Uniform Definition and 1000 Threads

Homework Statement uploaded Homework Equations rocket equation The Attempt at a Solution i can calculate the force acting on the chain by the ground using rocket equation but i cannot show that the velocity is that.

Homework Statement you are sitting in an airplane. you have a window seat. the plane makes a level turn of 2km at speed 400km/hr. the coefficient of static friction btwn you and the seat is .35 Then they ask is the frictional force sufficient to keep you moving in a radius of 1km at a speed...

A ball rolling with an initial velocity of 40 m/s [W] undergoes an acceleration of 5.0 m/s^2 [N] for a period of 6.0 seconds. a) What is the final velocity of the ball? b) What is the displacement of the ball in the 6.0 seconds? Can someone explain how I would draw this vector...

Homework Statement A stone rests in a pail that is moved in a vertical circle of radius 60 cm. What is the least speed the stone must have as it rounds the top of the circle if it is to remain in contact with the pail? Answer: 2.4 m/s Homework Equations v= 2 pi r / t The Attempt at...

Homework Statement A mass of 1.5 kg moves in a circle of radius 25 cm at 2 rev/s. Calcualte (a) the tangential velocity, (b) the acceleration, (c) the required centripetal force for the motion. Answers: A) 3.14 m/s B) 39.4 m/s^2 radially inward C) 59 N Homework Equations v=2piR/T...

Homework Statement Didn't know what to put for thread title, my notes and textbook were a little to ambiguous A large, flat, nonconducting surface carries a uniform charge density σ. Into the middle of this sheet has been cut a small, circular hole of radius R. Ignoring fringing fields from...

Homework Statement "In class we calculated the electrostatic self energy of a uniform density sphere of charge, i.e., the work required to assemble the sphere from "infinite dispersal." Along the same lines, calculate the electrostatic self energy of a spherical shell of charge, of negligible...

Homework Statement As the title suggests. Rω is the space of all infinite sequences of real numbers. The uniform topology is induced by the uniform metric, which is, on Rω, given with: d(x, y) = sup{min{|xi - yi|, 1} : i is a positive integer} The Attempt at a Solution I am trying to show...

Homework Statement A cat sits on a merry go round at a radius of 4.0m from the center. The ride makes one complete rotation every 6.3 seconds. What is the least coefficient of static friction to keep the cat in place? Homework Equations Circumference = 2Pi*r V=d/t a=v^2/r The...

Homework Statement A particle's position is given by the formula r(t) = Rcos(ωt)î + Rsin(ωt)ĵ The particle's motion at t=0 can be described as a circle starting at time t=0 on the positive x axis. a) When does the particle first cross the negative x axis? b) Find the speed of the particle at...

Homework Statement A ball starts from rest and rolls down a hill with uniform acceleration, traveling 180 m during the second 4.4 s of its motion. Homework Equations The Attempt at a Solution How far did it roll during the first 4.4 s of motion?

A proton (mass= 1.7×10-27 kg, charge= 1.6×10-19 C) traveling with speed 106 m/s enters a region of space containing a uniform magnetic field of 1.2 T. What is the time t required for the proton to re-emerge into the field-free region? I plugged the numbers into r=mv/qB and then t=pi r/ v...

Homework Statement A uniform solid sphere,rolls without slipping on a horizontal surface with an angular velocity \omega,meets a rough inclined plane of incination 60(degrees).The sphere starts pure rolling up the plane with an angular velocity.Find the new angular velocity . Homework...

Homework Statement A uniform electric field of magnitude 640 N/C exists between two parallel plates that are 4.00 cm apart. A proton is released from the positive plate at the same instand that an electron is released from the negative plate. Determine the distance from the positive plate that...

To put a uniform charge on the surface of a conducting hollow sphere one just needs to touch it at one point with an electrode. To put a uniform charge on the surface of an insulating hollow sphere, do you have to somehow physically spray charge all over it?

Homework Statement Let (a1, a2, ...) and (b1, b2, ...) be sequences of real numbers, where ai > 0, for every i. Let the map h : Rω --> Rω be defined with h((x1, x2, ...)) = (a1x1 + b1, a2x2 + b2, ...). One needs to investigate under what conditions on the numbers ai and bi h is continuous...

Homework Statement S solid uniform glass sphere is surrounded by air. The sphere has radius R and refractive index n. As shown in the picture, a light ray traveling in air, parallel to a diameter of the sphere, enters the sphere, reflects off the far side, then exits the sphere traveling in a...

How can we show that Dirichlet distribution with parameters α = (α1, ..., αK) all equal to one is uniformly distributed on a K-dimensional unit simplex?

Homework Statement If a curve with a radius of 60 meters is properly banked for a car traveling 60 km/hr, what must the coefficient of friction be for a car on the same curve traveling 90 km/hr? Homework Equations Fmax = u * Fn where Fmax = force causing the friction, u = coefficient of...

Homework Statement Fuzzy dice hang from the rear-view mirror of a car rounding a curve. If the curve has a radius of 275 meters and the dice are hanging at an angle of 12° from the vertical, how fast is the car going? Homework Equations a = v2/R for an acceleration with a constant...

I would like to ask how to define a uniform distribution on a high dimensional spaceR^n. What is the density of such distribution?

Homework Statement A uniform bar AB of length l and weight W is hinged to the wall at its end A and supported by means of a string of length a which is tied to the wall as shown. Find the angle \theta that the bar will make with the wall corresponding to the position of equilibrium...

Homework Statement A purse at radius 1.90 m and a wallet at radius 2.60 m travel in uniform circular motion on the floor of a merry-go-round as the ride turns. They are on the same radial line. At one instant, the acceleration of the purse is (1.70 m/s2) + (4.60 m/s2). At that instant and in...

Homework Statement A Machine at a cost of $5,000 was purchased 3 years ago. It can be sold now for $3,000. If the machine is kept, the annual operating and maintenance costs will be $1,500. If it is kept and operated for next five years, determine the amount at time 0 (now) equivalent to the...

Homework Statement Which, if any, of the following statements about a particle in uniform circular motion is/are true? Its acceleration vector is a constant. Its velocity and acceleration vectors are always perpendicular. The direction of its acceleration is toward the center of...

Homework Statement A non-uniform surface charge lies in the xz-plane. At the origin, the surface charge density is (sigma)=3.01C/m^2; other charges are present in the vicinity as well. Just to the right of the origin the y-component of the electric field is 520,000N/C. What is the y-component...

Homework Statement The graph shows the potential energy of an electric dipole which is in a constant electric field; only the electric force is acting on the dipole. Consider a dipole that oscillates between +/- 51 degrees. What is the dipole's kinetic energy when it is aligned with the...

Homework Statement We have a rectangular box with diagonal corners at (0,0,0) and (-1,2,3)cm. We place charge inside this box with distribution, ρ(r)=2x-3(z-1) with units of nC/m3. What is the total charge inside this box? Homework Equations The Attempt at a Solution I have an...

Homework Statement An 80kg person is preparing to dive into a pool. The diving board is a uniform horizontal beam that is hinged to the ground at point A and supported by a frictionless roller at D. B is the point directly under the center of gravity of the person. The distance between A to B...

Homework Statement Alright, here is the problem. Given a compact metric space X, and a sequence of functions fn which are continuous and f_{n}:X->R (reals), also f_n->f (where f is an arbitrary function f:X->R). Also, given any convergent sequence in X x_{n}->x, f_{n}(x_{n})->f(x). The problem...

Homework Statement Does the following series converge uniformly? [sum from n=1 to inf] \frac{e^{-nx}}{n^2} on [0, inf) Homework Equations I know I need to use the M test or Cauchys Principle of uniform convergence. My tutor suggests using the former if there is uniform convergence...

Homework Statement A uniform thin rod 7.0 cm long with a mass of 40.0 g lies on frictionless horizontal table. It is struck with horizontal impulse at right-angle to its length, at a point 2.0 cm from one end. If the impulse is 8.5 mN*s: describe the resulting motion of the stick...

Homework Statement How to calculate the expected value of the log of a uniform distribution? Homework Equations E[X] where X=ln(U(0,1)) The Attempt at a Solution integral from 0 to 1 of a.ln(a) da where a = U(0,1) = -1/4 However I know the answer is -1

Homework Statement [edit]: In case anyone didn't get a clear picture, in a nutshell the experiment involves us releasing a glider down an air track within a fixed distance x, where the time, t taken is then recorded down. Sorry for not mentioning this before if it's of any use. To determine...

I would like to determine the MLE for k in U(0,k) where U is the uniform pdf constant on the interval [0,k] and zero elsewhere. I would like this estimate in the case of missing data. To be specific, what is the MLE for k given the three draws X={1,3,*} where * is unknown.

Homework Statement a) What is the value of an electrostatic potential V, a distance r from a point charge Q? b) A uniform line of charge, of linear charge density (\lambda), extends along the x-axis from x = 0, to x = a. i) By considering the contributions from the infitisimal elements...

A function is pointwise bounded on a set E if for every x\in E there is a finite-valued function \phi such that |f_n(x)|<\phi(x) for n=1,2,.... A function is uniformly bounded on E if there is a number M such that |f_n(x)|<M for all x\in E, n=1,2,.... I understand that in uniform...

hi everyone I was reading one example about Uniform continuity, say that the polynomials, of degree less than or equal that 1 are Uniform continuity, my question is, for example in the case polynomial of degree equal to one Which is \delta, that the Uniform continuity condition satisfies...

Homework Statement We know that f is uniformly continuous. For each n in N, we define fn(x)=f(x+1/n) (for all x in R). Show that fn converges uniformly to f. Homework Equations http://en.wikipedia.org/wiki/Uniform_convergenceThe Attempt at a Solution I know that as n approaches infinity...

<p> and <p^2> for uniform "psi" Homework Statement What is <p> and <p^2> for state: \begin{array}{l} \psi (x) = {\rm{constant for x}} \in {\rm{[ - a,a]}} \\ \psi (x) = {\rm{0 for x}} \notin {\rm{[ - a,a]}} \\ \end{array} ...that is: a "psi" that is constant within...

Hi. I'm curious, how would a charged particle, let's say an electron, move in a simple uniform electric field? My first guess would be that it would follow Newton's second law of motion and move with a constant acceleration: $ \dot{x}=\frac{Eq}{m} $ where E is the fields intensity, q the...

Homework Statement A spherical source radiates sound uniformly in all directions. At a distance of 9 m, the sound intensity level is 100 dB. What power is radiated by this source? Just a simple answer check to see if my answer is reasonable. Homework Equations \beta = 10 db log (I/I0)...

Hello guys. I am taking an introductory course in computer programming. For one assignment I was to make up a word problem, then write a program to solve it. I wrote a program to calculate the radius of a circular orbit based on the orbiting object's current velocity, and other parameters. Can...

Here the extra credit question I'm stuck on: A square loop (perimeter of 4L and hinged along one side) is made of a wire that has a mass per unit length of 0.1000 kg/m and carries a current of 5.000 A. A uniform magnetic field of 10.00 mT directed perpendicular to the hinged side exists in...

Homework Statement Which of the following is not true in relation to an object moving in uniform circular motion? a. KE of the object is constant b. net force is zero c. net work is zero d. the magnitude of acceleration is constant e. momentum is non-constant The Attempt at a...

Homework Statement Suppose: f(x)\ and\ f'(x)\ are\ continuous\ for\ all\ x \in R For\ all\ x \in R\ and\ for\ all\ n \in N\ f_n(x)=n[f(x+\frac{1}{n})-f(x)] Prove\ that\ when\ a,b\ are\ arbitrary,\ f_n(x)\ is\ uniform\ convergent\ in\ [a,b] The Attempt at a Solution\lim_{n\rightarrow...

Homework Statement Determine the dipole moment, \mathbf{p}, of a sphere of radius R with a uniform volume charge, total Q, with respect to its center. Homework Equations \mathbf{p}=\int \mathbf{r} \rho(\mathbf{r}) d\tauThe Attempt at a Solution I know that \mathbf{p}=\mathbf{0}, but I have a...

Homework Statement The diagram shows two charged spheres X and Y, of masses 2m and m respectively, which are just prevented from falling under gravity by the uniform electric field between the two parallel plates. If the plates are moved closer together A X and Y will both remain...

Let y_n be a sequence of functions in \mathcal{C}([0,1], \mathbb{R}) Suppose that every subsequence of y_n has a subsequence that converges uniformly. Prove that they all converge to the same limit.

1.kn (x) = 0 for x ≤ n x − n, x ≥ n, Is kn(x) uniformly convergent on R? I can show that it is uniformly convergent on any closed bounded interval [a,b], but I don't think it is on R. Could anyone please give me some hints how to prove it? 2.Fix 0 < η < 1. Suppose now...