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
Homework Statement
Find
\frac{\partial z}{\partial y} [/itex]
where z=F(u,v,y), u=f(v,x), v=g(x,y).
The Attempt at a Solution
If I remember multivariate calculus at all, this should be (please forgive the abuse of notation)
\frac{\partial z}{\partial y} = \frac{\partial z}{\partial...
I want to simulate the (probably chaotic) two dimensional movement of a chain, given that there is no gravity, and all of the links of the chain have some constant mass. Additionally, there is an assumption that the chain cannot collapse - all of the links of the chain will always be touching at...
I wrote a program to find the percent of each element in the decay chain for U238 after a certain amount of time. I used the Bateman equations for serial decay chain below:
N_n(t)= \frac{N_1(t)}{\lambda_n } \sum_{i=0}^n \lambda_i \alpha_i \exp({-\lambda_i t})
\alpha_i=\prod_{\substack{j=1 \\...
Hi
I've just been reading something which is essentially how to work out what the deriviative of y=b^x is.
Basically the explanation gets to the point which I understand and says
\frac{dx}{dy} = \frac{1}{yln(b)}
It then says because of the chain rule you can simply flip this to get...
http://www.youtube.com/watch?v=xePgC8wHDXI&playnext_from=TL&videos=7LWJAQz6KJ8
Maybe the world really is going to end in 2012 with people running around raising their kids like that.
Homework Statement
express (\frac{\partial u}{\partial s})_{v} in terms of partial derivatives of u(s,t) and t(s,v)
Homework Equations
The Attempt at a Solution
I'm pretty stuck with this problem. I know that
dv = (\frac{\partial v}{\partial s})_{t} ds + (\frac{\partial...
Homework Statement
The derivative of the function
h(x) = sin((x2 + 1)2)Homework Equations
Chain Rule
The Attempt at a Solution
h(x) = sin((x2 + 1)2)
f(u) = sinu^2, f'(u)= 2ucosu^2
g(x) = x^2+1 g(x)= 2xI get lost putting this back together but:
2(sinu^2)[cos(sinu^2)^2](2x) ?
Homework Statement
A winch is positioned on top of a building, a distance 70 m above ground level. A chain of length 95 m and a mass per unit length of 1.2 kg/m hangs from the winch along the side of the building. Find the work done (in Joules) in reeling up 60 m of the chain.Homework...
Homework Statement
What is the resistance of the (semi-)infinite resistor chain below, between points A and B, if R = 25 ohms?
The Attempt at a Solution
I am not sure where to begin exactly, but I am thinking of this formula:
VAB=VB-VA=∑ε-∑i.R
or...
chain rule someone help please
1. let z=y^2-x^2cosy; x=t^3 y=cost, find dz/dt
2. let z=(x-y)^3;x=u+2v,y=2u-v,find dz/dvmy attempt:
so i know the chain rule is (dz/dx)dx+(dz/dy)dy
1. should i substitute the x and y into t first or should i do the partial derivative first?
2. same thing what...
Homework Statement
We say that a differentiable function f : \mathbb{R}^n \rightarrow \mathbb{R} is homogenous of degree p if, for every \mathbf{x} \in \mathbb{R}^n and every a>0,
f(a\mathbf{x}) = a^pf(\mathbf{x}).
Show that, if f is homogenous, then \mathbf{x} \cdot \nabla f(\mathbf{x}) = p...
Homework Statement
A chain consisting of two links, each of mass 0.5 kg, is lifted vertically with an acceleration of 3.0 m/s2 upward.
The magnitude of the downward force exerted on the top link by the bottom link is?
Homework Equations
F = ma
The Attempt at a Solution
1 is...
Homework Statement
If T is implicitly defined via the relationship f(x, y, z, T) = 0 to be a differentiable function of x, y and z, show that the first partial derivative of T with respect to z can be found using:
\frac{\partial T}{\partial z} = -\frac{\partial f}{\partial z} / \frac{\partial...
Homework Statement
Suppose the differentiable function f(x,y,z) has the partial derivatives fx(1,0,1) = 4, fy(1,0,1) = 1 and fz(1,0,1) = 0. Find g'(0) if g(t) = f(t2 + 1, t2-t, t+1).Homework Equations
The Attempt at a Solution
Ok I'm given the solution for this and I'm trying to work through it...
Homework Statement A chain in the shape of y = x^{2} between x = -1 and x = 1, has density of |x|. Find M, and CM.
Homework Equations
The Attempt at a Solution
\int^{1}_{-1}|x|dx = \int^{0}_{-1}-xdx + \int^{1}_{0}xdx = 1
I got this far and realized that I did nothing with...
Not sure if this is in the right subforum but:
A chain of uniform mass density, length b, and mass M hangs in a loop from the ceiling (both its ends are adjacent to each other) At time t = 0, one end, end B is released. Find the tension in the chain at point A after end B has fallen a distance...
If I have u = u(x,y) and let (r, t) be polar coordinates, then
expressing u_x and u_y in terms of u_r and u_t could be
done with a system of linear equations in u_x and u_y?
I get:
u_r = u_x * x_r + u_y * y_r
u_t = u_x * x_t + u_y * y_t
is this the right direction? Because by...
Homework Statement
n=y*sqrt((V)/(v*x) and Q=sqrt(v*V*x)*f(n)
so i have V=-dQ/dx=(dQ/dn)*(dn/dx) and the final answer is V=(1/2)*sqrt((v*V)/x)(n*df/dn-f)
Homework Equations
The Attempt at a Solution
i have tried diff. by hand and also by maple and cannot get the answer. What am i...
I have a function F(u,v) that I need to get first and second order partial derivatives for (Gradient and Hessian). F(u,v) is very ugly, so I'm thinking of it like F(x,y,z) where I have another function [x,y,z]=G(u,v).
So, I got my first orders, e.g.:
dF/du = dF/dx*dx/du + dF/dy*dy/du +...
A water distribution company in southern California gets its water supply from the north and sell it back to its customers in Orange county. Assume the following simplified scheme: 3 MG (millions of gallons) of water arrives from the north at the beginning of the month. The company can store up...
Okay so I'm doing chain rule work to go over the stuff from calc 1 before I take a departmental exam and I've run into this problem:
Homework Statement
Take the derivative of:
f(x) = \frac{sin(x^2)}{ln sinx}
Homework Equations
Here's the formula I used (and always do) for the...
Homework Statement
A 20 m length of chain weighing 2.0 N/m is hung vertically from one end on a hook.
Answer in Newtons
1.What is the tension three quarters of the way up?
2.What is the tension 1 m from the top?
3.What is the tension 1 m from the bottom?
Homework Equations
F...
In a simple electric circuit, Ohm's law states that V = IR, where V is the voltage in volts, I is the current in amperes, and R is the resistance in ohms. Assume that, as the battery wears out, the voltage decreases at 0.03 volts per second and, as the resistor heats up, the resistance is...
Ok, I had a homework problem that I cannot for the life of me, figure out. I've tried to google for different sources that would show me how to find the stationary distribution of a markov chain, but I can't seem to find one that makes sense to me.
The transition matrix of a markov chain is...
Homework Statement
f(x) = ((x^2+2)^2)/(x+2)^1/2
Use the chain rule to find the derivative
Homework Equations
None
The Attempt at a Solution
((x^2+2)^2)(x+2)^-1/2
PS: Answer in the book is 3x((x^2+2)^1/2)
I have no idea how they get it there, would like some help, thx!
Hello hello. In class we went over the ''mini-chain rule'' once, and haven't gone over the real chain rule yet. I really want to understand how to go about solving this equation, and to really understand what is happening here.
x=u3-3uv2
y=3u2v-v3
z=u2-v2
Define z as a function of x and...
Homework Statement
Problem 5 from: http://www.swccd.edu/~jveal/phys274/images/hw01.pdf in case you don't understand my text.
A chain of linear mass density u, and length L is hang-
ing from a ceiling. There is a wave moving vertically
along its length. a) Is the propagation speed...
I looking for help on a problem I am trying to solve here at work. I am not an ME, so my mechanics knowledge is low. This isn't helped by the fact that my mechanics class was 13 years ago. I have a label applicator that is not geared correctly, so it runs slower than the wrapper that it is...
Homework Statement
z=f(x,y)
x=escos(t)
y=essin(t)
show d2z/dx2+d2z/dy2 = e-2s[d2z/ds2+ d2/dt2
Homework Equations
dz/dt=dz/dz(dx/dt)+(dz/dy)dy/dr
The product rule
The Attempt at a Solution
I found d2x/dt2=2e2ssin(t)cos(t)d2z/dydx + e2scos2(t)dz/dy2
But, now I'm...
Homework Statement
What would happen to the level of ATP synthesis in the respiratory chain if you make the intermembranal space more acidic more acidic? What if it were made more basic?
Homework Equations
The Attempt at a Solution
ATP synthesis is triggered by chemiosmosis - the flow of H+...
I stumbled upon this document that discusses the single variable chain rule:
http://math.rice.edu/~cjd/chainrule.pdf
At the bottom, there is an incorrect proof of the validity of the chain rule, but the author does not cite why the proof is wrong. I'm wondering if the problem is...
I am trying to find the second derivative of the function
C:[0,1]^{2} \rightarrow [0,1] ,\quad \mbox{defined by }C=C(u,v)
evaluated at
u=F(x)=1-\exp(-\lambda_{1} x),\quad \lambda_{1} \geq 0
and
v=G(x)=1-\exp(-\lambda_{2} x),\quad \lambda_{2} \geq 0
First I work out the first...
I am trying to lift a load with a drill motor. I have a chain drive with a 3.7x1 ratio - 13 teeth on the drive gear with a 2.5" diameter and 48 teeth on the driven gear with a 7.75" diameter. It lifts the load easily.
I also have a geared drive (no chain) with a 4.0x1 ratio - 16 teeth on...
Hello there,
yet another trivial problem:
I've attended the 'stochastic process' course some time ago but the only thing I remember is that this kind of problem is really easy to compute, there is some simple pattern for this I presume.
thanks for your help,
rahl.
Hi there, I'm a new user to the forums (and Calculus) and I 'm hoping you can give me your opinion on my chain rule form below. When learning the chain rule, I was taught two forms. This form:
\frac{d}{dx}f(g(x))=f'(g(x))g'(x)
As well as the Leibniz form...
I'm trying to find the derivative of 0 = 3xcosƟ with respect to time.
I know I should use the product rule for x and cosƟ. But I don't know what I should do with the constant 3.
would it be like this?
0 = 3x(-sinƟ)(dƟ/dt) + 3(dx/dt)(cosƟ)
A 10-ft chain weighs 24 lb and hangs from a ceiling. Find the work done in lifting the lower end of the chain to the ceiling so that it is level with the upper end.
since you just take a little piece and add them up through an integral
wouldnt it be the integral from 0 to 10 of 2.4x...
Homework Statement
Two chain links are connected together and are suspended by a string. The mass of the top link, link#1 is 8kg, while the mass of the second/bottom link #2 is unknown. If an applied force on the string attached to link #1 of 216N[up], and the links experience an acceleration...
Hi I'm trying to do a question on nuclear decay chains. The question is:
Bi-210 decays to Po-210 by beta decay (half life = 7.2 days), and this decays by alpha decay to Pb-208 (half life = 200 decays). If A substance is initially pure Bi-210, when does the alpha emmision peak?
So far I've got...
Hi I'm trying to do a question on nuclear decay chains. The question is:
Bi-210 decays to Po-210 by beta decay (half life = 7.2 days), and this decays by alpha decay to Pb-208 (half life = 200 decays). If A substance is initially pure Bi-210, when does the alpha emmision peak?
So far I've got...
Homework Statement
2 straight roads intersect at right angles. Car A, moving on one of the roads, approaches the intersection at 60km/h and car B moving on the other road, approaches the intersection at 80km/h. At what rate is the distance between the cars changing when A is 0.5km from the...
Use the chain rule to compute the partials of
F(z,w) = f(g_1(z,w),g_2(z,w),z,w)
where f(x,y,z,w)=x^2 +y^2 +z^2 −w^2
and g_1(z,w) = wcosz , g_2(z,w) = wsinz
Evaluate the partials at z = 0, w = 1. Confirm your result by writing out F explicitly as a function of z and w, computing its...
Homework Statement
A function f is called homogeneous of degree s if it satisfies the equation
f(x1, x2, x3,... xn)=t^s*f(x1, x2, x3,... xn) for all t
Prove that the \sum from i=1 to n of xi * df/dxi (x1, x2, x3,... xn) = sf(x1, x2, x3,... xn).
Homework Equations
The Attempt at a Solution...
Homework Statement
A (uniform) chain with a mass of 4.7 kg and a length of 2.0 m lies on a table with 0.7 m hanging over the edge. How much energy is required to get all of the chain back on the table?
Homework Equations
W= integral(sumF)dx
The Attempt at a Solution
NO idea where...
If z = f(x,y) and x = r \cos{v}, y = r\sin{v} the object is to show that d = \partial since it's easier to do on computer
Show that:
\frac{d^2 z}{dr^2} + \frac{1}{r} \frac{dz}{dr} + \frac{1}{r^2} \frac{d^2 z}{dv^2} = \frac{d^2 z}{dx^2} + \frac{d^2 z}{dy^2}
It's from Adams calculus, will...
Homework Statement
Skethch the greaph of x^3/(x^3+1). Identify all extrema and points of inflection, asymptote equations, and easily found intercepts
Homework Equations
If a/b=0, a must be 0.(thats how I got critical points from first derivative)
And chain rule: F'(x) = f '(g(x)) g '(x)
And...
Could someone explain this to me please where n=y/squareroot(4vt)
∂C/∂t=(dC/dn)(∂n/∂t)=-(1/2)(n/t)(dC/dn)
When i take the derivative of 1/t^1/2 i get -(1/2)t^(-3/2) so where does the (-3/2) go to in the final answer of -(1/2)(n/t)(dC/dn). Thank you very much!