for my stupid but I really need some help of someone who knows about structure mechanics. I need to write an report on the topic that I myself don't understand it in normal English " DIMENSION ON THE GOVERNING...

My question, because I keep seeing this on the internet, is that if S is a subset of R and Hausdorff dimension greater than 0, it is uncountable... is this true. It seems not to be. If one were to modify the Cantor third set and remove some length of 1/n from the middle of the sets at each...

In its final trip upstream to its spawning territory, a salmon jumps to the top of a waterfall 1.9m high. What is the minimum vertical velocity neeeded by the salmon to reach the top of the waterfall? This uestion has no velocity so, do you think that final velocity is Zero... solution...

Hi to all, I have a problem to share with you guys. How can I calculate the thickness of my solenoid if I have these values; Solenoid long : 20cm magnetic field, B : 5Tesla Current, I : 20A Thanks a lot for your help. I appreciate that

i need some help here, say if there's a ship, no matter how it steers, it will always end up at the starting point, becauses it is in a new dimension, but how do i go about explaining it? thanks!

I'm confused about how to understand the ct dimension. I cannot get passed thinking that physically real dimensions mean more degrees of motion. If a flatlander went to the store to buy a can of Coke, the closed container would be a circle. The container is closed simply because there...

new to physics and my first question first,i am a nearly newbie high school student in physics, please i would like to learn physics from the internet enough to let me think ?...also i have a question in dimensions and please anyone explain how can you measure the 4d of matter although (i...

Alright, I'm in my first QM course right now, and one of the topics we've looked at is solving the one-dimensional time-independent Schrodinger equation for various potentials, such as the harmonic oscillators, infinite and finite square wells, free particles, and last, but not least, the dirac...

subspaces and dimension! Consider two subspaces V and W of R^n ,where V is contained in W. Why is dim(V)<= dim(W)...? "<=" less than or equal to

Find the Dimension of the null space of the given matrix A: | 1 3| |-2 -6| The Attempt at a Solution I honestly don't know how to work this at all. I think I'm confused as to what Null Space actually is, so that's making this a difficult problem to understand. please help.

Homework Statement Given the vectors: x1=(3,-2,4), x2=(-3,2,-4) and x3=(-6,4,-8) , what is the dimension of Span(x1,x2,x3) Homework Equations The Attempt at a Solution I know x1,x2 and x3 are Linearly dependent since its determinant is zero. There are a total of 3 vectors in...

Homework Statement bloks b and c have m asses 2m and m respecti vely, and are at rest on a firctionless surface black a also of mass m.. is heading at speed v toward block b as show... determine te final velocity of each block after alll subsequent collisions are over, assum all collision are...

Is it a fact that in an infinite dimensional normed linear space, the closed unit ball is never compact? If so, how does one go about seeing this?

Homework Statement Given x_{1}= \begin{pmatrix} 2 \\ 1 \\ 3 \end{pmatrix}, x_{2}= \begin{pmatrix} 3 \\ -1 \\ 4 \end{pmatrix}, x_{3}= \begin{pmatrix} 2 \\ 6 \\ 4 \end{pmatrix} Find the dimension of Span(x_{1}, x_{2}, x_{3}) Homework Equations If V is a vector space...

Okay how can someone explain the four dimension in so that someone like me can under stand them? I'm asking this question because my math teacher will not talk about it so that the other students would not get confused. I get the theory (or how ever you want to say it)a little bit but i still...

Hello, I am in the process of reading Black Holes, Wormholes & Time Machines and am somewhat confused, even though it is aimed at people like myself who have very little knowledge on the subject. I am reading about the 4th dimension now but I do not understand the relevance of researching into...

Homework Statement Suppose that U and V are finite-dimensional vector spaces and that S is in L(V, W), T is in L(U, V). Prove that dim[Ker(ST)] <= dim[Ker(S)] + dim[Ker(T)] Homework Equations (*) dim[Ker(S)] = dim(U) - dim[Im(T)] (**) dim[Ker(T)] = dim(V) - dim[Im(S)] The Attempt at a...

In Hartshorne's book definiton of a dimension is given as follows: İf X is a t.s. , dim(X) is the supremum of the integers n s.t. there exist a chain Z_0 \subsetneq Z_1...\subsetneq Z_n of distinct irreducible closed subsets of X My question is: Can we conclude directly that any...

what is dimension of target space?? is it the R^4 on top(which says that we have 4 coordinates like x y z t or 4 vectors in the matrix (whats it called the total number of the vectors??)

See the New Scientist article on how the explosive evaporation of primordial mini-black holes could prove the existence of extra dimensions. http://space.newscientist.com/article/dn13279-exploding-black-holes-could-expose-hidden-dimensions.html

I have no schooling in physics but for the past 3 years I have had this idea floating around in my head and figured i'd tell somebody and see what they thought. my theory is about the 4th Dimension. I believe that energy is the 4D and not time. Energy can be measured like width, heigth and...

[SOLVED] Motion in one dimension Homework Statement To protect his food from hungry bears, a boy scout raises his food pack with a rope that is thrown over a tree limb at height h above his hands. He walks away from the vertical rope with constant velocity V^{1}_{boy}, holding the free end of...

Let's say the universe exists as a collection of related static 3-d spaces, like in Julian Barbour's book The End of Time. Nothing ever actually moves. The illusion of movement comes from moving from one of these spaces to another which is closely related to the previous one. It's similar to the...

A car traveling at 16.0 m/s runs out of gas while traveling up a 21.0 degree slope. How far up the hill will it coast before starting to roll back down? I tried 1/2mv^2=mgh 1/2(16)^2=9.8h 13.06=h can anyone confirm if this is correct or not. I;m not sure if I have to use trig to...