A composite material (also called a composition material or shortened to composite, which is the common name) is a material which is produced from two or more constituent materials. These constituent materials have notably dissimilar chemical or physical properties and are merged to create a material with properties unlike the individual elements. Within the finished structure, the individual elements remain separate and distinct, distinguishing composites from mixtures and solid solutions.Typical engineered composite materials include:
Reinforced concrete and masonry
Composite wood such as plywood
Reinforced plastics, such as fibre-reinforced polymer or fiberglass
Ceramic matrix composites (composite ceramic and metal matrices)
Metal matrix composites
and other advanced composite materialsThere are various reasons where new material can be favoured. Typical examples include materials which are less expensive, lighter, stronger or more durable when compared with common materials.
More recently researchers have also begun to actively include sensing, actuation, computation and communication into composites, which are known as robotic materials.Composite materials are generally used for buildings, bridges, and structures such as boat hulls, swimming pool panels, racing car bodies, shower stalls, bathtubs, storage tanks, imitation granite and cultured marble sinks and countertops. They are also being increasingly use in general automotive applications.The most advanced examples perform routinely on spacecraft and aircraft in demanding environments.
Original question:
A system contains two particles: the spin of particle 1 is 3/2 and the spin of particle 2 is 1. Motion of particles can be ignored.
Part A asked to find the total spin state |5/2 3/2> using Clebsch-Gordon coefficients.
I did so, and came up with,
\mid 5/2\ \ \ 3/2\...
Hi,all.
My lecture said, two fermion can form a composite boson. two spin half plus together get 1.
Yes I agree, but i think that's depend on whose frame of reference.
say A and B is two fermions, C and D is another two fermions (observers). AB form a boson.
if:
AB...
Homework Statement
The forward-back function is
f (t) = 2t for 0\leq{t}\leq{3} ,
f(t)= 12-2t for 3\leq{t}\leq{6}. Graph f(f(t)) and find
its four-part formula. First try t = 1.5 and 3.
The Attempt at a Solution
There are four possible composite functions from the two given...
Homework Statement
let A,B,C be sets, and let f : A--> B and g : B--> C be functions. The composite function denoted by g o f is a function from A to C defined as follows:
Homework Equations
g o f(x)=g(f(x)) for every x in A.
Prove that if g o f is one-to one, then f is one-to...
Homework Statement
Given g(x)=|x| and f(x)=secx
1)Determine an equation for (f(g(x))
2)State the domain
3)x and y intercepts
4)any asymptotes
Homework Equations
N/A
The Attempt at a Solution
f(g(x))=sec|x| or 1/cos|x|
[b]1.) If (-4,8) is the image under the composite transformation Th,3 x T-2,k(-3,0), what are the coordinates of the image of (2,-1) under the same composite transformation?
The Attempt at a Solution
I'm lost on this one.
Homework Statement
Given the equation y= f(x) , at a certain point the slope of the curve is 1/2 and the x-coordinate decreases at 3 units/s. At that point, how fast is the y-coordinate of the object changing?
The Attempt at a Solution
Dy/dx = f ' (x) dx/dt
Would that be...
This is not so much a problem as it is a conceptual question. You're calculating the moment of inertia of a composite shape, let's say a square and a triangle. The square however has a hole inside of it. How does this change the computation of the moment of inertia? This is in a 2-D plane.
My...
1. Find the domain of f(g(x)) where f(x)= radical 25-x^2 and g(x)= ln(x+3)
2. For the domain of f I got x < or equal to +/- 5 and for the domain of ln(x+3) I got x+3 > 0
3. (0, 145)
Thanks for your time. :P
Homework Statement
Determine the deformation of a composite bar is subjected to a centric force P.
This is a general question. The composite bar is made of 2 materials. The top and bottom layer is material 1, and the middle layer is material 2. I can't think of a better way to describe...
Homework Statement
The attempt at a solution
g(f(x)) = h(x)
4f(x) + y = 4x - 1
4x + 16 + y = 4x - 1
y = -1 - 16
y = -17
so, g(x)= 4x + y = 4x - 17
Is this the correct way of going about this question? I used a guessing approach to this question. Is enough work shown to get...
Homework Statement
Given:
a\partial\psi/\partial t = \widehat{H}\psi
Consider a is an unspecified constant. Show this equation has the following property. Let \widehat{H} be the Hamiltonian of the system composed of two independant parts:
\widehat{H}(x_{1},x_{2}) =...
Homework Statement
If f(x) = x3+3x2+4x+5 and g(x)=5, then g(f(x)) = ?
Homework Equations
The Attempt at a Solution
I don't know if I am correct.
g(f(x)) =
g(x3+3x2+4x+5)= 225?
I plugged 5 into the equation. Am I right?
Homework Statement
http://img171.imageshack.us/img171/543/pro3.png
The Attempt at a Solution
= f(g(h(x)))
= f(g(\sqrt{x+3}))
= f(cos\sqrt{x+3})
= \frac{2}{cos\sqrt{x+3}+1}
Is this right, and am I showing enough work to get full marks? Do I need restrictions for example?
Homework Statement
If p>=5 is prime, prove that p^2 +2 is composite.
Homework Equations
If we took p and divided it by 6 we would get remainder possibilities of 0, 1, 2,3,4,5
The Attempt at a Solution
p=6q p^2=36q^2 P^2=6(r) P^2+2=6r+2=2(3r+1) composite
p=6q+1...
First of all, I hope this problem is supposed to be here - I'm Swedish and in Sweden "calculus" & "precalculus" are rather odd terms. Anyway..Homework Statement
Prove that n3 - n is divisible by 6 if n is a natural number, and divisible by 24 if n is an odd natural number.Homework Equations
The...
Does it correspond with the centroid of the transformed section? For example, if a wood beam had a steel plate fixed along the bottom, would the neutral axis be lower than that of a pure wood beam of similar cross section?
Any links showing example probs would be nice too. Sorry that this is...
I just read http://www.newscientist.com/article/mg20327224.400-why-large-carbonfibre-planes-are-still-grounded.html" article and I had to ask something. Will the 787 have to go through a de Havilland Comet phase in order to be perfected? I mean, how do we know the composite airframes won't break...
Homework Statement
http://img21.imageshack.us/img21/8175/46521897.jpg
The Attempt at a Solution
I think I have a starting point, but I'm not 100% sure
Basically I thought of just computing grad(f(α(t)) · dα/dt and showing its equal to zero.
Am I on the right track, or shall I try...
Homework Statement
Find the derivative of the function: cos(x)^(cos(cos(x)))
Homework Equations
The chain rule
The Attempt at a Solution
I know how the chain rule works, and I've done many problems with composite functions. However, I just don't know where to start with this one...
On http://en.wikipedia.org/wiki/Aurora_(astronomy ), about 1/2-way down the page, there is an image of, quote, "Aurora australis (September 11, 2005) as captured by NASA's IMAGE satellite, digitally overlaid onto the The Blue Marble composite image." Next to it, there is a rolling video of...
Homework Statement
Use the composite trapezoidal sum rule to evaluate
I = integral from 0 to 1 of: (exp(x)-1)/x
At x = 0 the integrand evaluates to 1.
Select the step size h in order to guarantee an approximation error less than
10e-5.
Carry out your calculation with at least 10 decimal...
Some years ago I used the device of representing composite numbers by rectangular forms to demonstrate the structure of numbers to third grade students. Primes were represented by lines of various lengths. Number 10 would be a 2x5 rectangle and 20 a 2x2x5 rectangular solid. (I used various...
Homework Statement
I need to find the Exact Solution for this problem(Displacements)
I already did it using MATLAB but I need to compare it to the exact solution
I am not sure what equations to use for this problem and where to start?
Homework Equations
-Plane strain
-E and v are...
How masons can be massless while their composites quark (q) and antiquark (\bar{q}) are both massive?
Is there any clear physical scenario to understand this?
Homework Statement
http://www.apeg.bc.ca/reg/past-exams/documents/May2005-98-BS-6.PDF
Page 3 - Question 2
Except that let M=60 N.m (instead of 75)
Homework Equations
Transformation Equations: Z = z * E / E(ref)
The Attempt at a Solution
Transforming the composite bar to a...
Hello :smile:
I was wondering if someone could check my working and answers to these three homework questions. I've done the inverse functions in class, but not the composite inverse functions, if that's what they're called.
Homework Statement...
Homework Statement
"A polymer, with Young’s modulus 2GPa and yield stress 50MPa, is reinforced by
uniaxially aligned glass fibres which have Young’s modulus 70GPa and fracture at
1400MPa. The volume fraction of fibres is 40%.
(a) Calculate Young’s modulus for the composite in the...
Homework Statement
What is the maximum angle you can rotate the cone before the scoop falls out? Assume that the scoop of ice cream acts like a perfect sphere and does not stick to the cone.
calculated already that the center of mass is located at z = 5.02
Assume that the scoop of...
Hi,
I have an aluminium/lead composite material with density of 8,3 g/m^3. How do I find volume/volume and weight/weight persentages of aluminium and lead in the material, if the masses of the composites are not given?
The volume of the material is also not known.
Thanks.
Dear All,
Currently we have changed from our epoxy tooling (molds) to aluminium tooling to obtain more accuracy in the dimensions of our final product.
Our resin is preheated to 50 degrees Celsius before injection and our epoxy tooling have similar temperature levels. At these levels the...
Homework Statement :
discuss continuity of the composite function h(x)=f(g(x)) when A} F(x)=X^2 , g(x) = x-1
B} f(x) = 1/x-6 , g(x) = X^2+5
where should I start ?
Advice needed for composite...
Hello guys. Newbie here this is my first post ;-). I am a 2nd year Eng. Mech. Univ student.
An assignment for one of the credits is to design a composite material (made up of 2 materials)of rectangular section width 30mm and thickness 20mm, length 400mm. The...
Homework Statement
A disc of mass m is moving horizontally to the right with speed v on a table with neglibible friction when it collides with a second disc of mass 2m. The second disc is moving horizontally to the right with speed v/2 at the moment of impact. The two disc stick together upon...
In a urine sample (Relman JCI 1961) urine is analyzed. We have a [Na] of 132 mmol/l, K of 62.7 mmol/l, Cl of 182 mmol/l, sulfate of 21.2 mmol/l and some other minor species. The ionic strenght is about 0.22 - now I need to compute the Na+K-Cl-2*SO4. So the ionic strength is higher than 0.1, but...
Homework Statement
Let T1 be the reflection about the line 2x–5y=0 and T2 be the reflection about the line –4x+3y=0 in the euclidean plane.
(i) The standard matrix of T1 o T2 is: ?
Thus T1 o T2 is a counterclockwise rotation about the origin by an angle of _ radians?
(ii) The...
If two boson are each composed of two identical fermions in opposite spin states, can the composite bosons occupy the same state? If so wouldn't that cause their fermions to also occupy identical states? (Certainly, they can't occupy four different spin states, can they?)
Suppose we are given that
d
--F(y) = f(y)
dy
Then is it true that
dF(h(u))
-------- = f(h(u)) dh(u)/du ?
du
Why or why not? In particular, I don't understand how to get the red part...
Thanks for explaining!
What is the actual meaning of the notation of
df[g(x)]
-------
dx
Here do we actually differentiate f with respect to x first and then evaluate it at g(x), or do we first evaluate f at g(x), then differentiate it with respect to x? Does the order matter?
df
--[g(x)]
dx
d...
Homework Statement
Let F(z) = a0 + a1z-1 + a2z-2 denote the composite transfer function of the transmitter, channel and the matched filter in this ultra wide band system. Find a two tap digital equalizer Heq(z) = w0 + w1z-1 that approximates an IIR zero-forcing equalizer for F(z)...
Homework Statement
A reversible composite heat engine operates between three reservoirs at temperatures of 400K, 300K and 200K. One engine operates between the 400K and 300K reservoirs and a second engine operates between the 300K and 200K reservoirs and is synchronised with the first. In...
Homework Statement
Use proof by contradiction to show that every integer greater than 11 is a sum of two composite numbers.
The Attempt at a Solution
The question sounds a bit awkward for me since for the numbers I have tested so far. The number can be consists of 1 prime 1 composite or...
Let f:X->Y and g:Y->Z be functions. Suppose A is a subset of Z. I'm wondering whether (g o f)-1(A)=f-1(g-1(A)).
I'm lost as to where to go with this problem. I know I need to do something using images, but manipulating the inverses of composite functions is proving to be very confusing; I...
Hey guys,
Im a bit baffled on this one.
I have been told to perform the following integration:
\int y dx from -1 to 14. I have been given some values of x and the corresponding values of y.
I just have one question, the fact that it is y dx is throwing me off. The trapazoidal rule...
Can anyone help me solve this question??
Given f(x) = x2- 16 and g (x) = √x-3, find f(x) - g(x), g(x)/f(x), f(x)g(x) and (fog)(x) and state their domains.
A photon annihilates into an electron and a positron (both having spin 1/2). The reverse process is also a reality. Can the photon therefore be viewed as a composite of an electron and a positron having a total spin 1?