Bead Definition and 128 Threads

Hello : There is this example ,on analytical mechanics , which I am not able to understand why he solve it in that way We have a bead moving on a parabola that it's equation is y = b*x^2 Find the equation of motion Constrain equations : y=b*x^2 z=0 The bead have only one coordinate call it x...

https://www.guardianmag.us/2023/02/scientists-levitate-glass-nanosphere.html "the nanosphere was suspended in its lowest quantum mechanical state, one of extremely limited motion where quantum behavior can start to happen." To my reading, the glass bead was cooled down and then suspended with...

Hi, In David Morin's "Introduction to classical mechanics", Problem 6.8, when deriving Hamiltonian of the bead rotating on a horizontal stick with constant angular speed, the Lagrangian derivative over angular speed isn't included. Why is that? Specifically, the Lagrangian takes form...

A bead is kept at the bottom of a vertical frictionless ring , if the ring is given an acceleration a horizontally, what is the maximum angular displacement of the particle? The problem is easily solved from the frame of reference of the moving ring, I am however Intrested in a solution without...

For whatever reason, I'm having a hard time conceptualizing this problem. I understand that the tangential components of all forces involved need to cancel out in order for the bead to be stationary. I also understand that there is a mgsinθ in the negative θ-hat direction. What I don't...

The relevant equations has been me working out the gravitational potential energy. I was told to take the derivative twice from here, but I do not understand why. It leads into a taylor series expansion, which seems excessive, but I was not informed on any other way to do it. Any advice would be...

Hi, this is a question from my textbook that I can't quite make sense of. I don't really know where even to begin, to be honest. The only thing I can think of is that the bead is at equilibrium, thus the force of gravity is equal to the pressure exerted by the gas. I don't know where the heat...

To be honest I am a bit clueless first with how to interrupt this question I think the bead is going around a wall type thing where there is friction both in the up and X direction. Some hint to get some ideas running would be great

I can evaluate the first beads motion easily A to B is -2Rj considering the point B as y=0 the motion of the bead will be -gt^2/2+2R=0 which implies t=2√(R/G) , this is ok but what I am struggling with is A to C I can see that the angle between the beads weight and it's negative normal force...

Hi I am working through some notes and came across this example. The wire rotates at angular frequency ω so the polar angle is given by θ = ωt. The generalised coordinate is r. Using the Euler-Lagrange equation leads to d2r/dt2 = rω2 The notes then state that this leads to the solution r = Aeωt...

Hi I've written D'Alembert's principle as you can see in the attached files. I computed the virtual work done by the weight and the elastic force (since the work done by the normal force is zero) and then I used the fundamental hypothesis, which states that the constraint forces can be written...

A stick is pivoted at the origin and is arranged to swing around in a horizontal plane at constant angular speed ω. A bead of mass m slides frictionlessly along the stick. Let r be the radial position of the bead. Find the conserved quantity E given in Eq. (6.52). Explain why this quantity is...

Homework Statement: A small bead is fixed on a circular loop of radius R as shown in the figure below. The loop is rotating about YY axis with constant angular acceleration ‘α’. The loop starts from rest, then, the bead is in circular motion, then acceleration of the bead at instant ‘t’...

A long horizontal rod has a bead which can slide along its length and is initially placed at a distance ## L ## from one end A of the rod.The rod starts from rest in angular motion about A with a constant angular acceleration ##\alpha## .If the coefficient of friction between the rod and the...

For the case first case U=x^2/2 : 1) Find the Serret-Frenet Triad for a any curve y = f(x): For a curve on a plane, the Triad could be find in this way: 2) The vector force resultant acting in the bead could be discribed in this way: 3) The vector force acting in the bead could be discribed...

Homework Statement Homework EquationsThe Attempt at a Solution I am pretty sure that I solved part a correctly. However, I feel as though my solutions for parts b and c are not quite correct because they seem simple. For instance, my solution for part b argues that the tangential force is...

Bead sort is a not practical sorting algorithm that suppose to have a time complexity of ##O(\sqrt{n})##in the real world. I thought it would be great if a device that can take numbers from the computer,then turn it into analog stuff that the device can read,drop the beads,and return it...

Homework Statement I know that a bead is threaded on an metal sring (no T), and the bead is not moving/ The metal string moves in circular motion at a slope of 60 degrees. The string moves one spin in one second/ which powers works on the bead? Homework EquationsThe Attempt at a Solution

Homework Statement Homework Equations $$\mathcal{L}=T-U$$ $$\omega= \frac{d\phi}{dt}$$ $$I=mr^{2}$$ The Attempt at a Solution My problem is not finding the Lagrangian. But finding the kinetic energy! The translational kinetic energy would obviously be the following: $$K.E...

Homework Statement Homework Equations K = (1/2)mv2 U = mgh W=Fd Integration/Calculus The Attempt at a Solution I'm not sure what I should be doing for this question, if height changes how is it possible that velocity stays the same, according to the conservation of energy (frictionless wire)...

Homework Statement A bead of mass ##m## slides (without friction) on a wire in the shape, ##y=b\cosh{\frac{x}{b}}.## Write the Lagrangian for the bead. Use the Lagrangian method to generate an equation of motion. For small oscillations, approximate the differential equation neglecting terms...

Homework Statement A bead slides under the influence of gravity on the frictionless interior surface of the paraboloid of revolution z = (x^2+y^2)/2a = r^2/2a Find the speed v_0 at which the bead will move in a horizontal circle of radius r_0 Find the frequency of small radial...

Homework Statement A bead is placed on a rod with coefficient of friction m, it's accelerated from rest with angular velocity a, find the time it takes to start moving. Neglect gravity Homework Equations Force of friction =Nm The Attempt at a Solution They said there's no gravity, so i don't...

Homework Statement A bead of mass m slides in a frictionless hollow open-ended tube of length L which is held at an angle of β to the vertical and rotated by a motor at an angular velocity ω. The apparatus is in a vertical gravitational field. a) Find the bead's equations of motion b) Find...

Homework Statement Homework EquationsThe Attempt at a Solution I know we can solve it by letting x=acos(\omega t)+acos(\theta+\omega t)\\ y=asin(\omega t)+asin(\theta +\omega t) and put their derivatives into the Lagrangian. But, I want to check the other points of view whether it is wrong...

Homework Statement Three lead spheres, of mass 10.0 kg each, are located at three corners of a square of ice length 45.0 cm, as shown. A bead is released at the forth corner. By considering the gravitational forces among the four objects only, determine the magnitude and direction of the...

Homework Statement A bead slides without friction on a horizontal rigid wire rotating at constant angular speed ω. The problem is to find the force exerted on the bead by the wire. Neglect gravity. Homework EquationsThe Attempt at a Solution The physical force acting on the bead is the force...

Homework Statement Homework EquationsThe Attempt at a Solution For ##0 \ge \theta \ge \pi/2## Forces on the ring, ##Mg + 2N\cos \theta = F\qquad 1## Forces on the beads ##mv^2/R = - N + mg \cos \theta## By conservation of energy when the bead has fallen through some angle ##\theta##...

Homework Statement A bead rests at the top of a fixed, frictionless hoop of radius R that lies in a vertical plane. The bead is given a tiny push so that it slides down and around the hoop. At what points is the bead's acceleration vertical? What is the acceleration at these points? This...

Homework Statement Verify the Work-Energy Theorem W=ΔK for a bead of masd m constrained to lie on a frictionless stick rotating with angular velocity ω in a plane. Homework Equations W =∫ F⋅dr, K =m/2 v^2 [/B] The Attempt at a Solution Adopting polar coordinates the velocity is v = r' +r*Θ'...

Homework Statement A bead slides on a wire, which is in a vertical plane, as shown in the diagram. Gravity acts in the -y direction. The bead starts at A, moving to the right with an initial velocity v. The wire is frictionless between A and D and between F and G, but there is friction between...

Homework Statement A small bead is threaded on a smooth circular wire of radius r which is fixed in a vertical plane. The bead is projected from the lowest point of the wire with speed √6gr. FInd the speed of the bead when it has turned through: (a) 60°, (b) 90°, (c) 180°, (d) 300°. Answers...

Hi guys, I see ferrite beads used on the input of V1 on some high end tube guitar amp designs without any indication of type and value. Can you give me some idea how to select this component and at what other places in a tube amp it could prove useful? Thanks, Billy

Homework Statement A bead of mass m kept at the top of a smooth hemispherical wedge of mass M and radius R is gently pushed towards right.As a result,the wedge slides due left.Find the magnitude of velocity of bead relative to the wedge. Homework Equations $$MV=m(v\cos(\theta)-V)$$ and...

Homework Statement In the figure shown, friction force between the bead and the light string is ##\dfrac{mg}{4}##. Find the time in which the bead looses contact with the string after the system is released from rest. Homework Equations Weight of the bead ##(m_1)=mg## Friction acting on the...

I am asked to find the shape of a wire that will maximize the speed a sliding bead when it reaches the end point(Similar to the brachistochrone problem expect that the speed is to be maximized and not time minimized). But shouldn't the speed at the end be independent of the shape of the wire...

Hi, I am a Reliability Engineer. Currently, I am facing difficulties in finding the root cause to a defective EMI filter bead. Resistance measurements across the four leads (vertically, horizontally, diagonally) show that they are all shorted. However, a good ferrite bead should only be...

Homework Statement Calculate the frequency of a bead with a mass of m vibrating on a parabolic track equals to y=Ax2 Homework Equations F=ma The Attempt at a Solution Looking at the bead at any point which isn't equilibrium, I have: 1. may =N-mgcosθ 2. max=mgsinθ I tried to look at a...

Hello! I would like to ask for your help with understanding a few things connected to the following problem: 1. Homework Statement There is an (infinitly) long thread, on which small beads can move without friction. The beads with mass m are lined up on the thread with a constant distance d...

Homework Statement Consider a system made up of joining together ##N## beads and ##N-1## springs. The positions of the beads is indicated by ##N## real numbers ##\left\{x_i\right\}_{i=1,...N}.## The Hamiltonian which characterises it is $$\mathcal H =...

Homework Statement A rod of length L is fixed at one end, and rotates in the X-Y plane with angular velocity ω. (To be clear, it is sweeping out an area of ##π (L/2)^{2}##.) A bead starts at position ##r(0)=L/2## with ##\dot{r}(0)=0##. Find ##r(t)## and the time it takes for the bead to fly...

Homework Statement The bead of mass m starts to slide without friction from point A. the mass of the cart and the rail is M. What is the max displacement of the wagon during the motion of the bead? What is the force the rail exerts on the cart when the cart's velocity is maximum? What is the...

Suppose that a ferrite bead is put around a cable where a constant current I flows, just like in this image. The coordinate system has the z axis along the cable. Let's evaluate the current through the (x,y) plane: according to the Ampère's law, the only magnetic field component generated by...

Hello! (Wave) We have a necklace with $64$ beads from $8$ different colours. Is it possible that they are put in such a way that if we go along the necklace in one direction (in any of the two) then we see all the possible successions of two colours exactly once?

Homework Statement 'Consider the system consisting of a bead of mass m sliding on a smooth circular wire hoop of mass 2m and radius R in a vertical plane, and the vertical plane containing the hoop is free to rotate about the vertical axis. Determine all relative equilibria of the bead.'...

A bead of mass m is threaded on a metal hoop of radius R. There is a coefficient of kinetic friction µk between the bead and the hoop. It is given a push to start it sliding around the hoop with initial speed v0 . The hoop is located on the space station, so you can ignore gravity Find the...

Homework Statement A bead of mass m slides without friction on a smooth rod along the x axis. The rod is equidistant between two spheres of mass M. The spheres are located at x = 0, y = ± a, and attract the bead gravitationally. (a) Find the potential energy of the bead. (b) The bead is...

Homework Statement A bead of radius R(=5 μm) is trapped by an optical beam and moved through a viscous fluid at a speed vd of 20 μms-1. If the viscous drag is given by Stokes law: F_{d}=6\pi \eta Rv_{d} obtain an expression for the laser power (intensity). If the process only has an...

Bead is at rest on a thin rod pivoted at one end. Bead is about a cm from the pivoted end of the rod. Rod now starts rotating with an uniform angular velocity w rad/sec. 1.What curve does the bead trace from the point of view of an inertial observer? Here what i think... solution of the...

I think I'm not understanding some conceptual part of rotational kinematics because all the questions seem connected. I want to figure it out as best I can so please don't solve it but any hints in the right direction would be really appreciated, thanks! The Question: A stiff piece of wire is...