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. M

    Tension in Chain in Multiple Pulley Station

    This is for a graded online homework due at 11. I got everything else on it right, but this is giving me trouble for some reason. We get to resubmit answers once, and my first answer of 215.6N was wrong Question: The pulley system in the figure is used to lift a crate of mass m = 44 kg. Note...
  2. M

    Why Chain Rule for Differentiating f(u) = e1/u?

    Differentiate the function: f(u) = e1/u So, I used the chain rule and figured out that f '(u) = (-u-2) e1/u My question is, why do you have to use the chain rule? I know that if f(x) = ex then f '(x) = ex Why can't I pretend that 1/u is x and then say that f '(x) = ex = e1/u In...
  3. V

    Aptitude for Supply chain Management & Logistics

    I have an aptitude test in a Suppy chain management Company for the post of Software developer ( fresher). What kind of questions should I expect? Thanks !
  4. Pengwuino

    Efficiency of Eating Grass & Produce to Reach 2000kcal Daily

    I've always heard (from professionals as well) that each step in a food change has a roughly 10% efficiency rate. That is, you earn 10% of the energy the lower chain animal/plant earned when it ate/did whatever. Now my question is in regards to what you hear a lot of hippie-types say: Humans...
  5. J

    Find Forces at Hooks on 42N Flexible Chain

    A flexible chain weighing 42.0 N hangs between two hooks located at the same height (Fig. P12.19). At each hook, the tangent to the chain makes an angle = 41.5° with the horizontal. (a) Find the magnitude of the force each hook exerts on the chain. (b) Find the tension in the chain at its...
  6. T

    Why is U235 used for chain reaction but not U238

    i want to ask why only U235 is used for the chain reaction but not used U238
  7. J

    Calculating dQ/dt: Chain Rule Applied

    Question: Let Q = \sqrt{x^2 + y}e^t where (for t > or = 0) x = \sqrt{1 - e^{-2t}} and y = 2 - e^{-2t} Using the chain rule calculate dQ/dt, expressing your answer in as simple a form as possible. My work so far Subbing in values of x and y: Q = \sqrt{1 - e^{-2t} + 2 - e^{-2t}}e^t =...
  8. E

    Trig step in a chain rule question

    I need to show that two equations equal one another. It's too complicated to display fully on here but I'm stuck on a step: dF/dr = df/dx cos2(h) + df/dy sin(h) (dF/dr)^2 = (df/dx)^2 cos^2(h) + (df/dy)^2 sin^2(h) Does anybody know how to get rid of the cos squared and sin squared...
  9. U

    Chain Rule Help: Solving (g o f)'(4) with f'(8)=5, g'(8)=3, f(4)=8, and g(4)=10

    f '(8)=5 g '(8)=3 f(4)=8 g(4)=10 g(4)=10 g(8)=2 f(8)=5 find (g o f)'(4) how do I go about setting up these types of problem.
  10. B

    Stationary points and chain rule

    Hi, I would like some help verifying the nature of a stationary point of the following function of two variables. f\left( {x,y} \right) = \sin \left( x \right) + \sin \left( y \right) + \sin \left( {x + y} \right) Ok so I equated grad(f) to zero and solved for x and y. I got three...
  11. O

    Chain falling off a table-Lagrange Method

    Chain falling off a table--Lagrange Method Chain of length L and mass M with uniform linear mass density slides off a frictionless table with dimensions L x L x L. Find the Lagrangian that describes this system. Then find the time when the last length leaves the table top. I'm thoroughly...
  12. G

    Normal modes of diatomic linear chain

    Hello, I'm preparing for my condensed matter exam and I'm trying to solve problem 3a) of chapter 22 in Ashcroft & Mermin. The problem is basically to prove that the dispersion relation of a diatomic linear chain will reduce to the monoatomic one when the coupling constants are equal...
  13. B

    Exploring the Matrix Version of the Multivariable Chain Rule

    Hi, does anyone know of any websites which have some theory and perhaps some examples of the matrix version of the chain rule. Neither of the books I have covers this particular topic so I'd like to read up on it. Any help would be appreciated thanks.
  14. N

    Mastering the Chain Rule for Complex Derivatives

    I understand hhow to use the chain rule for a simple 2 part composite function, however, I tend to have problems when it gets past that. Can someone please help me master these complex derivatives, or just a few quick tips would be nice --Thanks
  15. B

    Proving Change of Variables Formula for Double Integral w/ Chain Rule

    Hi, I'm having trouble understanding the solution to a question from my book. I think it's got something to do with the chain rule. The problem is to prove the change of variables formula for a double integral for the case f(x,y) = 1 using Green's theorem. \int\limits_{}^{} {\int\limits_R^{}...
  16. T

    Understanding the Chain Rule in Multivariable Functions

    Hi, here is what I'm trying to do: Find \frac{\partial}{\partial x} f(2x, 3y) First of all, I'm confused by the f(2x, 3y) How does the function look like? I imagine that it is for example f(x,y) = cos(xy) - sin(3xy^2} and that therefore f(2x, 3y) = cos(6xy) - sin(54xy^2) I'm...
  17. J

    Using the Chain Rule to Differentiate f(g(x^2))

    I'm a little confused as to when to stop taking the derivative of the inside function when using the chain rule... Lets say I have f( g(x^2) ) Would this be correct? f`( g(x^2) ) * g`(x^2) * 2x ? Or do I keep on going until the x is completely gone from the equation?
  18. D

    When should the Chain Rule be applied for finding derivatives?

    I've been having some trouble grasping the conditions necessary to apply the chain rule to achieve the derivative of an algebraic expression or even apply it to a real world situation. So, my question to those skilled in qualitatively explaining the conditions for applying the Chain Rule and...
  19. N

    How Do You Apply the Chain Rule to Differentiate f(x) = x^5(4^(x^2))?

    I'm so confused. I have to find the derivative of f(x) = x^5(4^(x^2)). All of the powers are messing me up. Any help would be much appreciated. Thanks!
  20. D

    Efficient Composition of Functions for the Chain Rule Problem

    I have the function: y=\sqrt{x+\sqrt{x+\sqrt{x}}} I need to find separate, smaller functions which will result in the composition of this function. I tried but all I ended up with was: f(x)=\sqrt{x} g(x)=x+\sqrt{x+\sqrt{x}} Therefore, y=f(g(x)) However, this is obviously a...
  21. R

    Using the chain rule with 2 variables ?

    Hey, I am a bit confused oh how to use the chain rule when i have 2 variables in an equation... Example : f(x,y) = (Squareroot(x)).(cosh(x+y^2)) x(s,t)=st y(s,t)=s/t When i have 2 variables, I am not sure how to split it up and use the chain rule, all the examples i found only have 1...
  22. M

    Chain rule confusion partial derivatives

    Hello everyone... I'm very confused... i'm suppose to find dz/dt and dw/dt but for some of the questions there is no w variable! so what do u put for dw/dt?! Also i have the following: w = xy + yz^2; x = e^t; y = e^t*sint; z = e^t*cost; so I'm trying to find dz/dt and dw/dt; dz/dt =...
  23. F

    Chain Rule Differentiation

    h = 3x^2.y^3 find dh/dt, if x=1, and y=2 Also, dx/dt = 0.2, dy/dt = 0.1 Any ideas where i should start in order to get this out? Thanx
  24. R

    Struggling to Solve Chain Rule Problem: Help Appreciated!

    I'm thoroughly confused as to how and work this problem. I thought I had an ok understanding of the chain rule when I started the section's homework, but this question has me ready to gorge out my eyeballs! The Problem: --------------- Find:dy/dx at x = 2 Given: y = (s+3)^2, s = sqrt(t-3)...
  25. S

    Modeling Forces in Free Falling Chain Problem

    A chain of mass M and length L is suspended vertically with its lowest end touching the scale. The chain is released and falls ono the scale. What is the reading of the scale after a length x of the chain has fallen? So what I really have to find is the force applied by the string onto the...
  26. W

    Master the Chain Rule with These Easy Steps - Check Your Work for Accuracy!

    chain rule agian - check my work please w = -xy-5yz+3xz, x = st, y = exp(st), z = t^2 dw/ds(5,-2) = ________________________ here's what i did: dw/ds = dw/dx*dx/ds + dw/dy*dy/ds + dw/dz*dz/ds dw/ds = (3z-y)*(t) + (-x-5z)(exp(st)*t) + (3x-5y)(0) plug in x,y and z... dw/ds =...
  27. W

    How Do You Evaluate dw/dt at t=0 Using the Chain Rule Results?

    Suppose w = x/y + y/z x = exp(t), y=2+sin(5t), and z= 2+cos(7t) A.) Use the chain rule to find dw/dt as a function of x, y, z, and t. Do not rewrite x, y, and z in terms of t, and do not rewrite exp(t) as x. I got this one right, the answer is 1/y*exp(t) +(- x/y^2+1/z)*(5*cos(5t)) +...
  28. G

    Work required to pull a hanging chain

    A chain is held on a frictionless table with one-fourth of its length hanging over the edge. If the chain has length L= 28 cm and mass m=0.012 kg, how much work is required to pull the hanging part back onto the table? I have used this model: W horizontal + Work due to gravity = Work...
  29. M

    I found a proof for the vector chain rule, but it makese no sense to me

    Hello everyone, our professor wanted us to find the vector chain rule proof and i found one here: http://web.mit.edu/wwmath/vectorc/scalar/chain.html But it makes no sense to me, where are the limits?
  30. A

    Stumped Calc Students: Can You Solve This Diff. Equation?

    This is a problem that has stumped my entire class of Calc 1 students and two Calc 2 students. Find \frac {dy} {dx} y = \frac {(2x+3)^3} {(4x^2-1)^8} I know that the answer is (from the textbook, but I don't know how it got there) -\frac {2(2x+3)^2(52x^2+96x+3)} {(4x^2-1)^9}...
  31. I

    Is my Multivariable Chain Rule Derivation Correct?

    Please let me know if I derived this correctly (I did it a while back, and can't find the notebook): v(x,y)=u(r(x,y),s(x,y)) (derivations) At some point I come across this: \frac{\partial}{\partial x} \frac{\partial u}{\partial r} which I wrote as \frac{\partial^2 u}{\partial...
  32. T

    Chain rule substitution help

    Let f: \Re^3 \rightarrow \Re be differentiable. Making the substitution x = \rho \cos{\theta} \sin{\phi}, y = \rho \sin{\theta} \sin{\phi}, z = \rho \cos{\phi} (spherical coordinates) into f(x,y,z), compute (partially) df/d(rho), df/d(theta), and df/d(phi) in terms of df/dx, df/dy...
  33. Orion1

    Why Did Euler Choose 'e' for His Famous Chain Theorem?

    Expired Thread... Expired Thread...
  34. E

    How To Choose A Sprocket Chain

    How I can choose a chain's sprockets for my Mechanical System ... Please need Sprocket's Tables Depending On Shafts Daimeters Or The Power . For Example If I have 35 mm shaft Need any tables for that ...
  35. N

    Is My Chain Rule for Limits Proof Correct?

    I would like to prove a chain rule for limits (from which the continuity of the composition of continuous functions will clearly follow): if \lim_{x\to c} \, g(x)=M and \lim_{x\to M} \, f(x)=L, then \lim_{x\to c} \, f(g(x))=L. Can someone please tell me if the following proof is correct? I am...
  36. J

    How does the product and chain rule apply to this problem?

    Could someone please help me, I do not understand how the author of my textbook gets from one point to another. Here is the problem worked out, after the problem I will explain which part I don't understand. f(x)=x(x-4)^3 f'(x)=x[3(x-4)^2]+(x-4)^3 =(x-4)^2(4x-4) I do not understand how...
  37. C

    Chain rule in functions of two variables

    Please help me on this. I am trying to make and exercise from an author M.D. Hatton (an english). Let x = x(r, w) = r. cos (w) Let y = y(r,w) = r. sen (w) Let V = V(x,y). So V depends on r and w. By chain rule (I put "d" for the partial derivative) dV = dV . dx + dV. dy --...
  38. E

    Understanding Partial Fractions and the Chain Rule in Integration

    Hi, I have 2 questions: 1. partial fractions: if I have following integral: Itegral[(1-2x^2)/(x - x^3)]dx; my question is do I break down the denominator to x(1-x^2) or do I go further: x(1-x)(1+x); this way it becomes more complicated; 2. chain rule: how does chain rule work in this...
  39. Cyrus

    The Chain Rule, death to anyone that breaks the rule

    Ok so I am reviewing multivariable now that i have some time; (why is it taking me so long to grasp some of these concepts!? :mad: ) anyways, and I am reading the proof of stokes theorem. The book I use is Stewart, but it seems to be ripped off word for word from swokowski, which in turn rippes...
  40. S

    Information needed on two wheels and chain apparent paradox in SR

    I hope someone can point me to some information to assist resolving this apparent SR paradox. I have two gear wheels with an endless chain passing round them. The axles of the wheels are 100 chain_link_lengths apart, so we have 100 chain links along the top; 100 chain links along the bottom...
  41. Z

    Calculating Probability of Markov Chain State in Discrete Time

    Let \left( {X_n } \right)_{n \ge 0} be a Markov chain (discrete time). I have {\bf{P}} = \left[ {pij} \right]_{i,j} = \left[ {P\left( {X_1 = j|X_0 = i} \right)} \right]_{i,j}, and the initial probability distribution {\bf{p}}^{\left( 0 \right)}. I need to calculate P\left(...
  42. J

    Electrophoresis: SingleStrain vs DoubleStrain DNA chain speed

    Why does single strain DNA moves slower then double strain DNA in gel electrophoresis? I think that it is because single strain DNA has less electrical charge than double DNA helix, and single strained binds with H bonds uncharged molecules thus increasing it’s mass.
  43. I

    Can I Prove the Chain Rule with the Definition of a Total Differential?

    If I was trying to prove the chain rule for partial derivatives, can I start with the definition of a total differential? What I mean is: Let f(x,y)=z where x=g(t) and y=h(t). I'm looking for \frac{dz}{dt}. By definition, dz = \frac{\partial z}{\partial x}dx + \frac{\partial...
  44. N

    Solving the Puzzling Physics Problem: Chain Falling Off Table

    I have this question which is confusing as it should be harder than it appears... A uniform chain of length L lays on a frictionless table top. Suppose one link just hangs over the table's edge so that the chain begins to fall. Let x be the amount of chain that has fallen. What is the...
  45. G

    Finding Resistance in Infinite Chain of Resistors

    Consider the above infinite chain of resistors. Calculate the effective resistance, R in ohm of the network between the terminals A and B given that each of the resistances labelled r=4180 ohm. I've split the resistor and I've done R^2-Rr-r^2=0, solving for R and I don't get the right...
  46. T

    Bicycle Chain: Exploring Force, Torque & Improvement

    Hi again. So, my teacher has requested that we do an explanation of how this chain works and to some how improve the method. http://home.comcast.net/~p.jectz/bike.jpg There's the basic idea with the force acting downwards and the teeth of the chain pulling. So we could find torque to...
  47. M

    What is the Connection Between the Chain Rule and Differentials?

    Hi, I've seen a couple of proofs for the chain rule, and I know this probably sounds stupid, but I'm wondering why it can't be proved as follows: given the real valued functions y=f(u), u=g(x) since dy, du, dx, are all real valued functions as well can't you just state...
  48. J

    Question: localised mode, localisation effect of linear atomic chain

    urgent question: localised mode, localisation effect of linear atomic chain Hello everyone, it is great place you have here, hope I can learn a lot from you I am doing some readings and there are couple of concepts that I haven't been familiar with and if you spend a little time to help me...
  49. J

    Ly : localized modes in linear chain and localization effects

    urgently need help: localized modes in linear chain and localization effects Hello everyone, it is great place you have here, hope I can learn a lot from you I am doing some readings and there are couple of concepts that I havent been familiar with and if you spend a little time to help me...
  50. M

    Why Does a Chain Snap Between Train Cars at High Speeds in Relativity?

    I have been informed that if: There is two train cars connected by a chain that will snap if extended by more than 1%. The cars accelerate at exactly the same rate, so the distance between them remains constant. As they speed up to very high velocity and special theory of relativity start...
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