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. deep838

    Work done to pull the entire chain

    Homework Statement A chain of mass 4Kg and length 2m is lying on a table, such that 60 cm of one end is hanging from one edge off the table. Find the work done to pull the entire chain on the table. Homework Equations (anything that'll work i suppose) The Attempt at a Solution I...
  2. J

    Chain rule question: if f is a differentiable function

    If f is a differntiable function, find the expression for derivatives of the following functions. a) g(x)= x/ f(x) b) h(x) [f(x^3)]^2 c) k(x)= sqrt (1 + [f(x)]^2) First off, I am not even sure what they are asking. I am assuming that they want the derivative for each component of the...
  3. R

    Partial derivative and chain rule

    How is the double derivative equal to that in the equation 2 in the attachment? =|
  4. D

    Calculating Time for Sliding Chain through Hole

    Homework Statement A flexible chain of mass M and length L lies on a frictionless table, with a very short portion of its length L0 hanging through a hole. Initially the chain is at rest. Find a general equation for y(t), the length of chain through the hole, as a function of time. (Hint: Use...
  5. I

    MHB The union of an ascending chain of subgroups is a subgroup

    Let $G$ be a group, and $\left \{ H_{i} \right \}_{i\in \mathbb{Z}}$ be an ascending chain of subgroups of $G$; that is, $H_{i}\subseteq H_{j}$ for $i\leqslant j$. Prove that $\bigcup _{i\in \mathbb{Z}}H_{i}$ is a subgroup of $G$. I don't need the proof now. But can you show an example for me...
  6. C

    Proving Linearity of a Function Using Chain Rule

    Homework Statement g:ℝ^{ 2 }\rightarrow ℝ is everywhere differentiable. For all (x,y) and for all t: g\left( tx,ty \right) =tg\left( x,y \right) . Prove g is linear (that there exist constants A, B such that for all (x,y): g\left( x,y \right) =Ax+By . I think my solution is correct, but the...
  7. Saitama

    Find Force to Lift Chain of Length L and Mass ρ Up

    Homework Statement The end of a chain of length L and mass per unit length ρ, which is piled up on a horizontal platform is lifted vertically with a constant velocity u by a variable force F. Find F as a function of height x of the end above platform. A)ρ(gx+2u^2) B)ρ(gx+u^2) C)ρ(2gx+ρu^2)...
  8. H

    Vacuum metastability referenced in Simplified chain inflation and Hubble time

    Vacuum metastability referenced in "Simplified chain inflation" and Hubble time In this paper http://power.itp.ac.cn/~huangqg/Publications/JCAP-Simplified%20chain%20inflation.pdf it is referenced(Ctrl+F 'with the lifetime of the metastable vacua much shorter than the Hubble time') that basically...
  9. T

    Definition of the boundary map for chain complexes

    I've been poking around, learning a little about homology theory. I had a question about the boundary operator. Namely, how it's defined. There's two definitions I've seen floating around. The first is at: http://en.wikipedia.org/wiki/Simplicial_homology The second, at...
  10. K

    D'alembert's solution to the wave equation, on Chain Rule

    Homework Statement Please have a look at the picture attach, which shows the proof of the D'alembert's solution to the wave equation. If you can't open the open, https://www.physicsforums.com/attachment.php?attachmentid=54937&stc=1&d=1358917223 click onto this...
  11. P

    Chain of Similar Pendula (Soltion)

    I have a chain of similar pendula which is mounted equidistantly along a horizontal axis with adjacent pendula being connected with light strings. Each pendulum can rotate within the axis but can not move sideways. at the page http://btakashi.jp/archives/935 scroll to the bottom of the page and...
  12. P

    Partial derivative chain rule for gradient

    Homework Statement compute the gradient: ln(z / (sqrt(x^2-y^2)) Homework Equations ∇=(∂/(∂x)) + ... for y and z I just want to know how to do the first term with respect to x The Attempt at a Solution I am so rusty I don't know where to begin.
  13. B

    Simulating a discrete time markov chain

    Hi, I'm trying to simulate a discrete time time markov chain in matlab. Unfortunately I am neither a markov chain expert or a good MATLAB coder. My problem is simple, I have a transition probability matrix with 100 states (100x100) and I want to simulate a 1000 steps beginning from state 1...
  14. P

    MHB Chain Rule and 'The Mob'....Pretty darn good explanation

    This guy relates the calculus chain rule to a popular mob movie. You should really check it out. This is one of the newer videos but people like the way this guy explains things. Here is the link: Ghetto Dude Relates Calculus Chain Rule To "THE MOB" - YouTube
  15. Astrum

    Question about the application of the chain rule

    Air is being pumped into a spherical balloon at a rate of 5 cm3/min. Determine the rate at which the radius of the balloon is increasing when the diameter of the balloon is 20 cm. So, to solve, I know HOW to do it, I just don't know WHY it's right. \frac{dv}{dr}=4pi r^{2}...
  16. S

    Exploring the Relationship Between the Chain Rule and Tangent Vectors

    Homework Statement Show that: \frac{dx^\nu}{d \lambda} \partial_\nu \frac{dx^\mu}{d \lambda} = \frac{d^2 x^\mu}{d \lambda^2} The Attempt at a Solution Well, I could simply cancel the dx^nu and get the desired result; that I do understand. But what about actually looking at...
  17. A

    Taylor's approximation formula for an IVP and the chain

    Homework Statement f(x,y) = y' = \frac{y+x^2-2}{x+1} , y(0) = 2 Write the formula for the 2nd order Taylor approximation I just want to ask a question Homework Equations Taylor seriesThe Attempt at a Solution Taylor: y(x) = y(x_0) + y'(x_0)(x-x_0) + \frac{y''(x_0)(x-x_0)^2 }{2} = \\...
  18. B

    Contracting over indices chain rule

    Homework Statement As part of a problem I am doing I am asked to show uβ∂βuα = aα where u is 4 velocity and a refers to 4 acceleration. The way to do this is not immediately obvious to me, especially since the problem implies there should be a chain rule step involved which I am not seeing. I...
  19. M

    General first-order markov chain of 2 states

    Hi, Hope you can give me an answer regarding this trellis diagram. why in this picture of a general first-order markov chain of 2 states,we should know the prob. of each state at each time? A general first-order markov chain, can be Time-dependent(non stationary) so Transition prob. can change...
  20. P

    Partial derivative chain rule proof

    Homework Statement If u=f(x,y) where x=escost and y=essint show that d2u/dx2+d2u/dy2 = e-2s[d2u/ds2+d2u/dt2 Homework Equations http://s11.postimage.org/sjwt1wkvl/Untitled.jpg The Attempt at a Solution ok i don't understand how they got to that i don't know what d/ds is...
  21. B

    Chain Rule Trig Derivative Problem

    Homework Statement Find the derivative of y = sin(πx)2 Homework Equations Chain Rule: y' = f'(u) * u' The Attempt at a Solution (See attached image) The answer according to the textbook is 2π2xcos(πx)2. What am I doing wrong here?
  22. T

    Chain Rule Exercise: Find dg/dx + dg/dy

    Homework Statement Suppose g(x,y)=f(x-y,y-s) Homework Equations Nothing else The Attempt at a Solution Find dg/dx + dg/dy
  23. fluidistic

    Probability of Finding a Random Walker in D Dimensions After N Steps

    Homework Statement Hi guys, I'm absolutely desperate on the following problem: Consider a random walker who can make steps only to neighbor sites in "D" dimensions where D is an arbitrary natural number. Assume that the distance between 2 adjacent sites is the same for all sites and that the...
  24. D

    Bloch function of an infinite, 1-D linear chain of dz2 orbitals.

    Homework Statement Consider an infinite, one-dimensional linear chain of dz2 orbitals separated at a distance a. Write an expression of the BLOCH FUNCTION that describes this chain. Homework Equations ψk=Ʃexp(ikna)χn The Attempt at a Solution I read this...
  25. W

    What is the Velocity of the Last Angstrom in the Falling Chain Problem?

    Homework Statement the question is about a very flexible strain falling on a rigid table and ask for expression of normal reaction of table at a certain instant Homework Equations when i was trying to solve problem , i resolve N(normal reaction) into N1, N2 which N2 is the weight of...
  26. L

    Showing this Euler's equation with a homogeneous function via the chain rule

    Homework Statement Ok I have this general homogeneous function, which is a C^1 function: f(tx,ty)=t^k f(x,y) And then I have to show that this function satisfies this Euler equation: x\frac{\partial f}{\partial x}(x,y)+y\frac{\partial f}{\partial y}(x,y)=k\cdot f(x,y) Homework...
  27. F

    One dimensional spring chain and density of states

    I have a classic infinite, linear chain of atoms, each of mass m, each separated by a spring with spring constant b and equilibrium distance a between each adjacent one. I know from my textbook that the dispersion relationship you get for this is: \Omega(k) = 2\sqrt{\frac{b}{m}} |sin(ka/2)|...
  28. T

    [Astro] Proton-Proton Chain Energy

    Homework Statement Find the energy released for the reactions in the Proton-Proton chain. Homework Equations Proton-Proton Chain: 1H + 1H -> 2H + e+ + v e+ + e- -> γ + γ 2H + 1H -> 3He + γ 3He + 3He -> 4He + 2 1H The Attempt at a Solution To find the energy released in each...
  29. S

    Multivariable Chain Rule of sin(x)cos(2y)

    Hi all, I've got a Calculus III Question Homework Statement Find the derivative zs and zt, where z=sin(x)cos(2y)Homework Equations x=s+t y=s-t The Attempt at a Solution I had a go at the solution and this was what I ended up getting for zs, I ended up getting (cosxcos2y)(1)-2sinxsin2y(1)...
  30. J

    Implicit Differentiation, chain rule, and simplifying

    Okay so, I am having trouble figuring out what exactly to do in implicit differentiation and usage of the chain rule. Like, I keep getting the wrong answer somehow. See, from what I understand you have to find the derivative of both sides then use the chain rule or something and then solve for...
  31. STEMucator

    Is the Chain Rule Application for Second Partial Derivatives Correct?

    Homework Statement I'm curious to know if I'm actually doing this correctly. Suppose f(x,y) is a function where x = p(s,t) and y = g(s,t) so that w(s,t) = f(x,y). Compute ws and then wst Homework Equations Chain Rule. The Attempt at a Solution So! Let's compute ws first. Whenever I use a...
  32. D

    Confusion on the chain rule

    Let g(t) = f(tx, ty). Using the chain rule, we get g'(t) = (\frac{\partial f}{\partial x})(tx, ty) * x + (\frac{\partial f}{\partial y})(tx, ty) * y this was actually part of a proof and what i don't understand is that why didn't they write (\frac{\partial f}{\partial (tx)}) and...
  33. J

    Evaluate partial derivative. chain rule?

    Evaluate partial derivative. chain rule?? I would like to represent the term identified in the image as (term 1) in terms of those partial derviatives that are known. Unfortunatly I just can't seem to wrap my head around it at the moment. :bugeye: A prod in the right direction would be...
  34. J

    Calculating force between links in a chain

    A chain consisting of five links, each of mass 0.145 kg, is lifted vertically with a constant acceleration of a = 2.6 m/s2. Consider the force link 3 exerts on link 2. (Chains are numbered 5 to 1 going down) Find the magnitude of this force. F=ma I don't know what to consider...
  35. C

    How Do You Apply Chain Rule for Functions in Polar Coordinates?

    Homework Statement Given that f(x,y) = g(r,\theta), where x = r\cos\theta and y = r\sin\theta, find formulae for \frac{∂f}{∂x} and \frac{∂f}{∂y} expressed entirely in terms of r, \theta, \frac{∂g}{∂r} , \frac{∂g}{∂\theta} . The Attempt at a Solution I said \frac{∂f}{∂x} =...
  36. D

    MHB Chain rule partial derivatives

    $x = r\cos\theta$ and $y=r\sin\theta$ $$ \frac{\partial u}{\partial\theta} = \frac{\partial u}{\partial x}\frac{\partial x}{\partial\theta} + \frac{\partial u}{\partial y}\frac{\partial y}{\partial\theta} = -r\sin\theta\frac{\partial u}{\partial x} + r\cos\theta\frac{\partial u}{\partial y} $$...
  37. P

    Dna chain termination sequencing

    Homework Statement A DNA 5-[32P] CCT TCG T TCG TTG TTC CCT A GGC TGT ATA GCC CCT ACC TTT TTG GTA GGG GCT ATA CAG CC was elongated by DNA polymerase in four reaction mixtures in the presence of dATP, dTTP, dGTP (dCTP was omitted due to an experimental mistake) and one ddNTPs. The four reaction...
  38. T

    Trying to find force on a chain.

    I am trying to find out how much force is being transferred into a drive chain. Here's the info as I was given: Motor: 150HP RPM: 1750 Gearbox information: ratio: 39:44 Input HP 223 Output shaft to sprocket 6" dia. Sprocket 20" dia. Top of tooth to bottom of root 1-3/8" 4" pitch of chain No...
  39. T

    Accelaration of the chain as a function of x

    Homework Statement A uniform flexible chain of length L ,with weight per unit length λ , passes over a small frictionless peg..It is released from a rest position with a length of chain x hanging from one side and a length L-x from the other side .Find the accelaration a as a function of x...
  40. W

    Two main drives in one chain conveyor

    Hi, Is it possible to install two main drives in one chain conveyor to boost up the chain conveyor speed? If possible how to synchronize between the two main drive motors. The motors will control by inverter. Thanks!
  41. S

    Partial Derivates - Chain Rule

    Homework Statement Parametrize the upper half of the unit circle by x = cos(t), y = sin(t), for 0\leq t \leq\pi Let T = f(x,y) be the temperature at the point (x,y) on the upper half of the circle. Suppose that: \frac{\partial T}{\partial x} = 4x - 2y \frac{\partial T}{\partial y} = -2x +...
  42. H

    Chain falling on weighing scale-find total reading

    Homework Statement A chain of length l, mass M falls on a weighing scale vertically down. We need to find the reading of the scale when a length 'x' has fallen on the scale. Homework Equations F= dP/dt W=Mg dm= (M/l)x dm/dt=m(v^2)/l The Attempt at a Solution So initially, I...
  43. H

    Systems Engineering and Management MS or Supply Chain Analyst MS?

    Straight up, I want to be a Chief Office eventually. I can concentrate the SEM MS into many categories--probably choosing healthcare for a few reasons--including their high salary and necessity. However, what about Supply Chain Management...honestly, I don't like the idea of working in a...
  44. B

    Chain rule with partial derivatives and divergence

    say you have a function f(x,y) \nablaf= \partialf/\partialx + \partialf/\partialy however when y is a function of x the situation is more complicated first off \partialf/\partialx = \partialf/\partialx +(\partialf/\partialy) (\partialy/\partialx) ( i wrote partial of y to x in case y was...
  45. V

    Explaining Chain Rule: vdv/dx=1/2(dv^2)/dx

    ok stupid question probably- take v(velocity) to be a function of x and x to be a function of t(time). then dv/dt=vdv/dx that's cool but in the hint in problem 2.12 classical mechanics by john r taylor he equates vdv/dx and 1/2(dv^2)/dx that is- vdv/dx=1/2(dv^2)/dx Could someone please...
  46. L

    Why does a rotating chain become horizontal?

    Hi Homework Statement A chain rotates fast. Observation: the chain gets into a horizontal position. Why? Homework Equations L=I \omega E= \frac 1 2 I \omega² E=\frac 1 2 \frac {L²} I The Attempt at a Solution Well, I have two equations for the energy. I know that I...
  47. T

    Chain Problem involving Kinetic Friction

    Homework Statement A heavy chain with a mass per unit length ρ is pulled by the constant force F along a horizontal surface consisting of a smooth section and a rough section.The chain is initially at rest on the rough surface with x=0 .If the coefficient of kinetic friction between the...
  48. DeusAbscondus

    MHB Solving Chain Rule Problems with e^(u): An Explanation for Beginners

    Hi folks, I don't know if my experience is at all common (and I would like some feedback on this if possible), but I can't seem to nail down the properties of euler's number in the context of chain rule problems. Here is the nub of my difficulty: 1. $\text{If }f(x)=e^x \text{then }f'(x)=e^x$...
  49. DeusAbscondus

    MHB Chain rule problem and choice of notation

    I have attached a pdf setting forth my question. This is a write up of a lesson i just had on yourtutor, in which i think the tutor might have made an error: this is a direct quote from the whiteboard: $Let g(x)=2x, f(y)=e^y\Rightarrow(fog)(x)=f(g(x))=f(2x)=e^{2x}$$\\Now...
  50. V

    Impulsive force due to a falling chain

    A uniform chain of mass M and length L is held in vertically in such a way that its lower end just touches the floor. The chain is released from rest in this position. Any portion that strikes the floor comes to rest. Assuming that the chain does not form a heap on the floor, calculate the force...
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