Uniform Definition and 1000 Threads

Homework Statement Where exactly is the center of mass of a triangle ? the file attached shows a diagram of a triangle which is equilateral, and the blue spots are the mid-points of each side. Homework Equations a distance = 2/3 from the vertex (along the median) The Attempt...

Homework Statement The attachment shows an equilateral triangle of side length "2d" It is a uniform triangle in the 2-D space. Mass of triangle = M I have to find the moment of inertia about one of its side . I am taking the side \overline{AB} as the axis of rotation (hence i would be...

There are no actual paradoxes in mathematics (we hope). There are only things that appear to be paradoxes to fallible intuitions. Here is one that bothers me. There can be no translation invariant probability measure on the non-negative integers. Yet it is possible to imagine a general class...

Homework Statement The sphere has radius R, and uniform volume charge density P. This sphere remains stationary (levitates) when placed above an infinite sheet of paper with a uniform surface charge density u. What is this sphere's mass? Homework Equations 4/3 pi R^3 is the volume of a sphere...

The sphere has radius R, and uniform volume charge density P. This sphere remains stationary (levitates) when placed above an infinite sheet of paper with a uniform surface charge density u. What is this sphere's mass?

The relation between the vector operator curl and rotation in fluids and vector fields is treated thoroughly in many texts. And the uniform (pure or simple) shear of a solid is adequately described by the strain tensor. I'd like to put the two together. My guess is that an alternative...

Given a power series \sum a_n x^n with radius of convergence R, it seems that the series converges uniformly on any compact set contained in the disc of radius R. This might be a silly question, but what's an example of a power series that doesn't actually also converge uniformly on the whole...

Homework Statement A body starts from rest along the straight line with uniform acceleration .it covers a distance of 150 m during 8th second of its motion calculate acceralation of body Homework Equations s= ut+1/2 at^2 The Attempt at a Solution u = 0 ; a = (2*150)/64 =...

Homework Statement A solid ball of radius r1 has a uniform charge density ρ. a) What is the magnitude of the electric field E(r) at a distance r>r1 from the center of the ball? b) What is the magnitude of the electric field E(r) at a distance r<r1 from the center of the ball? Express your...

Homework Statement 7) A uniform electric field of magnitude of E=5.5 ×10^3 N/C points in the positive x axis direction. The electric potential at the origin (x,y)=(0,0) of the xy-coordinate system is 0V. Find the electric potential at the point (x,y)=(10.0 cm, 10.0 cm). A) -777.8 V B)...

Why is it that when you have an insulator, the charges are uniformly distributed but in a conductor, the charges are only at the surface?

Homework Statement I was just wondering in what instances you would use the two equation belows, and what the difference is between them. Homework Equations average velocity: vave = Δx/Δt Uniform Acceleration: vave = (vi+ vf )/2 The Attempt at a Solution I'm...

During discharge tube experiment, the cathode rays are emitted from cathode at very low pressure...it is said that these rays move at very high velocity(if we apply high Potential Difference between 2 electrodes)...do these rays( stream of electrons) travel in uniform velocity or aren't they...

Homework Statement A car is moving with a speed of 30m/s on a circular path of radius 500m. It's speed is increasing at a rate of 2m/s2. What is the acceleration of the car.Homework Equations That is my problem.The Attempt at a Solution Well i know equations for uniform circular motion but this...

Hello For my dynamics I had been going through some examples and verifying them using Staad Pro. However, I been having issues with some of the examples as some do not show the full detail of calculation description. The one example been having problem with is where you must calculate the...

Homework Statement Find the Electric field at distance z above the mid point of a length L straight line segment, carrying a non-uniform line charge \lambda = \frac{1}{C} |x| where C is a constant 2. The attempt at a solution I note that the horizontal component cancels out...

I keep reading that a random vector (X, Y) uniformly distributed over the unit circle has probability density \frac{1}{\pi}. The only proof I've seen is that f_{X,Y}(x,y) = \begin{cases} c, &\text{if }x^2 + y^2 \leq 1 \\ 0 &\text{otherwise}\end{cases} And then you solve for c by integrating...

Homework Statement Jake leaves home at a random time between 7:30 and 7:55 a.m. (assume the uniform distribution) and walks to his office. The walk takes 10 minutes. Let T be the amount of time spends in his office between 7:40 and 8:00 a.m.. Find the distribution function F_T of T and draw...

Homework Statement the current is i, the circuit is in a uniform magnetic field B normal to the plane of the circuit as indicated Attached is the circuit Homework Equations Get the forces acting on each of their sides. Direction and data module for the following: L = 10cm R = 10cm I =...

Homework Statement A cilindrical copper disk (radius R, thickness a) at time t=0 is spinning around its axis with angular speed w in a uniform magnetic field B parallel to its axis. The edge of the disk is connected to the center with a "wire" which we assume to have negligible resistance and...

Two particles move in a uniform gravitational field with an acceleration $g$. At the initial moment the particles were located at one point and moved with velocities $v_1 = 3 \text{ms}^{-1}$ and $v_1 = 4 \text{ms}^{-1}$ horizontally in opposite directions. Find distance between the particles...

Homework Statement A uniform chain with a mass of M and a length of L is put on a horizantal table in a way that half of it is hanging from the air. At the moment t=0 the chain is released from rest. 1. What is the speed of the chain as its tip will leave the table? 2. Answer question 1...

Let X be standard normal and Y uniform [0,1] find the distribution of Z=X/Y. i think i managed to deal with this problem up to the integral stage: P(X/Y< t ) = P(X<Y*t ) thought of : 1. F_{z}(t) = \int^{1}_{0}\int^{yt}_{0}f(x,y)dxdy 2. F_{z}(t) = \int^{yt}_{0}f(x)dx maybe is neither one of...

Homework Statement A 1200-N uniform boom at ∅=55° to the horizontal is supported by a cable at an angle θ=25.0° to the horizontal. The boom is pivoted at the bottom and an object of weight 2 000 N hangs from its top. Find (a) the tension in the support cable and (b) the horizontal and...

Homework Statement Charges 1 and 3 in the figure below have the same mass and the same speed. Which has the greater magnitude of charge? What are the signs of the charges? http://www.webassign.net/colfunphys1/21-p-001.gif Homework Equations F = |q|v*B*sin(θ) The Attempt at a...

Hi, I'm getting some confusing results and can't figure out what is wrong Suppose we have a uniform field E=[0,0,E_z] in a dielectric media. By E=-\nabla\psi we can deduce that \psi(x,y,z)=-z E_z But, taking the Laplacian \nabla^2\psi=\frac{\partial^2 (-zE_z)}{\partial z^2}=0...

Homework Statement I'm working on a summer project dealing with high altitude balloons and I am trying to come up with a way to calculate the altitude at any given time, but I have not dealt with non uniform acceleration before. The formula I have for acceleration deals with both pressure...

Homework Statement show that the integral of the poisson kernel (1-r^2)/(1-2rcos(x)+r^2) converges to 0 uniformly in x as r tend to 1 from the left ,on any closed subinterval of [-pi,pi] obtained by deleting a middle open interval (-a,a) Homework Equations the integral of poisson...

Hi all, I am currently working to build a Joule Heater that will be used to heat samples to upwards of 1000*C in seconds in vacuum. While the temperature and speed is definitely there, the contacts are always non-uniform -- making the data hardly repeatable. I am using a ~70mmx10mm Silicon...

There are two point masses in space, each 1kg and one metre apart from each other. The only Force acting on the masses is the gravitational force between them. After what time do they collide? Gravitational Force F = Gm1m2/(2s)2 where m is the mass and s the distance to the center of both...

Hi! I’ve recently done an experiment that I didn’t completely understand and now it seems I’ve lost all my notes as well (the notes written down from the teacher’s board, with a formula I really need, but didn’t understand). This work is supposed to be completed during the summer holiday, so I...

Any advice on deriving the lagrangian for a particle in a magnetic field? L=\frac{1}{2}mv^{2} + \frac{q}{c}\mathbf{v}\mathbf{.} \mathbf{A} I've been searching through Griffith's, Jackson, and google to no avail. Can we start from the lorentz force and work backwards? Thanks for the help.

Dear Forum, I am attempting to make a treatment mattress or pad for PEMF treatment of osteoporosis. I have osteo, and there are commercial units available, but they cost ~$3K+! I have a capacitor discharge circuit, but need a coil design for the pad. I created a gauss probe with a linear hall...

Hi Dear All, Hope I can have some suggestions to tackle this weird problem. I have an axisymmetric ball, with CAX8R elements being inflated with hydrostatic fluid elements. Fluid elements surface is put on the internal surface of the ball (defined by picking the surface of the CAX8R...

So l have got 16 data points and l would like to know if this data follows a uniform distribution. I have tried using the punif function in R, but l am not sure about the results l am getting. Can someone please tell me what is the best way and hopefully easiest way to see if data is uniformly...

In Spivak's Calculus, there is a theorem relating the derivative of the limit of the sequence {fn} with the limit of the sequence {fn'}. What I don't like about the theorem is the huge amount of assumptions required: " Suppose that {fn} is a sequence of functions which are differentiable on...

Homework Statement I'm trying to show that U(X+Y) = X in distribution, where X and Y are independent exp(λ) distributed and U is uniformly distributed on (0,1) independent of X+Y.Homework Equations The Attempt at a Solution X+Y is gamma(2,λ) distributed. But I can't figure out how to deal with...

As shown in the figure, a rod of length 9.8 m lies along the x-axis, with its left end at the origin. The rod has a non-uniform linear charge density λ = αx, where α = 0.009 C/m2 and x is the position. Point A lies on the x-axis a distance 3.59 m to the left of the rod, as shown in the figure...

Homework Statement This actually returns to an older question I posted here (and got answer, thanks!). I have hard time with the interpretation of the solution and part (2) of the question. A monopolist can produce a widget at a cost C. The monopolist then has to find a price that would...

For calculating I of a uniform solid sphere, why can't we use thin spherical shells? When I try to use spherical shells I get (3/5)MR^2. Every single derivation uses thin cylindrical shells and end up with the correct expression((2/5)MR^2) but they never explain why it is correct to use...

A short circular cylinder carries a uniform magnetization M parallel to its axis. I want to know what the divergence of M is. Using divergence in cylindrical coordinates I get that ∇\bulletM = 0. Now I was pretty sure of this result until I read the following in my book: "∇\bulletH =...

Homework Statement Hi Can anyone help with this question? It will be highly appreciated. An object of mass 6kg is whirled round in a vertical circle of radius 2m with the speed of 8m/s. If the string breaks when the tension in it exceeds 360N, calculate the maximum speed of rotation and...

Penelope wants to buy a car that is worth $43,195 by making a $4300 down payment and arranging a four-year lease that calls for monthly payments in advance, interest of 2.91 percent compounded monthly, and a buyout payment of $20,000 at the end of the lease. Calculate the amount of the...

A NONCONDUCTING sphere with uniform volume charge density ? HELP! Homework Statement so this is the problem, a nonconducting sphere of radius \alpha has a uniform volume charge density with total charge Q. the sphere rotates about an axis through its center with constant angular velocity...

Am I right? Thank you!Problem: A cereal brand of cereal claims that the mean number of raisins in each box is 80 with a standard deviation of 6. If the raisins are normally distributed, what are the chances that an arbitrary box has 1) fewer than 70 raisins and 2) more than 90 raisins. What...

1 ) If a body is rotating at uniform angular velocity then in t sec , the angular displacement is ... (complete ) my answer the angular displacement is increase . 2 ) If a body is making N revolutions in one second then its angular velocity in rad/sec is my answer the angular...

I just did exercise 1.22 in Modern Quantum Chemistry by Szabo and Ostlund. This is a practice problem about linear variational method. ---------------------------------------------------------------------------------------- Question: The Schrodinger equation(in atomic units) for a hydrogen atom...

I am reading about uniform circular motion currently, but I am sort of confused by this paragraph: "We next determine the magnitude of the centripetal centripetal (radial) acceleration, ar. Because CA in fig. 5-2a is perpendicular to V1, and CB is perpendicular to V2, it follows that the...

Imagine a body moving to the right with velocity v, I then apply a force that accelerates the body leftwards by v and downwards by v. After one second, the body has stopped moving to the right and is only moving downwards with velocity v. Then, while I keep accelerating the body to the left...

Homework Statement At what distance along the central axis of a ring of radius R = 0.200 m and uniform charge is the magnitude of the electric field due to the ring's charge maximum? What is the positive solution for z? Homework Equations E = \frac{kqz}{(z^2+R^2)^(3/2)} The...