Uniform Definition and 1000 Threads

Homework Statement http://img200.imageshack.us/img200/2524/drawingsave.jpg Weight W that's 15 [N] does circular motion around shaft AB in a frequency of 300 turns per minute A) calculate the max tension force on shaft CD [there's another clause, but I rather just try A for now]The Attempt at...

Homework Statement a particle with initial velocity Vo=6.00 x10r^3 m.s-1 in the +x direction enters a region of uniform electric and magnetic fields. the magnetic field in the region is B=0.300 T in the -y direction. calculate the magnitude and direction of the electric field in the region if...

Homework Statement A girl is running around a circular fountain with a diameter of 6.5m. If it takes her 72 seconds to run all the way around, what's her angular speed? The Attempt at a Solution I appear to be getting a wrong answer: (look only at the thick black marker)...

Homework Statement Let X~UNIF(0,1). Find y = G(u) such that Y = G(U)~BIN(3,1/2) Homework Equations The Attempt at a Solution after a bit of searching/reading, i found how to do this with a continuous distribution (the problem i had was an exponential, so i took the inverse)...

I came across in a journal that for a \nabla\times A=0 where A is vector, if y-component of that A is uniform then author claims that y-component of curl of a A is zero? Can anyone explain the above context?

Could anyone help me figure out a formula to calculate a Center of mass for a non uniform object. In my case it would be a "shell" that would go over a body of a solar car. If anyone could help me that would be great.

Homework Statement This is a very easy derivation (I think), I forgot how to do it though. How do you derive a = \frac{4\pi^2R}{T^2} or a = 4\pi^2Rf^2? Homework Equations The Attempt at a Solution They both mean the same thing since T is Inverse Frequency but I don't understand how...

In uniform linear motion, an object moves at a constant speed v0. And as long as no acceleration is applied onto the object, it will continue move at the same speed and direction forever. For uniform circular motion to happen, an object must move at a constant speed v0 with a constant...

Homework Statement A uniform plank 10m long and of mass 40kg is supported by two posts...? A uniform plank 10m long and of mass 40kg is supported by two posts, the first 1m from the left end and the other 6m from the left end. A mass of 10kg is placed 8m from the left end. Find the force...

Homework Statement Prove that the series \sum_{n=0}^\infty e^{-n^2x^2} converges uniformly on the set \mathbb{R}\backslash\ \big] -\epsilon,\epsilon\big[ where \epsilon>0Homework Equations n/aThe Attempt at a Solution I have tried using Weierstrass M-test but I have not been able to find a...

Homework Statement A 10.0 kg box is slid down15.0 m along a 20.0o ramp. The force of friction is 40.0 N. What is the change in the gravitational potential energy of the box? Homework Equations W=Fdcos of theta The Attempt at a Solution W=(40 N)(15 m)(cos 20) =563.8J The actual...

Homework Statement It is estimated that 3.0 x 1010 kg of water flow over Niagara falls each hour. The height of the fall is 65 m. What is the total gravitational potential energy of the water relative to the bottom of the falls that falls in one hour. What is the power represented by the...

Homework Statement For each of the following sequences (fn), find the function f such that fn --> f. Also state whether the convergence is uniform or not and give a reason for your answer. Homework Equations a.) fn(x) = 1/xn for x greater than or equal to 1 b.) f[SUB]n[SUB](x) =...

Homework Statement show a function f_n is not uniformly convergent using a theorem: Homework Equations if f_n converges uniformly to F on D and if each f_n is cont. on D, then F is cont. on D The Attempt at a Solution not really sure what to do. use the contrapositive? would that...

i am given a set of numbers. I have already found the mean, standard deviation, etc. i am now asked to find the confidence interval. but was not given a formula in order to compute this. does anyone know one?

Homework Statement A random variable X is distributed uniformly on [-1,1]. Find the distribution of X^2, its mean and variance. The Attempt at a Solution Define a transformation of random variable as Y=X^2. Problem is that the transformation function is not monotonic on the range. If it...

Homework Statement Problem A: A random variable T is selected from a uniform distribution over (0,1]. Then a second random variable U is selected from a uniform distribution over (0,T]. Determine the probability Pr(U>1/2). Problem B: Suppose 3 identical parts are chosen for inspection. Each...

1. Let g_n (x)=nx*exp(-nx). Is the convergence uniform on [0, ∞)? On what subsets of [0,∞) is the convergence uniform? 3. I am looking for a proof of how the convergence is uniform (possibly using Weierstrass' M Test?). I understand that the subset that determines uniform convergence is...

I was reading Royden when I came across this cryptic statement:pg 222, "The concept of uniform convergence of a sequence of functions is a metric concept. The concept of pointwise convergence is not a metric concept." Can anyone illuminate this?

Homework Statement A proton, with mass 1.67*10^-27 kg and charge +1.6*10^-19C, is sent with velocity 5.0*10^4 m/s in the x-direction into a region where there is uniform electric field of magnitude 390 V/m in the y direction. What is the magnitude and direction of the uniform magnetic field in...

Homework Statement A proton, with mass 1.67*10^-27 kg and charge +1.6*10^-19C, is sent with velocity 5.0*10^4 m/s in the x-direction into a region where there is uniform electric field of magnitude 390 V/m in the y direction. What is the magnitude and direction of the uniform magnetic field in...

Homework Statement Find the center of mass of the solid of uniform density bounded by the graphs of the equations: Wedge: x^2+y^2=a^2. z=cy(c>0), y>=0, z>=0 Homework Equations Mx=int(y*p(x,y) dA) dA=area of integration, dydx/dxdy The Attempt at a Solution I set up all the...

I was reading a Ph.D. thesis this morning and came across the claim that "a uniform limit of absolutely continuous functions is absolutely continuous." Is this true? What about the sequence of functions that converges to the Cantor function on [0,1]? Each of those functions is absolutely...

Hey there I need to find the natural frequency of a Cantilever Beam. The beam is tapered in breadth, but has a uniform thickness. So basically the end goal is an equation for f as a function of the angle of the side cut. Clamped at one end L=constant B=changes though the length of the...

Homework Statement This is a concept question on a study guide I came across and I really didn't know how to answer it or think about it...I havn't seen anything like this question before How could you prepare a spherical chamber that has a uniform electric field everywhere inside?

Homework Statement An electric dipole placed in a uniform electric field experiences a torque which tends to align the dipole parallel to the field. At the same time, due to two equal and unlike parallel forces Eq and -Eq acting at q and -q, the net force is zero. When the net force is zero...

Hello, Calculating the moment of inertia of a solid uniform sphere about it's center I get (3/5) Ma2. I know I am supposed to be getting (2/5) Ma2. I am using a differential volume dm as 4*pi*rho*r*r*dr, where rho is density, and r is the distance from the center to the differential volume...

Homework Statement Uniform time varying magnetic field \vec B_{(t)} pointing at z direction, filling up a circular region on xy-plane. Find the induced E field. I tried two different ways and get two different answers. Please tell me what did I do wrong. Homework Equations Emf...

http://img715.imageshack.us/img715/2616/physicss.jpg Uploaded with ImageShack.us Homework Statement A uniform slender beam of mass 10kg and length 1.2m is resting on a corner which is knife edged. The vertical wall on the left is smooth. What is the angle for equilibrium? a = .5m...

Homework Statement Let f_n be a sequence of holomorphic functions such that f_n converges to zero uniformly in the disc D1 = {z : |z| < 1}. Prove that f '_n converges to zero uniformly in D = {z : |z| < 1/2}.Homework Equations Cauchy inequalities (estimates from the Cauchy integral formula)The...

I cannot find the meaning of the uniform vector field. I know \hat z k_x+\hat y k_y +\hat z k_z is a uniform vector field if k_x,k_y,k_z are constants. Does this means a uniform vector field: 1) Points to the same direction in all locations? 2) Have the same magnitude in all...

Hey Guys. I am having issues with one of my physics homework questions, and i was seeking help. The question is as follows: While traveling around a roundabout, John notices that the fluffy dice suspended from his rear-vision mirror swing out. If John is traveling at 8m/s and the roundabout...

If a uniform beam was in space (no gravity or resistance of any kind) and only was applied a force F on only one side, does the inside of the beam feel a stress and deform? If so, what does the stress equal? Can you explain why/why not the beam feels a stress or not? I know that that if...

Can someone tell me how I am plugging this in wrong? And am I using the right equations? Thanks! Homework Statement A pilot is flying a vertical loop of radius 290 m, and at the top of the loop is pushing against the seat with a force of .25 "g's" {or Normal force = .25mg}. What is the...

Can someone look at this and tell me what I'm doing wrong? Thanks! Homework Statement You place a penny on a level rotating wheel at a point 5.00 cm from the center of rotation. You increase the speed of rotation gradually, and once you reach a rotational speed of 0.825 revolutions each...

Homework Statement Let f(x)=x^{1/3} show that it is uniform continuous on the Real metric space. Homework Equations By def. of uniform continuity \forall\epsilon>0 \exists\delta>0 s.t for \forall x,y\in\Re where |x-y|<\delta implies |f(x)-f(y)|< \epsilon The Attempt at a Solution...

Homework Statement A pilot flies an airplane in a vertical circular loop with a radius of R = 1200 m. The plane is gaining speed as the pilot makes a dive, and its speed is measured to be 150 m/s when the plane reaches the bottom of the circle. If the total acceleration of the plane at the...

Homework Statement A drag car starting from rest and accelerating uniformly acquires a speed of 60 m/s while traveling a distance of 270m. Calculate the acceleration. Homework Equations No idea The Attempt at a Solution No idea

determine if these functions are uniformly continuous :: 1- \ln x on the interval (0,1) 2- \cos \ln x on the interval (0,1) 3- x arctan x on the interval (-infinty,infinty) 4- x^{2}\arctan x on the interval (infinty,0 5- \frac{x}{x-1}-\frac{1}{\ln x} on the interval (0,1)...

Homework Statement Suppose you wish to fabricate a uniform wire from a mass m of a metal with density \rhom and resistivity \rho. If the wire is to have a resistance of R and all the metal is to be used, what must be the a)length and b) the diameter of this wire? (Use any variable or symbol...

Homework Statement A uniform elastic plank moves due to a constant force F distributed uniformly over the end face. The area of the ned face is S and Young's modulus = E . What is the average strain produced in the direction of force ? Homework Equations E*strain=stress... The...

Homework Statement show if has a uniform convergence of pointwise also we know that x gets values from 0 to 1The Attempt at a Solution for the pointwise I think its easy to show that limfn(x) as n->infinity is 0 but I am really stuck in uniform convergence I know that fn converges...

A function is uniformly continuous iff for every epsilon>0 there exists delta>0 such that for all x in the domain of f and for all y in the domain of f, |x-y|<delta =>|f(x)-f(y)|<epsilon. Here is what confuses me. How can there be a delta such that |x-y|<delta for ALL x and y. Since epsilon...

Homework Statement Show that there are continuous functions g:[-1,1]\to R such that no sequence of polynomials Q_n satisfies Q_n(x^2)\to g(x) uniformly on [-1,1] as n\to\infty The Attempt at a Solution Suppose there is a sequence Q_n such that Q_n(x^2)\to g(x) uniformly for g(x)=x. Then...

Suppose a sample of random size N is taken from the continuous uniform(0, θ) distribution, and N has a discrete distribution with p.m.f. P (N = n) = 1/(n! (e − 1) ) for n = 1, 2, 3, . . . . Determine the distribution of the i) first order statistic (the minimum) of X1 , X2, . . . , XN ...

Homework Statement For a rectangular, uniform wing or beam, where would the location of the elastic axis be relative to the mid-chord position? Also, what's the difference between semi-chord and mid-chord for a uniform rectangular wing? Thanks in advance for any help, Carl

Homework Statement A particle of mass 0.000103 g and charge 87 mC moves in a region of space where the electric field is uniform and is 4.8 N/C in the x direction and zero in the y and z direction. If the initial velocity of the particle is given by v_y = 3.2 × 10^5 m/s, v_x = v_z = 0, what is...

Homework Statement Throughout space there is a uniform electric field in the -y direction of strength E = 450 N/C. There is no gravity. At t = 0, a particle with mass m = 4 g and charge q = -19 µC is at the origin moving with a velocity v0 = 40 m/s at an angle θ = 25° above the x-axis. (a)...

Homework Statement An electron is originally moving at 6.8 x 107 m/s in positive x direction as it enters a region of confined, uniform, electric field. Magnitude of field is 2.6 x 106 N/C in negative y direction and its length in x direction is 6.2 x 10-4 meters. If one ignores weight of...

Hi all, Supposed if I have an air tight container, containing air with an initial pressure p0 and temperature T0. If I heat up the container from its bottom, and assuming its volume does not change, the temperature in the constainer will become non-uniform (highest at the bottom and lowest at...