Uniform Definition and 1000 Threads

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...

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...

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...

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...

Hi all, I'm trying to generate uniform random vectors with n dimensions. To be more precise, each of the elements of the vector must be a uniform distributed variable in [0,1] The constraint is that the sum of the elements of the vector must be 1. I tried different solutions for over a week but...

Homework Statement Curved portions of highways are always banked (tilted) to prevent cars from sliding off the highway. When a highway is dry, the frictional force between the tires and the road surface may be enough to prevent sliding. When the highway is wet, however, the frictional force...

It sounds like an easy-enough problem, but even writing down the ridiculously nonlinear equation that would need to be solved is making my face hurt. I'm talking classical/Newtonian gravitation, action-at-a-distance, constant-force. It could really be any external non-EM conserved force...

Hi guys, I have this doubt but i am not sure, if i have an uniform distibution can i conclude that the events or random variables are independent? Thank you

Homework Statement I have a physics final coming up and instead of problems, the final will cover multiple choice conceptual questions. "Several identical charged particles, each with charge Q and mass M, move in a region of uniform magnetic field B. The only force any of the particles...

I don't understand uniform continuity :( I don't understand what uniform continuity means precisely. I mean by definition it seems that in uniform continuity once they give me an epsilon, I could always find a good delta that it works for any point in the interval, but I don't understand the...

Homework Statement A 1380 N uniform boom of length ℓ is supported by a cable, as shown. The boom is pivoted at the bottom, the cable is attached a distance 3/4ℓ from the pivot, and a 3604N weight hangs from the boom’s top. Find the tension of the cable. here is a picture of the diagram...

Homework Statement (X,d1),(Y,d2) and (Z,d3) are metric spaces, Y is compact, g(y) is a continuous function that maps Y->Z with a continuous inverse If f(x) is a function that maps X->Y, and h(x) maps X->Z such that h(x)=g(f(x)) Show that if h is uniformly continuous, f is uniformly...

Homework Statement A straight uniform stick of L= 1m and mass m = 1 KG lies on a surface of a frozen lake.Someone kicks the stick at one end,imparting an impulse of 2Ns normal to the stick.Describe the subsequent motion of the stick. Homework Equations I=mΔV The Attempt at a...

Homework Statement A solid, insulating sphere of radius a has a uniform charge density of ρ and a total charge of Q. Concentric with this sphere is an uncharged, conducting hollow sphere whose inner and outer radii are b and c, as shown. A). Find the magnitude of the electric field in the...

Homework Statement A uniform electric field between two parallel plates has magnitude of 20N/C and is directed downward. 1) A charge brought into this field experiences a force of 10.0 N downward. The charge must be...? 2) The potential energy of this charge when moving downward...

I'm really struggling to get my head around some of the mechanics applications in my calculus module and would really appreciate it if somebody could help me get my head around it. I have this question: A particle P of constant mass m has a position vector: r=x(t)i+y(t)j, and moves...

Hi guys, New here, i have a question which has been doing my head in for days now. Hope someone might know how to answer it. The question is: A car travels with uniform acceleration from rest and is observed to cover distances of 6m and 7.5m respectively in two consecutive intervals of 1...

Homework Statement d\hat{S}/dt = γ\hat{S} \times \hat{B} What is the physical interpretation of this equation i.e. what is the behavior of the magnetic moment in an uniform magnetic field?Homework Equations I don't think I need any equation for this, just intuition or vector calculus identity...

Homework Statement Hi I'm doing a physics lab about uniform circular motion to measure frequency and to compare it to mass,radius and force tension. (A & B) I did (C,D, E) I need help (a) What variables are being measured / manipulated in this lab? What type of relationship is being...

Homework Statement A charged cork ball of mass m is suspended on a light string in the presence of a uniform electric field, as shown in the figure below. When E = (A + B) N/C, where A and B are positive numbers, the ball is in equilibrium at the angle θ. (a) Find the charge on the ball...