Uniform Definition and 1000 Threads

Homework Statement Find the Center of Mass locations of a thin stick of mass M and length L, whose left ends are at x=0. The stick has uniform mass density λ1 = 2M/3L along the left half, and has uniform mass density λ2 = 4M/3L along the right half. Homework Equations I know that this is...

IMPORTANT! TEXT IN GREEN HAS BEEN ADDED AND IS CORRECT TEXT IN RED HAS BEEN REMOVED AND IS INCORRECT 1. Homework Statement Question: An energetic father stands at the summit of a conical hill as he spins his 25 kg child around on a 5.7 kg cart with a 2.3-m-long rope. The sides of the hill are...

https://i.imgur.com/4nynNBg.png I cannot understand for the life of me why this problem doesn't just use T = 2πr/v to solve for the period to get T = 2π(Lsinβ)/v. Instead, it rearranges the formula for a(rad) = (4π^2R)/T^2 to solve for T, and arrives at a totally different answer, T =...

Homework Statement A 40 cm rod is rotated about its centre inside a region of uniform magnetic field of 6.4 T. Given that the speed of rotation is 15 rad/s, find potential difference between the centre and either end of the rod Homework Equations emf = - ΔΦ / Δt ω = 2π / T The Attempt at a...

Homework Statement persons 1 & 2 are initially at rest (vi=0m/s) 48m (d) apart. they then run towards each other at constant accelerations person 1 acceleration = 0.50m/s2 person 2 acceleration = 0.30m/s2 how long until they reach each other/collide (t)? at the instant they collide, how far...

Hello, I am working on a project for an EE class and am brushing back up on the basics of strain and stress. My question was to do with how strain works in a material and if it is constant throughout. Say for example you had a setup like this The change in resistance the strain gauge...

I was thinking that if a uniform rod of mass M and length L remains static ,then it's centre of mass will be at L/2 from one end (e.g total mass assumed to be concentrated at L/2 ) But if this rod is moving with uniform angular velocity ω about an axis passing through it's one end and...

Hello, could someone help answer this question for me: How would the path of a conducting sphere (i.e. AL) be affected as it passes through a strong uniform magnetic field orthogonal to the direction of motion. I believe the Lenz effect/Eddy currents will create a magnetic field opposing the...

Homework Statement We have an uncharged, conducting wire with radius a. We surround it by a linear dielectric material, εr, which goes out to radius b. We place this in an external electric field, Eo. Homework Equations We have electric potential inside (a < s < b) Vinbetween=Acosφ +...

In analysis, the pasting or gluing lemma, is an important result which says that two continuous functions can be "glued together" to create another continuous function. The lemma is implicit in the use of piecewise functions. Can we have a similar situation for uniform continuous functions?

Homework Statement While learning to drive, you are in a 1 320-kg car moving at 34.0 m/s across a large, vacant, level parking lot. Suddenly you realize you are heading straight toward a brick sidewall of a large supermarket and are in danger of running into it. The pavement can exert a...

Homework Statement This is a translation so sorry in advance if there are funky words in here[/B] f: ℝ→ℝ a function 2 time differentiable on ℝ. The second derivative f'' is bounded on ℝ. Show that the sequence on functions $$ n[f(x + 1/n) - f(x)] $$ converges uniformly on f'(x) on ℝ...

Homework Statement Let ##X \subset \mathbb{C}##, and let ##f_n : X \rightarrow \mathbb{C}## be a sequence of functions. Show if ##f_n## is uniformly Cauchy, then ##f_n## converges uniformly to some ##f: X \rightarrow \mathbb{C}##. Homework Equations Uniform convergence: for all ##\varepsilon >...

Homework Statement The series is uniformly convergent on what interval? Homework EquationsThe Attempt at a Solution [/B] Using the quotient test (or radio test), ##|\frac{a_{n+1}}{a_{n}}| \rightarrow |x^2*\sin(\frac{\pi \cdot x}{2})|, n \rightarrow \infty##. However from here I'm stuck...

Homework Statement Homework Equations dV= integral(kdQ/dR) The Attempt at a Solution So, I'm familiar with these type of problems but in 2D (like a line of uniform charge). When the y,z component is added, I'm kinda lost. i know dQ = p*dV= p*dx*dy*dz. (atleast i think it is). also the dR =...

In an ideal world with uniform gravity field, what does its space-time curvature look like? Is it non-zero? If not, how a free particle would be accelerated with the point view of space-time curvature? By uniform gravity field, I mean a gravity field with same value, same direction everywhere...

Homework Statement A 60 g ball is tied to the end of a 40-cm-long string and swung in a vertical circle. The center of the circle is 150 cm above the floor. The ball is swung at the minimum speed necessary to make it over the top without the string going slack. If the string is released at the...

A point mass in an uniform circular motion is continuously changing the velocity direction. To do it, it continuously need force (energy). If we don't give any energy to the system it will anyhow continues its uniform circular motion. How it's possible, who gives the energy ? (It's seems a...

I seek a little help in understanding why we can see so far into the past to be able to view events where the light from these events should have long ago overtaken wherever the masses ended up. I get it that there was a considerable time during which the limits of the space expansion exceeded...

frfr1. Homework Statement A 15 kg uniform wooden board of length L is balanced at its center. A 6 kg object is to be placed on the right end. How far from the balance point must a 9 kg object be placed to keep the board in equilibrium? Homework Equations ##m_1d_1 = m_2d_2## The Attempt at a...

I'm in the chapter of Uniform Circular Motion and I have a hard time understating centipetal acceleration. Until now I knew that acceleration describes "how fast velocity changes in magnitude" except projectile motion because when it reaches maximum height then g is going to change the direction...

Homework Statement There is a uniform electric field=100 V/m inclined at 45 degrees with the x axis. My doubt boils to which is greater? V(0,0) or V(10√2,0) (since my answer has the wrong sign) Homework Equations All electrostatics formulas The Attempt at a Solution The work done to move a...

I am looking at a couple of very interesting papers, published in MNRAS, that deduce, that the accelerated expansion of the Universe we observe can be attributed to gravitational waves, produced by a very distant merger of two or more universe-mass-scale black holes. The last one is on the...

Has anyone ever looked for reversible weight changes while materials are subjected to uniform, strong magnetic fields, such as those involved in nuclear magnetic resonance imaging (MRI) or spectroscopy? I suspect no one ever has, for lack of a reason, and any such effects would have to be...

I am trying to understand why an accelerating charge emits radiation/electromagnetic waves but a uniformly moving one does not. I saw one video on Youtube where it seemed that it was explained by the fact that with a uniformly moving charge the Poynting vector was pointing 'in to the volume' -...

Hi I have read one excellent explanation on the question I am posting again, at another thread on PF, because I am not able to completely understand the concept. Please spare some more time. I need help to understand how an electric field due to an infinite sheet of charge can be uniform where...

I need a little help here when calculating the work done in a uniform electric field on a positive charge to move it from point a at higher potential to point b at lower potential that means the charge is going towards the negative plate we first use V = - ED and then we have a...

<< Mentor Note -- thread moved from the New Member Introduction forum because of the general nature of the question >> Hi guys, I'm Liszzy newly join physics group. How are you everyone? I'm doing my Canadian diploma in physics and need help from you guys. I've doubt in Kinematic chapter...

Hello everyone! I'm a student of electrical engineering, preparing for the theoretical exam in math which will cover stuff like differential geometry, multiple integrals, vector analysis, complex analysis and so on. So the other day I was browsing through the required knowledge sheet our...

A point is chosen at random inside a circle.Find the probability 'p' that the point chosen is closer to the center of the circle than to its radius. This comes from the noncountable uniform spaces sections.

A uniform rod of mass m and length l is pivoted at a point on the ground. The rod is initially in vertical position and touching a block of mass M which is at rest on a horizontal surface. The rod is given a push of negligible force and it starts rotating about that point. This causes the block...

1. Homework Statement In picture Homework Equations f=ma v^2/r The Attempt at a Solution ΣFy=-mg - Fn = m(-v^2/r) -55*9.8 - Fn = m(-v^2/r) v= 16π/4.5 since circumference = 2πr divide by the rotations time taken per second = 11.17m/s -Fn = 55(-15.6) + 55*9.8 Fn = -319 What am i doing wrong here??

I am writing a lab report on the effect of the radius of a string on the frequency of rotation on an object in horizontal uniform circular motion. My hypothesis is: If the radius of the string from the origin of rotation increases, then the frequency will decrease because frequency has an...

Homework Statement Find the acceleration of a uniform solid sphere (of mass ##m## and radius ##R##) rolling without slipping down an incline at angle ##\alpha## using the Lagrangian method. Homework Equations Euler-Lagrange equation which says, $$\frac{\partial\mathcal{L}}{\partial...

Hi all, i tried to do this question but got stuck on the last point . Can anyone help me please? The general form of vector potential: I got the answer for A1 vector potential but don't know what assumptions i need to get the expression for the A2. Does anyone know how one can derive it...

The problem I am trying determine wether ##f_n## converges pointwise or/and uniformly when ## f(x)=xe^{-x} ## for ##x \geq 0 ##. Relevant equations ##f_n## converges pointwise if ## \lim_{n \rightarrow \infty} f_n(x) = f(x) \ \ \ \ \ ## (1) ##f_n## converges uniformly if ## \lim_{n...

in case of rolling without slipping of a solid sphere having uniform mass density the condition is Vcm (velocity of center of mass ) = Rω or [a][/cm] = Rα ,which comes from the fact that if an object that rolls without slipping the geometric center of the body travels 1 circumference along...

Homework Statement A uniform chain of mass 'm' and length 'l' rests on a rough incline (inclination is angle 'Q') with its part hanging vertically. The chain (inclined) starts moving up the incline (and the vertical part moving down) provided the hanging (vertical) part equals to 'n' times...

Homework Statement A closed hemispherical shell of radius R is filled with fluid at uniform pressure p. The net force of the fluid on the curved portion of the shell is given by:Homework Equations The Attempt at a Solution [/B] I'm not even posting the answers because I'm not looking to get...

Thank you for reading my post. I was thinking about induced emf and magnetic flux and I realized I have a huge misunderstanding, but I don't know exactly what it is. Below I will list 4 statements which I logically know cannot all be simultaneously true. Can you please tell me which one(s) are...

Homework Statement An Ohmic material with some conductivity has a uniform current density J initially. Let's say the current is flowing in the direction of the z-axis. A small insulating sphere with radius R is brought inside the material. Find the potential outside the sphere. Homework...

I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 1: Continuity ... ... I need help with an aspect of the proof of Theorem 1.8.15 ... ... Duistermaat and Kolk's Theorem 1.8.15 and its proof read as follows:In...

Homework Statement [/IMG] Homework Equations See Below The Attempt at a Solution Maybe my answer is right but not simplified enough. But if it is I am having trouble seeing the mathematical equivalency. Please help. Thanks in advance!

Can someone explain the math of how potential energy travels from higher potential energy to lower potential energy (PE) along a uniform electric field? I understand that in order for the point charge to move, gaining kinetic energy, it will lose potential energy. But using the equation...

Homework Statement Homework EquationsThe Attempt at a Solution I am having trouble understanding the setup as well as how to approach this problem . I am not understanding the orientation of the two pieces of the wire . They make angle 60° with each other , but then what does it mean when...

I am having trouble understanding tangential speed as it applies to uniform circular motion and I would appreciate any help. Say I have a ball on the end of a string that I hold with my hand and rotate at a constant speed. If the string provides the centripetal force and acceleration, where...

Homework Statement A uniform rod (mass = 5.0 kg, length = 0.3 m; the rotational inertia of the rod relative to the axis through its centre of mass is I = (1/12) ML^2 ) is free to rotate about a frictionless pivot at one end. The rod is released from rest in the horizontal position. What is the...

Let me give some context. Let X be a compact metric space and ##C(X)## be the set of all continuous functions ##X \to \mathbb{R}##, equipped with the uniform norm, i.e. the norm defined by ##\Vert f \Vert = \sup_{x \in X} |f(x)|## Note that this is well defined by compactness. Then, for a...

Hello everyone! I'm at a loss trying to figure out the specific force that pushes a missile at rest off the ground, to the high sky. Considering a missile with constant mass, and an independent initial total fuel mass. The rate of fuel mass being expelled out of the missile is constant, in...

I need to draw electric field lines of sphere in uniform electric field with LaTeX/TikZ. Can anyone show me equation of field lines in polar coordinates?