What is Chain: Definition and 976 Discussions

A chain is a serial assembly of connected pieces, called links, typically made of metal, with an overall character similar to that of a rope in that it is flexible and curved in compression but linear, rigid, and load-bearing in tension. A chain may consist of two or more links. Chains can be classified by their design, which can be dictated by their use:

Those designed for lifting, such as when used with a hoist; for pulling; or for securing, such as with a bicycle lock, have links that are torus shaped, which make the chain flexible in two dimensions (the fixed third dimension being a chain's length). Small chains serving as jewellery are a mostly decorative analogue of such types.
Those designed for transferring power in machines have links designed to mesh with the teeth of the sprockets of the machine, and are flexible in only one dimension. They are known as roller chains, though there are also non-roller chains such as block chain.Two distinct chains can be connected using a quick link, carabiner, shackle, or clevis.
Load can be transferred from a chain to another object by a chain stopper

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  1. P

    MHB How can i set this problem as a continuous markov chain?

    I request your help in order to know, how can i configure this problem as a continuous markov chain, need to define the main variable, the states, transition rates, and the matrix. I thought that it could be relationed with the independent status of the machines, because if the machine 1 is...
  2. K

    Given a uniform chain on an incline, find the work done by friction

    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...
  3. Suyash Singh

    Force due to a chain falling on a table

    Homework Statement a uniform fine chain of length l is suspended with lower end just touching a horizontal table. Find the pressure on the table, when a length x has reached the table.. Homework Equations Pressure = force/area The Attempt at a Solution let mass density, m= mass/l...
  4. PeroK

    Demystifying the Chain Rule in Calculus - Comments

    Greg Bernhardt submitted a new PF Insights post Demystifying the Chain Rule in Calculus Continue reading the Original PF Insights Post.
  5. Y

    How strong a long chain of c=c double bonds will be?

    How strong a long chain of carbon carbon double bonds will be compared to nano tubes? H>c=c=c=c=c=c=c=c=...=c=c=c=c=c=c=c=c=c=c=c=c<H
  6. K

    Thermal Energy Equation Term - Chain Rule

    Homework Statement I am going through a derivation of the thermal energy equation for a fluid and am stumped on one of the steps. Specifically, the text I am using converts the term: P/ρ*(Dρ/Dt) to: ρ*D/Dt(P/ρ) - DP/Dt where: ρ = density P = pressure D/Dt = material derivative The text...
  7. A

    Find the tension force in each pair

    Homework Statement You are presented with a circumstance in which three children are playing on a frozen pond. The three small children of mass 20.00 kg, 24.00 kg, and 16.00 kg, respectively, hold hands, and are pulled across a smooth frozen pond by a larger boy on skates, who pulls a...
  8. S

    1D atomic chain, Localized states

    Homework Statement 1D atomic chain with one atom in the primitive cell and the lattice constant a. The system in described within the tight binding model and contains N-->∞ primitive cells indexed by the integer n. The electronic Hamiltonian is $$H_{0} = \sum_{n} (|n \rangle E_{at} \langle n |...
  9. K

    Force exerted on a chain of wagons pushed by a car..

    Imagine a car that weights 1000Kg. Its engine pushes it forward with a force of 3kN. So the car is accelerating at 3m/s^2 (imagine there are no friction). After 100 seconds (the speed of car at that moment is 300m/s, very realistic), the car hits a wagon that weighs 1000Kg, that is on rest. And...
  10. Illuminatio fit

    XXh spin chain, colleration function

    Homework Statement So given XXh chain: $$\hat{H} = -J \sum ( S^x_j S^x_{j+1} +S^y_j S^y_{j+1}) + h \sum S^z_j $$ Requred to find $$\langle g| S^z_{j} S^z_{j+n} | g \rangle$$, where g is ground state. 2. The attempt at a solution Using Jordan-Wigner transform firstly I abtain: $$\hat{H} =...
  11. K

    Why Does the Chain Rule in Thermodynamics Include a Negative Sign?

    I'm trying to understand why $$\left(\frac{\partial P}{\partial T}\right)_V = -\left(\frac{\partial P}{\partial V}\right)_T \left(\frac{\partial V}{\partial T}\right)_P$$ where does the minus sign come from?
  12. D

    Homework question using the chain rule -- oil slick spreading on the sea....

    <Moderator's note: Moved from a technical forum and thus no template.> Question: A certain amount of oil on the sea surface can be considered as circular form and the same thickness throughout its surface. At a certain time, the following are noted Data: Oil is supplied to the spot at 5m^3/min...
  13. S

    Finding the Derivative of y=sqrt(x+sqrt(x+sqrt(x)))

    Homework Statement This is a chain rule problem that I can't seem to get right no matter what I do. It wants me to find the derivative of y=sqrt(x+sqrt(x+sqrt(x))) Homework Equations dy/dx=(dy/du)*(du/dx) d/dx sqrtx=1/(2sqrtx) d/dx x=1 (f(x)+g(x))'=f'(x)+g'(x) The Attempt at a Solution My...
  14. Math Amateur

    MHB Chain Rule - B&S Theorem 6.1.6 ....

    I am reading "Introduction to Real Analysis" (Fourth Edition) by Robert G Bartle and Donald R Sherbert ... I am focused on Chapter 6: Differentiation ... I need help in fully understanding an aspect of the proof of Theorem 6.1.6 ...Theorem 6.1.6 and its proof ... ... reads as follows: In the...
  15. J

    Net Vertical Force on a Slipping Chain on a Table

    Homework Statement Homework EquationsThe Attempt at a Solution The initial shape of chain is like an inverted "L" with end B just touching the floor . Height of table is "h" . My problem is in identifying the net force on the chain in vertical direction .At any instant of time there are...
  16. FallenApple

    A Markov Chain as a function of dimensions

    Here is an animation I created in R. I built this Markov chain of order 50 by correlating the information in one of the coordinates while randomly varying the rest. Is there an explanation for the clustering and flattening out over increasing dimensions of the vector space? Is it due to the...
  17. C

    Calculating Derivatives of f(x,y) with Respect to x

    I am having difficulty trying to figure the following . What is \frac{\mathrm{d} }{\mathrm{d} x}f(x,y) where x is a function of s and t. Here is my calculation \frac{\mathrm{d} }{\mathrm{d} x}f(x(s,t),y) = \frac{\partial f}{\partial x}\frac{\partial x}{\partial t}+\frac{\partial f}{\partial...
  18. Avatrin

    I Rigorously understanding chain rule for sum of functions

    In my quest to understand the Euler-Lagrange equation, I've realized I have to understand the chain rule first. So, here's the issue: We have g(\epsilon) = f(t) + \epsilon h(t). We have to compute \frac{\partial F(g(\epsilon))}{\partial \epsilon}. This is supposed to be equal to \frac{\partial...
  19. Kelly Lin

    Probability of the polymer chain

    Homework Statement Homework Equations I want to check if I think it right! The Attempt at a Solution If N=1: ← or → (2 configurations/ each length is l) N=2: ← or → or ←← or ←→ or →← or →→ ------→----← (6 configurations/ folded polymer's length is l/2 andunfolded polymer's...
  20. Toby_phys

    Quantum - infinite chain of wells

    An electron can tunnel between potential wells. Its state can be written as: $$ |\psi\rangle=\sum^\infty_{-\infty}a_n|n\rangle $$ Where $|n \rangle$ is the state at which it is in the $n$th potential well, n increases from left to right. $$...
  21. Pushoam

    Tension in a chain with circular motion

    Homework Statement Homework EquationsThe Attempt at a Solution What I know is tension is same in magnitude at all points of the chain along tangential direction due to the symmetry of the system. But how to find it out?[/B]
  22. A

    Velocity transformation using the chain rule

    Homework Statement How to obtain the famous formula of velocity transformation using a chain rule. I know that there is a straightforward way by dividing ##dx## as a function of ##dx`## and ##dt`## on ##dt## which is also a function of them. But I would rather try using the chain rule. Homework...
  23. A

    I Is a Photon Emitted in the Proton-Proton Chain Reaction?

    In the proton chain, a deuteron and proton fuse to make a nucleus of helium 3, releasing 5.493 MeV by E=mc^2. To have the same total momentum before and after fusion, at least two particles must be emitted, right? That way they can "cancel out" some momentum by having roughly opposite...
  24. Mr Davis 97

    Work problem -- raising a chain and load

    Homework Statement Consider a 40-foot chain that weighs 4 pounds per foot hanging from a winch 40 feet above ground level. Find the work done by the winch in winding up the entire chain with a 600-pound load attached to it. Homework EquationsThe Attempt at a Solution ##\displaystyle...
  25. binbagsss

    General relativity, geodesic, KVF, chain rule covariant derivatives

    Homework Statement To show that ##K=V^uK_u## is conserved along an affinely parameterised geodesic with ##V^u## the tangent vector to some affinely parameterised geodesic and ##K_u## a killing vector field satisfying ##\nabla_a K_b+\nabla_b K_a=0## Homework Equations see above The Attempt at...
  26. binbagsss

    Differentiation / Chain rule - Splitting Logarithms

    Homework Statement Use the top line to get 1) and 2) Homework Equations above The Attempt at a Solution So for 2) split the log up using ##log (AB)=log (A) + log (B) ## and this is simple enough I think I may be doing something stupid with 1) though. I have ##\frac{\partial}{\partial...
  27. yecko

    Solving Chain Work Problem: Find mgh | Physics Homework Help

    Homework Statement http://i.imgur.com/TdPWVgr.pngHomework Equations WD=mgh The Attempt at a Solution mass per length=0.8kg/m mgh= ∫(0,10)(0.8g(10-y))dy=[8gy-0.4y^2g](0,10)=80g-40g=40g However, the answer is 20g whats wrong with my calculation? thanks
  28. R

    MAR-6 MMIC amplifier chain saturation?

    Hello. I have devolopped a line amplifier with 3 x MAR-6 MMIC. Normal daisy chain is : antenna followed by a LNA which is followed by my line-amp. If nothing is connected at the input ofLNA, all 3 Mar-6 have normal operating voltage ie 3.5 V and resulting noise is very low (seen with a 100 MHz...
  29. L

    Sprockets, chains, and gears question

    hello. I'm tring to find a compatible sprocket for my chain. I need to know what these abbreviations mean here: http://www.ebay.com/sch/i.html?_odkw=sprocket+40&_sop=15&_osacat=0&_from=R40&_trksid=p2045573.m570.l1313.TR0.TRC0.H0.Xsprocket+40+3%2F4.TRS0&_nkw=sprocket+40+3%2F4&_sacat=0 For...
  30. E

    Chain Sliding on a Pulley: Acceleration and Force Analysis

    Homework Statement On a pulley with a very small radius and negligible inertia, that rotates without friction around its fixed horizontal axis, there is a chain of mass m and length l. The chain starts sliding from its equilibrium position. Let x be the distance between the ends of the chain...
  31. K

    Chain Conveyor Speed Calculation

    Okay this has has been driving me crazy. I would like to know how a conveyor speed can be calculated on the basis of chain pitch, sprocket PCD & no. of teeth and output RPM of gearmotor. So here is a practical example I'm having to solve at the moment: I have to drive a conveyor at a speed of...
  32. B

    I Heavyside step function chain rule

    Hi, I have a probably very stupid question: Suppose that there is an expression of the form $$\frac{d}{da}ln(f(ax))$$ with domain in the positive reals and real parameter a. Now subtract a fraction ##\alpha## of f(ax) in an interval within the interval ##[ x_1, x_2 ]##, i.e. $$f(ax)...
  33. mastermechanic

    Finding the Second Derivative Using the Chain Rule: A Step-by-Step Guide

    Homework Statement Question has been attached to topic. Homework Equations Chain rule. The Attempt at a Solution $$\frac {dy}{dt} . \frac{dt}{dx} = \sqrt{t^2+1}.cos(π.t)$$ $$\frac{d^2y}{dt^2}.(\frac{dt}{dx})^2 = 2 $$ $$\frac{d^2y}{dt^2}.(t^2+1).cos^2(π.t)= 2 $$ and for the t=3/4...
  34. Jr_Particle_Hunters

    B Is our cloud chamber showing correct tracks from U-238 decay chain?

    Hi. We are using a Pb-210 needle source for our cloud chamber science project. Are we correct that the tracks we are seeing inside the chamber radiating off the needle are: 1) Beta tracks from Pb-210 decaying into Bi-210 (in the .063 MeV range) 2) Beta tracks from Bi-210 decaying into Po-210...
  35. K

    B New to Nonlinear Diff. Equations? Ask Here!

    (Sorry for the mistakes first thread using hand held device) Hello, I was working on Harold T. Davis Introduction to Nonlinear Differential and Integral Equations I saw this following equations 1-So equation 4 came as a result of chain rule applies on equation. 3 ? 2- how did equation 5...
  36. Z

    Matrix Chain Multiplication: Optimal way of multiplying

    Hi, I am studying Matrix chain Multiplication to find out the optimal way of multiplying a series of matrices so that we can reduce the number of multiplications. I have got this example from the book which multiplies the matrices having dimensions given below: A1 30 * 35...
  37. Lacplesis

    Prompt neutrons, delayed neutrons, chain reaction control

    Hello, I am reading about this and I have a question , so let me explain how I understood this and please correct where I am wrong. I will ask about nuclear reactors because obviously in bombs only prompt neutrons matter since there is no need for any control only an exponential increase in...
  38. harpazo

    MHB How do I find partial derivatives with fractional exponents in the Chain Rule?

    Given k = ge^(x/y), find ∂k/∂x and ∂k/∂y. The fractional exponent throws me into a loop. Can someone show me step by step how to tackle this problem?
  39. Arman777

    Work Question (Pulling a chain on the Moon)

    Homework Statement At a lunar base,a uniform chain hangs over the edge of a horizontal platform.A machine does ##1.0J## of work in pulling the rest of the chain onto the platform.The chain has a mass of ##2.0 kg## and a length of ##3.0m##.What length was initally hanging over the...
  40. kolleamm

    B Chain rule for variable exponents

    I understand that when you use the chain rule you multiply the exponent by the number in front and then reduce the power by 1. So the derivative of 2x^3 = 6x^2 I'm confused now however on how you would solve something like e^-3x, the answer turns out to be -3e^-3x Am I missing a rule? Why...
  41. bwest121

    I How do I apply Chain Rule to get the desired result?

    I'm reading a textbook that says: "The directional derivative in direction ##u## is the derivative of the function ##f( \mathbf x + \alpha \mathbf u)## with respect to ##\alpha##, evaluated at ##\alpha=0##. Using the chain rule, we can see that ##\frac {\partial}{\partial \alpha} f( \mathbf x...
  42. J

    I Chain rule and change of variables again

    We start with: d2y/dx2 And we want to consider x as function of y instead of y as function of x. I understand this equality: dy/dx = 1/ (dx/dy) But for the second order this equality is provided: d2y/dx2 =- d2x/dy2 / (dx/dy)3 Does anybody understand where is it coming from? The cubic...
  43. S

    A Chain rule - legendre transformation

    let df=∂f/∂x dx+∂f/∂y dy and ∂f/∂x=p,∂f/∂y=q So we get df=p dx+q dy d(f−qy)=p dx−y dqand now, define g. g=f−q y dg = p dx - y dq and then I faced problem. ∂g/∂x=p←←←←←←←←←←←←←←← book said like this because we can see g is a function of x and p so that chain rule makes ∂g/∂x=p but I wrote...
  44. mastrofoffi

    3-species Lotka-Volterra food chain in Hamiltonian formalism

    Hello, I have been assigned to write a report on a topic of my choice for my Computational Physics class, and I chose to focus on the symplectic integration of Hamiltonian systems, in particular the Lotka-Volterra model. A 3-species model(\gamma eats \beta, \beta eats \alpha) is not, unlike the...
  45. Dilemma

    I Applying Chain Rule to a function of two variables

    Hello, Here is the question: I can not figure out how we are to apply chain rule to the second order derivative. May somebody clarify that?
  46. A

    I Evaluate using Leibniz rule and/or chain rule

    I want to evaluate $$ \frac{d}{dt}\int_{0}^{^{\eta(t)}}\rho(p,t)dz $$ where p itself is $$ p=p(z,t) $$ I have the feeling I have to use Leibniz rule and/or chain rule, but I'm not sure how... Thanks.
  47. evinda

    MHB Applying the Chain Rule to Derive Solutions of the Heat Equation

    Hello! (Wave) Suppose that $u(t,x)$ is a solution of the heat equation $u_t-\Delta u=0$ in $(0,+\infty) \times \mathbb{R}^n$. I want to show that $u_k \equiv u(k^2 t, kx)$ is also a solution of the heat equation in $(0,+\infty) \times \mathbb{R}^n, \forall x \in \mathbb{R}^n$. If we have a...
  48. P

    B Why can't a chain rule exist for integration?

    I was thinking if the known methods of integration are enough to integrate any given function. In differentiation, we've evaluated the derivatives of all the basic functions by first principles and then we have the chain rule and product rule to differentiate any possible combination (product or...
  49. D

    Uniform chain rising with constant velocity

    Homework Statement A uniform chain lies in a heap on a table. If one end is raised vertically with uniform velocity v, show that the upward force that mus be exerted on the end of the chain is equal to the weight of a length z + (v^2/g) of the chain, where z is the length that has been uncoiled...
  50. Ryan Hardt

    Calculating Uncertainty for a Chain of Trig Functions

    Homework Statement I have a series of 12 values that I need to calculate the Theoretical Intensity, I, using the formula below. I have found values for all variables and their uncertainties, and have calculated the I value for each set using the formula. Now I need to calculate the...
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