Uniform Definition and 1000 Threads

Homework Statement For question 19.2 in this link: http://people.ischool.berkeley.edu/~johnsonb/Welcome_files/104/104hw7sum06.pdf I came up with a different proof, but I'm not sure if it is correct... Homework Equations The Attempt at a Solution Let |x-y|< \delta For...

I'm taking my first course in Analysis, and we learned a couple of theorems about Uniform Continuity. I have been able to visualize most of what's been going on before, but I need some help with the following: E \subseteq ℝ, f: E \rightarrow ℝ uniform continuous. if a sequence xn is Cauchy...

Hello. I am attempting to build a fixture which will place uniform tension onto one surface of a rectangular beam. I know that I must force the beam to deflect along a set path, but I am having trouble determining what the equation for this path needs to be. Any guidance on this would be...

Hi PF, I have a device (with a microcontroller) which generates random numbers. when I analyzed those numbers using Matlab software I found that it is following a uniform distribution. How can I mathematically (any algorithm?) convert this random output to a gaussian one. Also I would...

If we have a uniform distribution on [0,x]...then the pdf is 1/x right? But what if we have [0,x)? Do we still have the same pdf? Thanks in advance.

Homework Statement Using work energy theorem, solve: The Attempt at a Solution The actual answer (3.11s) is exactly half of my answer. Does anyone know what I did wrong?

Homework Statement A uniform charge Q of length L is placed on the x-axis with one end at the origin as shown a) Find the contribution dE (vector) to the electric field at P on the y-axis a distance y from the origin, from the charge at x in dx, in terms of Q, L, dx, ke, x and y b)...

Homework Statement Find the voltage change going from 5.0cm to 10.0cm along the radius away from a long line of uniform charge density 5.0 μC/m Homework Equations V = (kq) / r (I believe... I'm very lost) The Attempt at a Solution ΔV = ∫.05 to .1 2∏rLdL = 2∏r((L^2) / 2 | from...

Homework Statement A thin, uniform metal bar, 3m long and weighing 75N, is hanging veritcally from the ceiling by a frictionless pivot. Suddenly it is struck 1.3m below the ceiling by a small 2 kg clay ball, initially traveling horizontally at 14m/s. The ball sticks to the bar Find the...

Homework Statement An unstable particle, initially at rest, decays into a pro- ton (rest energy 938.3 MeV) and a negative pion (rest energy 139.5 MeV). A uniform magnetic field of 0.250 T exists perpendicular to the velocities of the cre- ated particles. The radius of curvature of each...

Many sources on the web claim that when moving a conductor through a magnetic field, an emf is produced. However, some sources claim, that the intensity of the magnetic field also needs to change in order to produce a voltage over the conductor, for example...

f is a continuous function on [0,infinity) such that 0<=f(x)<=Cx^(-1-p) where C,p >0 f_k(x) = kf(kx) I want to show that lim k->infinity ∫from 0 to 1 of f_k(x) dx exists so my idea is if I have that f_k(x) converges to f(x)=0 uniformly which I was able to show and that f_k(x) are all...

Also, if a particle is traveling through a uniform electric field, does anything change as it leaves the field if the electric field strength increases? If you're asked to find the magnitude, is it just the modulus of those values? What is a vector?

Been doing some physics problems from my mechanics class. This is the first time I've attempted a problem like this and am not so confident with solving it, I could be correct and just being paranoid but I just have a feeling I've made a mistake somewhere, would appreciate if someone who is...

How can one create a uniform solid-angular distribution of vectors in 3D space from a common origin, or in other words a grid of points on the surface of a sphere wherein the points are equidistant from each other? Spherical polar coordinates/the latitude-longitude scheme is obviously not the...

The question as stated: Define the uniform linear splines Hk:=H0(x−k), k=−1,0,1,2,3, where H0={x, 0≤x<1, 2−x, 1≤x<2, 0, otherwise. For k=−1, I would get: H−1={x+1, 1≤x<2, 1−x, 2≤x<3, 0, otherwise. Is that correct? Thank you.

Hi all, I'm looking for some help in understanding one of the theorems stated in section 20 of Munkres. The theorem is as follows: The uniform topology on ##\mathbb{R}^J## (where ##J## is some arbitrary index set) is finer than the product topology and coarser than the box topology; these...

Let X be a uniform integrable function, and g be a continuous function. Is is true that g(X) is UI? I don't think g(X) is UI, but I have trouble finding counter examples. Thanks.

Homework Statement A uniform cylinder of mass m and radius R rests in equilibrium against a rough plane that is inclined at an angle α to the horizontal. The cylinder is supported by a cord under a constant tension, wrapped round it, so that the cord leaves the surface of the cylinder...

Homework Statement A sprinter runs a race with constant acceleration throughout. During the race he passes four posts A, B, C, D in a straight line such that |AB| = |BC| = |CD| = 20m. If the sprinter takes 5 seconds to go from A to B and 3 seconds to go from B to C, find out how long, the the...

Homework Statement A 990-kg race car can drive around an unbanked turn at a maximum speed of 42 m/s without slipping. The turn has a radius of 140 m. Air flowing over the car's wing exerts a downward-pointing force (called the downforce) of 12000 N on the car. (a) What is the coefficient of...

Homework Statement P and Q are points 162m apart. A body leaves P with initial speed 5m/s and travels towards Q with uniform acceleration 3m/s^2. At the same instant another body leaves Q and travels towards P with initial speed of 7m/s and uniform acceleration 2m/a^2. After how many...

Max. speed you can drive on a circular hill an still be in "Uniform Circular Motion" Homework Statement The top of a hill is in the shape of a circle of radius 25 meters. Homework Equations a) What is the normal force that the road exerts on an 1800kg car as it tops the hill with a...

Homework Statement A ground spherical conductor of radius a lies at the center of a uniform spherical sheet of charge QB and radius b. a) How much charge is induce on the conductor's surface? Ans(-QBa/b) Evaluate V(r) at position between the conductor and the sheet and outside the sheet...

hey guys and gals, I'm normally pretty good at my physics homework, but this problem has my STUMPED, I think I am starting it right, but I have no idea how to proceed or if I am on a good path. Homework Statement A Very Long Cylinder with a radius of 7.2cm (.072m) has a uniform density of...

I have tried finding a table's length using two methods. Both should be applicable, as using a ruler implies uniform distribution, does it not? The first method involved calculating the mean length from a set of measurements, finding the variance, and substituting it in the formula for the total...

Homework Statement A flat object shown here consists of a circle and square made of heavy, uniform wire and welded together at the corners of the square. The mass of the circle is M. The mass of the square is m and its side has a length d. To find the objects moment of inertia about Axis A...

Homework Statement A ball is thrown upward from a building 30 meters tall and misses the edge on its way down, hitting the ground 6 seconds after it was thrown. A) With what speed was it thrown? B) What is its highest height?Homework Equations Vf = Vi + at x = 1/2(Vi + Vf) x = Vi t + 1/2(at^2)...

Homework Statement If X,Y are independent RVs ~ U[-1,1], and W=X*Y, find the density of W.Homework Equations The Attempt at a Solution I feel my approach is right, but the bounds of my final integral don't make sense. F_{XY}(w)=P(XY \leq w)=\int_{-\infty}^{\infty} P(XY \leq w | Y=y)*f_Y(y)dy...

I am very confused with a particular aspect of part of my physics curriculum. Let's say there is an object swinging on a rope swinging in a circular motion. The mass of the object, length of rope, and angle of rope relative to y-axis are known. How does one derive the tension of the rope...

Homework Statement A long wire lying along the x-axis carries a current of 2.60 A in the +x direction. There is a uniform magnetic field present, given by B=0.003i + 0.004j + 0.002k, where i, j, k are the unit vectors along the cartesian coordinate axes') in units of Tesla. Calculate the...

Is a location anywhere where the force of gravity is perfectly uniform over a distance?

How do you use the angle of uniform slip to calculate the coefficient of static friction? Is there an equation for this? I cannot find it in the module on friction provided with the course... thanks! I found somewhere that tanθ=μk, but that doesn't really help me, as i am looking for μs...

I'm wondering about uniform convergence. We're looking at it in my complex analysis class. We are using uniform convergence of a series of functions, to say that we can interchange integration of the sum, that is: \int\sum b_{j}z^{j}dz=\sum\int b_{j}z^{j}dz=\int f(z)dz On an intuitive level I...

Hi there, I'm trying to create a sheet that produces a uniform magnetic field,using either rectangular or cylindrical neodymium magnets. I can't tell you much abut their strength, but they would be the common type purchased from a science/hobby shop. Dimensions for cylinder are 10mm dia x...

Homework Statement Help please,I have no idea...This is the last question of my hw A boy stands at the edge of a cliff which is 30m above the ground and throws a ball vertically upwards.It hits the ground 3.0s later.Find the initial velocity of the ball. Homework Equations The...

Homework Statement I need to show that f_{n}=sin(\frac{z}{n}) converges uniformly to 0. Homework Equations So I need to find K(\epsilon) such that \foralln \geq K |sin(\frac{z}{n})|<\epsilon I'm trying to prove this in an annulus: \alpha\leq |z| \leq\beta The Attempt at a Solution I'm having...

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...