Uniform Definition and 1000 Threads

1. The problem statement, and my attempt at a solution is given in pic Please help me.

Homework Statement An object moving with uniform acceleration has a velocity of 14.0 cm/s in the positive x direction when its x coordinate is 3.00 cm. If its x coordinate 2.00 s later is -5.00 cm, what is its acceleration?Homework Equations deltaX=V naught t + (1/2)at^2) The Attempt at a...

Homework Statement This is a nice one, if it's correct. Show that if (fn) is a sequence of elements of C(X, Y) (where Y is a metric space) which converges uniformly, then the collection {fn} is equicontinuous. The Attempt at a Solution Let ε > 0 be given and let x0 be a point of X...

Homework Statement If f:S->Rm is uniformly continuous on S, and {xk} is Cauchy in S show that {f(xk)} is also cauchy. Homework Equations The Attempt at a Solution Since f is uniformly continuous, \forall\epsilon>0, \exists\delta>0: \forallx, y ∈ S, |x-y| < \delta =>...

Homework Statement Hi All, I've been having great difficulty making progress on this problem. Suppose gn converges to g a.e. on [0,1]. And, for all n, gn and h are integrable over [0,1]. And |gn|\leqh for all n. Define Gn(x)=\intgn(x) from 0 to x. Define G(x)=\intg(x) from 0 to x...

Homework Statement See figure attached for problem statement. Homework Equations The Attempt at a Solution I don't really know how to start this problem. What should I be thinking about in this problem? We've never done a problem of this type so I'm having a hard time getting...

Homework Statement A uniform plank of length 4.7 m and weight 207 N rests horizontally on two supports, with 1.1 m of the plank hanging over the right support (see the drawing). To what distance x can a person who weighs 454 N walk on the overhanging part of the plank before it just begins to...

Homework Statement A plane monocromatic electromagnetic wave propagates in the air hitting a cristal plate with an incident angle of 60 degrees. The cristal plate has an area A=0.5m^{2}, and is fully illuminated by the wave. The average power density carried by the wave is...

Homework Statement For some reason, the uniform topology always causes me problems. So, let's work this through. Let Rω be given the uniform topology, i.e. the topology induced by the uniform metric, which is defined with d(x, y) = sup{min{|xi - yi|, 1}, i is in ω}. Given some n, let...

In textbooks or other texts that discuss electrodynamics at some point always the term 'uniform' is introduced to describe particularly simple (symmetric) charge distributions, electric fields, etc. In trying to imagine what a uniform charge distribution - which, of course, is a mathematical...

Homework Statement A uniform beam |AE| at 2m from A there's a 500N force at 60degrees to the negative x-axis direction. At 3.5m from A (1.5m from the 600N) There's a 200j N force and at 4.5m from A there's a -100i N force acting 0.5m above the beam. i)Determine the single force which is...

Homework Statement A uniform beam AB of mass 4.5 kg is 1.6 m long. A mass of M kg is attached to end A and a mass of 3 kg is attached to end B. The beam rests horizontally in equilibirum on a smooth support at point C, where AC = 0.5 m. Calculate the value of M and the reaction of the support...

1. A 2kg bucket of water is attached to a 1.5m long string and swung in a vertical circle with a constant speed of 12 m/s. What is the minimum speed the bucket can be swung at while still retaining the water. 2. The bucket has a maximum tension force on the string at the bottom, with 212 N...

Homework Statement Prove the series converges uniformly on R to functions which are continuous on R. \sumn\geq0 (-x)2n+1/(2n+1)! Homework Equations The Attempt at a Solution I'm having trouble actually figuring out what to use for this series.. It looks like a Taylor series...

Homework Statement As a pilot comes out of a dive in a circular arc she experiences an upward acceleration of 9.0 gs (i.e. 9 x 9.8). a) Mentions that the Pilot's mass is 60 kg, already solved this b) If the speed of the plane is 330 km/h, what is the radius of the plane's arc...

Homework Statement David spins a sling in a horizontal circle above his head. What would happen to the period of rotation if he applied the same force and the length was a) doubled, b) halved Homework Equations ac = (4π2r) / T2 The Attempt at a Solution Just not sure what to do in...

Homework Statement A car with mass 1200kg rounds a curve banked at 18 degrees. The radius of the curve is 130 m. Find the speed of the car if the frictional force between the tires and the road is 3.5 x 10^3 down the banked curve. Homework Equations ac = v2/r The Attempt at a Solution...

Homework Statement 1. Let X , Y and Z be independent random variables, uniformly distributed on the interval from 0 to 1. Use Theorem 3.8.1 twice to find the pdf of W = X + Y + Z . Thm. 3.8.1 States: If X & Y are continuous random varibles wth pdfs fx(x) and fy(y), respectively then...

Homework Statement Prove that f:(M,d) -> (N,p) is uniformly continuous if and only if p(f(xn), f(yn)) -> 0 for any pair of sequences (xn) and (yn) in M satisfying d(xn, yn) -> 0. Homework Equations The Attempt at a Solution First, let f:(M,d)->(N,p) be uniformly continuous...

Homework Statement Two equal uniform rods AB & AC of weight W & length 2a are jointed smoothly at A. Two rods are kept freely under equilibrium over a smooth circular cylinder of radius r where axis of cylinder to be horizontal. If both rods inclined at an angle ɵ to the horizontal. Show that...

Hello Physics Forums. I've read the forum on and off for a while and have always found that the folks here have given such thorough answers that I've had nothing more to contribute! :) But I finally have the need to ask a question. I work in a physics lab and we are trying to determine the...

I am stumped. I have that W=X+Y+Z and that S=X+Y These are all X, Y, & Z and Independent and Uniformly Distributed on (0,1) I found the pdf of S to be (Assume all these < rep. less than or equal to): S when 0<S<1 2-S when 0<S<1 So I continued: To do pdf of S+Z=W I figured...

I have a uniform rod laying on a table. A ball comes in and hits the rod making it move backwards but also rotating. Assuming that we are in a frictionless environment, how do describe the circle made by the rod?

Homework Statement Point A (2,3)m and point B (5,7)m are in a region where electric field is uniform and given by E=(4i+3j)N/C. What is potential diff Va-Vb? Homework Equations Not a clue The Attempt at a Solution I tried converting the (4i+3j) into magnitude and that is as far...

So I've been pondering on this question for quite a while and I'm a little stumped. It's not a homework problem; just a problem I came across yahoo answers a week ago. Basically it's a true or false question: Homework Statement If a highway curve is properly banked and posted at 45 mph, it...

Homework Statement A uniform piece of sheet steel is shaped as pictured. compute the x and y coordinates of the center of mass of the piece https://tdsal.homeserver.com/photos/photos%20hosted%20on%20internet/q6%20.jpg Homework Equations cm = sum of all of the masses multiplied by...

Hey, I've recently been studying electric fields, and our teacher told us that the field is approximately uniform between two charged parallel plates, ie the force acting on a unit charge is equal everywhere. This doesn't seem to tie with everything else we've been taught; surely, as you...

[PLAIN]http://img258.imageshack.us/img258/78/52649134.jpg So I've thought of a few ideas on how to prove this, but only one so far that I've sort of figured out what to do. What I want to do is split the interval up in two, so from [0,b] and from (b, ∞), for some b in the reals. Now since f is...

Homework Statement A 2 kg car travels in a flat circle. At a certain instant the velocity of the car is 24 m/s West and the total acceleration of the car is 9 m/s 2 at 53 degrees North of West. What is its radius? Answer in units of km. Homework Equations F=ma w=(2pi)/T a= w^2...

Homework Statement As in the question - Suppose that f_n:[0,1] -> Reals is a sequence of continuous functions tending pointwise to 0. Must there be an interval on which f_n -> 0 uniformly? I have considered using the Weierstrass approximation theorem here, which states that we can find...

I like thinking of practical examples of things that I learn in my analysis course. I have been thinking about functions fn:[0,1] --->R. What is an example of a sequence of piecewise functions fn, that converge uniformly to a function f, which is not piecewise continuous? I've thought of...

Homework Statement Let fn(x) = (1-x)^(1/n) be defined for x an element of [0,1). Does the sequence {fn} converge pointwise? Does it converge uniformly? Homework Equations The formal definition of pointwise convergence: Let D be a subset of R and let {fn} be a sequence of real valued...

Homework Statement X1, X2, X3 are three random variable with uniform distribution at [0 1]. Solve the PDF of Z=X1+X2+X3. Homework Equations The Attempt at a Solution PDF of Z, f_z=\int\intf_x1(z-x2-x3)*f_x2*f_x3 dx2 dx3 I saw the answer at http://eom.springer.de/U/u095240.htm, but I cannot...

Homework Statement The uniform rod (length 0.60 m, mass 1.0 kg) in Fig. 11-54 rotates in the plane of the figure about an axis through one end, with a rotational inertia of 0.12 kg·m2. As the rod swings through its lowest position, it collides with a 0.20 kg putty wad that sticks to the end of...

In a lab we were supposed to produce a rollercoaster ramp while it had a loop, and then to drop a marble at a height where it would finish the entire path without falling off, with enough centripetal acceleration at the loop. we were not given the mass of the marble, and we were only given a...

Homework Statement A particle of charge q enters a region of uniform magnetic field B (pointing into the page). The field deflects a particle a distance d above the original line of flight. Is the charge positive or negative? In terms of a, d, B, and q, find the momentum of the particle. x...

I was wondering if f and g are two uniformly continuous functions on a set such that g(x) is not zero is f/g uniformly continuous? I have a feeling it is not but I can't seem to find a counter example.

A new car is tested on a 200m diameter track. If the car speeds up at a steady 1.5 m/s^2, how long after starting is the magnitude of its centripetal acceleration equal to the tangental acceleration? So we know that our acceleration is equal to 1.5 m/s^2, our radius of our circle is 100m. I...

Homework Statement A proposed space station consists of a circular tube that will rotate about its center (like a tubular bicycle tire), as shown in the figure (http://session.masteringphysics.com/problemAsset/1057181/4/GIANCOLI.ch05.p048.jpg). The circle formed by the tube has a radius of...

Homework Statement consider a disc of radius 1 in the plane D in R^2 D = {(x,y) in R^2 | x^2 + y^2 <=1 } what is the marginal pdf of x and y Homework Equations The Attempt at a Solution so the joint distribution of xy is 1/Pi for x^2 + y^2 <=1 right? but how exactly? "density"...

Homework Statement Consider a disc of radius 1 in the plane D in R D = {(x,y) in R | x^2+y^2 <= 1} write the marginal pdf of x and y Homework Equations The Attempt at a Solution so the joint pdf is 1/Pi for x^2 + y^2 <= 1 <- correct? but how to I get the marginal pdfs?

Homework Statement If X~(-5,5) find E[||X|-2|] Homework Equations If a variable is distributed uniformly then f(x) = 1 / (b-a), with a mean of (a+b)/2. If x~u, then y~u. The Attempt at a Solution I think I should change the variable, so y = |X| - 2, and then find E[|y|]. So if I...

1. Homework Statement Here is the link to the old thread, https://www.physicsforums.com/showthread.php?t=349730 i tried posting but it doesn't seem active. I don't understand how they get the second pdf as i tried it and got the first pdf. I also don't know how to do the double integral as...

Homework Statement The figure to the right shows a single circular loop of wire filled with a uniform magnetic field pointing into the page The radius of the loop is R = 1.75 cm. The magnitude of the magnetic field in the loop is changing according to B(t) = B0 exp{-t / 2.15sec} (a) what is the...

Homework Statement General question:Decide wether an airplane will continue to fly in uniform circular motion while banking on a turn. Homework Equations m(v2/r) \SigmaFx= Lsin\theta=m(v2/r) \SigmaFy=Lcos\theta-mg=0 The Attempt at a Solution my question is if the centripetal force...

Homework Statement Assume f:(0,1) \rightarrow \mathbb{R} is uniformly continuous. Show that \lim_{x \to 0^+}f(x) exists.Homework Equations Basic theorems from analysis.The Attempt at a Solution The statement is intuitive but I'm having trouble formalizing the idea. Uniform Continuity means...

Homework Statement A uniform disk turns at 8.6 rev/s around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk's diameter, is dropped onto the freely spinning disk, see the figure. They then turn together around the spindle with their centers...

Homework Statement To get used to finding the center of mass of an object, I have decided to start with a uniform density square. The square is centered at the origin. The center of mass should be at the center of the square, and thus at the origin. When I tried to solve this however, my...

1. Alright say you have a simple pendulum with given mass, length, and velocity (I think.. correct me if I'm wrong) ... how would I go about calculating theta (in degrees)? 2. I'm assuming the quadratic eq will have to be used? Among a couple of the simple force formulas. 3. I...

Homework Statement Suppose that f: [0, \infty) \rightarrow \mathbb{R} is continuous and that there is an L \in \mathbb{R} such that f(x) \rightarrow L as x \rightarrow \infty. Prove that f is uniformly continuous on [0,\infty). 2. Relevant theorems If f:I \rightarrow \mathbb{R} is...