Components Definition and 911 Threads

hello forum, a tensor, say a 3X3, has nine components. Upon change of coordinate system, those 9 numbers change accordingly. If the change is a special rotation, then the nondiagonal elements vanish and only the diagonal ones remain. (diagonalization). That sounds all good, but then I...

Homework Statement Show using cartesian components that d/dt(a.b)=(da/dt).b+a.(da/dt) The Attempt at a Solution a= axi+ayj+azk b=bxi+byj+bzk a.b=axbx+ayby+azbz d/dt(a.b)= d/dt(axbx+ayby+azbz)

Homework Statement A 60 cm diameter wheel accelerates uniformly about its center from 120 rpm to 300 rpm in 5s. 1) Determine its angular acceleration. 2) Determine the radial component of the linear acceleration of a point on the edge of the wheel 2s after it has started accelerating...

Homework Statement Bob walks 200m south, walks 400m southwest, walks 200m in a direction 30 degrees east of north. Use either trig or components to find displacement that will return bob to his starting point by the most direct route. Homework Equations The Attempt at a Solution...

Homework Statement Man runs with velocity = 5m/s @ 25 degrees north of east for 10 minutes. How far to the north of his starting position does he end up? Homework Equations The Attempt at a Solution I know this has got to be the easiest problem to solve but I am not getting it...

If A is a p-vector and B is a (n-p)-vector, then the hodge dual, *A, is defined by: A\ \wedge\ B = (*A,B)E \ \ \forall B\in \Lambda ^{(n-p)} , where E=e_1 \wedge\ ... \ \wedge e_n I am having trouble in deriving the tensor components of the dual (n-p)-vector - *A. Specifically, I am...

Homework Statement Calculate the x- and y- components of the force C which member BC exerts on member ACD. The cables are wrapped securely around the two pulleys, which are fastened together. (Note the different diameters of the pulleys) Problem Homework Equations The sum of moment...

Different way to solve projectile motion components? Homework Statement solve projectile motion formulas for \Theta and v_0 all measurements are in m, t is seconds y_0=.005 x_0=0 the averages from my trials were: x=8.775 m t=1.3 s Homework Equations x=x_0+v_0*cos\Theta*t...

A wild horse starts from rest and runs in a straight line 29° north of west. After 27 s of running in this direction, the horse has a speed of 15 m/s. Find the magnitude of the horse's average acceleration. Assuming that north and east are the positive directions, find the component of the...

1. Homework Statement : Bob walks 360 m south, then jogs 490 m southwest, then walks 360 m in a direction 35 degrees east of north. Use either trigonometry or components to find the displacement that will return Bob to his starting point by the most direct route. Give your answer as a...

I want to understand this: In the case of a dropped object, the horizontal component of the velocity with which the object hits the ground is not the same thing as the horizontal velocity itself, am i right? The horizontal component of the velocity when the object hits the ground means the...

Homework Statement Bob walks 160 m south, then jogs 630 m southwest, then walks 160 m in a direction 32degrees east of north. a) Use either trigonometry or components to find the displacement that will return Bob to his starting point by the most direct route. Give your answer as a...

Homework Statement Particle B, with positive charge q_a, fixed in the yz-plane at (0,d_2,d_2). What is the net force F on particle A (positive) due to this charge? Express your answer (a vector) using k, q_0, q_3, d_2, x hat, y hat, and z hat. Include only the force caused by particle B...

I got this book here that mentions en passant that the connected components of a (topological) manifold are open in the manifold. That's not true in a general topological space, so why does Hausdorff + locally euclidean implies it? I don't see it.

Hey guys, I am stuck on this question. I was wondering if anyone can help me. I am going to attach a picture. Here is the question. The magnitude of the vertical force F is 82.5 N. If you resolve it into components Fab and Fac. What are the magnitudes of these components? (unit...

So I did an equilibrium experiment using pulleys and weights, where we set up different weights at different angles and had to get the right angle and weight to make the ring in the middle be centered. I am suppose to find the X and Y components of the forces. I am sort of confused on which...

1. A grasshopper makes four jumps. THe siplacement vectors are (1) 27 cm, due west; (2) 23 cm, 35 degrees south of west; (3) 28 cm, 55 degrees south of east; and (4) 35 cm, 63 degrees north of east. Find the magnitude and direction of the resultant displacement. Express the direction with...

In a rectangular coordinate system, a positive point charge q = 9.00 nC is placed at the point x= 0.250 m, y = 0, and an identical point charge is placed at x= -0.250 m, y = 0. Find the x and y components and the magnitude and direction of the electric field at the following points. (a) Find...

How do I find the x-component and y component for vector B?

Homework Statement A wire OA connects the collar A and a reel located at O as shown in the picture. Knowing that the collar moves to the right at a constant speed v0, determine θ'' (the 2nd-order-derivative of θ) in term of v0, b and θ. http://www.freeimagehosting.net/uploads/3cad8b54c6.jpg...

Given F = (-20i + 50j = 10k) 1. The component of the foce projected along the pole AO. 2. The magnitude of the projected component of the F along the pole AO. I have no idea where to begin, I think I need to find the angles but I'm not sure how in three dimensions. (please excuse...

The stress components in a circular cylinder of length L and radius r are given by sigmaij=[Ay+Bz, Cz, -Cy; Cz, 0, 0; -Cy, 0, 0] (a) Verify that in the absence of body forces the equilibrium equations are satisfied. (b) Show that the stress vector vanishes at all points on the curved...

Homework Statement A wedge with mass M rests on a frictionless table. A block with mass m is place on the wedge. There is no friction between the block and wedge. When the system is released, what is the acceleration of the wedge and the acceleration of the block. Give the accelerations in...

Homework Statement Let e_{i} with i=1,2 be an orthonormal basis in two-dimensional Euclidean space ie. the metric is g_{ij} = \delta _{ij}. In the this basis the vector v has contravariant components v^{i} = (1,2). Consider the new basis e_{1}^{'} = 5e_{1} - 2e_{2} e_{2}^{'} = 3e_{1} - e_{2}...

Let's say I have a field (electric or magnetic or something) and it's time-varying so I choose to represent its components as phasors. Say the field is: \vec{F} = X\hat{x} + Y\hat{y} + Z\hat{z} where, X, Y and Z are complex numbers. Now, I want to find the amplitude of the field. If...

How does one calculate the number of components a Dirac spinor in arbitrary dimensions? As far as I understand, the textbooks treat the four spacetime dimensions and here the spinor has four components because the gamma matrices must be 4x4 in nature to satisfy the required algebra. Now suppose...

Homework Statement A golfer drives a golf ball 214 m [E] off the tee, then hits it 96 m [28 degrees N of E], and finally putts the ball 12 m [ 25 degrees S of E ]. Determine the displacement from the tee needed to get a hole-in-one using (a) vector scale diagram and (b) components. Compare...

Consider the motion of an object on the xy-plane. Show that the force whose x and y- components are respectivley Fx= (3N/m)y and Fy= 0 is not conservative.

Homework Statement A person follows the path outlined below. 100m east, then 300m south then 150m 30 degrees south of west, then 200m 60 degrees north of east. Homework Equations I used component vectoring and have not been coming up with the resultant answer that the instructor has...

Homework Statement Forces F1 and F2 act on a mass m = 0.52 kg, as shown in the diagram below. The magnitudes of the forces and angles are as follows: F1 = 2.2 N, θ1 = 59 degrees F2 = 1.7 N, θ2 = 68 degrees http://loncapa.vcu.edu/res/vcu/delewis/physics/images/Two%20Forces%20(2).jpg...

Homework Statement For indices running from 0-3: R_{iklm} = -R_{kilm} = -R_{ikml} With the above conditions how do I know the number of independent component is reduced from 4^4 = 256 to 36. No idea how to figure this out.

[SOLVED] Geometric Algebra: Signs of electromagnetic field tensor components? Here's a question that may look like an E&M question, but is really just a geometric algebra question. In particular, I've got a sign off by 1 somewhere I think and I wonder if somebody can spot it. PF isn't...

Homework Statement I've derived the EM wave equations from Maxwell's equations, and I now need to show that the E and B components are both perpendicular to each other and to the direction of propagation. The textbook I've been using attempts to show why this is, but it isn't particularly...

Homework Statement The problem is :''Resolve the cartesian unit vectors into their cylindrical components(using scale factors) The Attempt at a Solution It's simple to do the inverse(resolving cylindricl unit vectors into cartesian components),but I'm having some ''trouble'' with the...

what does these electric components represent?? http://img257.imageshack.us/my.php?image=25544716ds5.gif

Hi, I have a conceptual question. In a project I am working on, we are dealing with \Re^{n} (with the usual topology), and I am working on characterizing some objects. In particular, I am dealing with the intersection of two simply connected open sets (that do not have any sort of...

[SOLVED] failure of a system of components logically arranged in series and parallel The performance of the valves in (V1 OR V2 OR V3) AND V4 AND V5 has been assessed in more detail under conditions closer to those experienced in-service and the distribution functions of the random time to...

Homework Statement An overhead view of the path taken by a ball of mass m as it bounces from the rail of a pool table. The ball's initial speed is v and the angle is a. The bounce reverses the y component of the ball's velocity but does not alter the x component. ... (b) What is the change...

If a block of mass m is pulled in the direction of (x-component) Tcos(theta) and (y-component) Tsin(theta) across a rough surface with a constant velocity. What is the magnitude of the frictional force? A) μkmg B) μkT cos θ C) μk(T – mg) D) μkT sin θ E) μk(mg – T sin θ) Since fk is in the...

The horizontal beam in the figure below weighs 140 N, and its center of gravity is at its center. http://session.masteringphysics.com/problemAsset/1026448/22/yg.10.59.jpg Find the tension in the cable. Find the horizontal and vertical component of the force exerted on the beam at the...

I am not sure if I am posting this in the right forum or not. I had impression that there is just no difference between projection of a vector and its components until I took the Statics course. We are following The Engineering Mechanics : Statics book by Meriam and Krage. I got stuck up in...

Homework Statement One end of a cord is fixed and a small 0.250 kg object is attached to the other end, where it swings in a section of a vertical circle of radius 2.50 m as shown in the figure below. When θ = 20.0°, the speed of the object is 7.70 m/s. At this instant, find each of the...

1. A path is defined by the function y=1/20 x^2. One instant x=10m and y= 5 m the speed is 6 m/s and increasing at 2 m/s^2. a)Find the directional angle of the velocity from the horizontal? The answer is 45 degrees b)What is the radius of curvature of her path at this instant? The answer...

Can anyone explain to me how to expand this expression for curl which I find in the GR book I'm reading (by Hobson, Efstathiou and Lasenby, page 71)? In a section entitled Vector Operators in Component Form they state the curl as a "rank-2 antisymmetric tensor with components": (curl)ab =...

[SOLVED] Vectors, finding components Homework Statement Determine the x and y components of the following three vectors in the xy plane a)a 10-m displacement vector that makes and angle of 30degree clockwise from the +y axis. Homework Equations The Attempt at a Solution The...

2-dimensional components for vectors is easy if you have the magnitude and angle. x is just magnitude*cos, and y is magnitude*sin. But consider this: Lets say you have a point charge q at (x, y, 0). You want to find the electric field at (0, 0, z). You know that the magnitude of the field is...

[SOLVED] Electric Force Homework Statement http://session.masteringphysics.com/problemAsset/1001926/10/knight_Figure_25_46.jpg What is the force F on the 1 nC charge at the bottom? Write your answer as two vector components, separated by a comma. Express each component numerically, in...

Hi, I'm new here, and I'm not really sure where this thread goes, so please feel free to move it Homework Statement basically, I'm doing a project involving converting raw data on pressure and temperature (and time) in a power plant situation (mainly the pipes carrying the steam) here is...

Homework Statement I need to find the component of W (the 400N force) that is parallel to the slide as in the attached picture. As you can see there is a 24 degree angle between the surface and ground.Homework Equations The Attempt at a Solution I should be using simple trigonometry. The...

Homework Statement Resolve the force F2 into components acting along the u and v axes and determine the magnitudes of the components. So! I was able to finally determine F2u. I cannot for the live of me get F2v. I am having a very hard time solving this problem. I have included the diagram...