Solid Definition and 1000 Threads

Homework Statement Use the method of Lagrange multipliers to find the maximum and minimum values of the function f(x, y) = x + y2 subject to the constraint g(x,y) = 2x2 + y2 - 1 Homework Equations none The Attempt at a Solution We need to find \nablaf = λ\nablag Hence...

Finding the critical point and its nature. With solid attempt! Homework Statement Find all critical points of the function f(x, y) = xy2 - 2xy - 2x2 - 3x +7 and determine their nature. Homework Equations none The Attempt at a Solution I know that to find the critical points you must...

Homework Statement Find the volume and the centroid of the solid E that lies above the cone z=√x^2+y^2 and below the sphere x^2+y^2+z^2=49. Homework Equations The Attempt at a Solution My bounds were: \theta=0 to 2\pi \varphi=0 to \pi/4 \rho=0 to 7cos(\varphi) So my integral...

So I want to use this solid state relay, to fast switch an electromagnet. About 2 times a second. Weight: 112g Size:5.9 x 4.5 x 2.3cm Color : Grey Fast switching Reduced electromagnetic interference Output voltage: AC 24-380V Output current: 25A Input voltage: DC 3-32V Control Method: DC to...

Homework Statement basically, my question is this, in relation to this diagram, https://www.physicsforums.com/attachment.php?attachmentid=12482&d=1202140386 wouldn't the electric field between the solid sphere and the hollow sphere be a uniform field? Homework Equations The...

I am trying to figure out what the actual efficiency of solid state hydrogen storage is. So how many kg of hydrogen can you store in a Xcm3 of metal hybride solid state storage. I was trying to find a conversion and only found a metric that was 500NL in a specific device that had some...

I was reading an article about phase transition, i read about thermodynamic process such as Adiabatic process - a process with no heat transfer into or out of the system. Isochoric process - a process with no change in volume, in which case the system does no work. Isobaric process - a...

Hi :) Well this is my first post here in the forum, I hope I put it into the right category. Im hoping that someone here might be able to help me with a little problem that I can't find the solution to. I am not a lab geek, unfortunately but I am trying to describe a process where I found...

Homework Statement Silicon at T= 300K contains acceptor atoms at a concentration of Na = 5*10^15 cm-3. Donor atoms are added forming an n-type compensated semiconductor such that the fermi level is 0.215 eV below the conduction band edge. What concentration of donor atoms are added...

Homework Statement Consider an electron gas in ONE and TWO dimensions i.e N electrons in a metal wire with length L or in metal sheet with area L^2. Pictures must be drwan of the fermi 'sphere' and the Fermi 'surface' . Why are the two words in quotation marks ? Homework Equations...

1. Consider the function f(x) = arcsin(2x^2 - 1). Write down, but do not attempt to solve, a definite integral in terms of y, which when evaluated will give the volume of the solid of revolution formed by rotating the graph about the y-axis. 2. Endpoints are at (-1, pi/2) and (1, pi/2)...

As part of my Intel Science Fair project "How to make Hydrogen a viable alliterative" I read that at 3,500,000 psi Hydrogen will become a "Solid" so that you can have more power in less space which will make the car much more efficient. I am doing this on a 1/10 scale. My question is what...

Homework Statement Homework Equations n\lambda = 2dsin(\theta) The Attempt at a Solution a) solving for d I get \frac{n*\lambda}{2*sin*(\theta)} = d substituting in the first value 50.85 to solve for d, with n=1 I get d= 1.754*10^-10m How do I solve the miller indices from the inter...

I have a B. Sc. in Electrical Engineering and I would like to work with photovoltaics / solid state device physics. My undergraduate degree is not quite enough to let me work in that field outright. So I'm looking to do a graduate degree. I applied for a 2-year M. Sc. in Physics program and I...

Chemistry: Reactions in Solution, But Not In Solid Form? Homework Statement "Calcium chloride and sodium carbonate are two ionic solids. If the solids are placed together, nothing seems to happen. However, if they are mixed in water, the following chemical reaction occurs: * See relevant...

Homework Statement We have to trace a pumpkin on graph paper and then find it volumne when rotated around the y-axis. Upon doing so we have 2 pieces we can do. One is a semi circle and the other just a rectangle. Refer to this image: Where we can see the diameter of the circle is 13.5...

Homework Statement The base region of a solid is bounded by y=x, y=(x-1)^2, and x = 1. The cross sections are semicircles perpendicular to the x-axis. Write a riemann sum and definite integral. Homework Equations The Attempt at a Solution First, I wrote down the formula...

Homework Statement A uniform solid disk of radius R and mass M is free to rotate on a frictionless pivot through a point on its rim (see figure below). The disk is released from rest in the position shown by the copper-colored circle. (a) What is the speed of its center of mass when...

Homework Statement A nonconducting solid sphere of radius 2.30 cm carries a uniformly distributed positive charge of 8.00×10-9 C. Calculate the magnitude of electric field at 1.60 cm away from the center of sphere Homework Equations E=kqr/R^3 The Attempt at a Solution...

Hi there, I should probably know this (attempting to do a PhD in physics!) but is there a way to differentiate between longitudinal and shear acoustic waves in a solid? I know that seismologists know which is which by using the time of flight difference for the two types of waves and the...

Homework Statement x=2y^2 x=0 y=+-6 rotated around y Homework Equations integral 2pi*x(f(x)dxThe Attempt at a Solution integral from -6 to 6 of 2pi*y*2y^2 dy but i get something far less than the correct answer

Homework Statement The base is the semicircle y = \sqrt{9-x2}(Square root of 9-x2.. i don't know why the formatting isn't showing up) where -3 <= x <= 3. The cross section perpendicular to the x-axis are squares. Homework Equations -3\int3 = A(y)dy A(y) = area of cross section...

I know that the first solid solid state device is: A semiconductor diode what about transistors? Is it not a solid state device? Explain me the difference between solid state device and semiconductor device.

Hi All, I had a question about this problem I was doing and was hoping to see if I did it right. Homework Statement Using Disk or Washer method Find volume of the solid generated by revolving the region bounded by y=sqrt(x), y=2, x=0 about the line y=2.Homework Equations Disk Method...

Homework Statement Find the volume of a solid bounded by the functions y=1-x2 and y=0 revolved around the x-axis Homework Equations (don't know how to show integrals) A=Pi * the integral from xa to xb of [f(x)]2-[g(x)]2 The Attempt at a Solution First, to find the lower and upper...

Here is the problem: The electron concentration in a region of silicon depends linearly on depth with concentration of 5x10^15 cm^-3 at surface (x=0) and 10^15 cm^-3 at depth of x=500nm. If the vertical electron current density in this region is constant at Jn=100 A/cm^2, calculate the...

Hi, I was reading my astrophysics textbook and came across solid angles. I'm not sure I fully understand, for example there was a problem in the book that went as follows. The attached "math.jpg" shows a light source (yellow) in the centre of an arc. The problem is 2D, but the arc is...

It is very common to see in the literature negative formation energies reported for point defects in solids using different simulation techniques ranging from Density Function Theory to Molecular Dynamics. The authors rarely comment on what does that mean physically. I will mention here two...

Are all acid have covalent structure in solid state?

I am very much interested in design engineering, development of consumer, scientific and medical devices. My favourite aspects of engineering include mathematics, CAD and computational engineering. I would say that my key strengths lie in analytical, mathematical thinking and very strong...

Homework Statement If a solid is generated by rotating the line (x=4tan(y*pi/3)) on the y-axis. Find the volume between the area 0≤y≤1. Homework Equations I know that, when slicing a section (A(x)), I will generate a circle. This gives me two of the dimensions (by using area of a...

How to dehydrate a solid crystal? I have a solid crystal with structural channels in it which are filled with water molecules. The size of each channel is 2.5 to 5 angstrom and a water molecule is 2.7 angstrom on its longest side. What is the best way to dehydrate it? I have tried heating it...

Homework Statement A solid ball of mass M and radius is connected to a thin rod of mass m and length L as shown. What is the moment of inertia of this system about an axis perpendicular to the other end of the rod? Image: http://imageshack.us/photo/my-images/35/helpfy.jpg/ Homework...

I am curious as to whether the force of solid sphere can be considered to be originating entirely at its center when the force is not of \frac{1}{r^2} nature. It is said that the field inside a uniform spherical shell is zero for any \frac{1}{r^2} type force and not for any others. It would...

The definition of Beam solid angle: For an antenna with single main lobe, the Beam solid angle defines as: The solid angle \; \Omega_A\; where all the radiated power would flow with radiation intensity equal to maximum and constant inside the Beam solid angle \; \Omega_A\;. The book gave...

Look at a simple single - component system. And PT diagram for this system. Suppose that supstance we looking at has three phases solid, liquid and gas. In that case we have critical point between liquid and gas phase, but not between solid and liquid phase. Why? Why solid - liquid coexistence...

Hi, All: This is a followup to the post : https://www.physicsforums.com/showthread.php?t=491211 Here Lavinia gave a couple of nice arguments showing that the complement of the solid torus the 3-sphere S^3 is a solid torus; one of which was using the Hopf fibration, taking a disk D^2...

Hello, I have to find the maximum rpm of the shaft that has ring mounted on the shaft with interference fit of 0.002". I want to know at what rpm the ring will come loose from the shaft? and If I run the shaft at 7000rpm at 400 degree Celsius, is the interference fit of 002" enough...

Hi all. I've just hit a block in the following question: [Find the volume of the solid...] "The region in the first quadrant bounded by the curve y = x^2, below by the x-axis, and on the right by the line x = 1, revolved around the axis x = -1." I've tried nearly 2 hours figuring the...

Homework Statement The question asked is to make a bowl out of polynomial equations rotated around the y axis. The bottom of the bowl has to have a maximum at the center and a minimum at some distance from the center. The equations I want to use are x^2+10, 1.3x^2 and -.7x^2 + 4. The...

I understand the surface of the sphere is 4\pi sr. where the area of one sr is r^2. My question is why d\Omega = sin \theta \;d \theta \;d\phi? Can anyone show me how to derive this. Is it because surface area dS = (Rd\theta)(R\; sin\;\theta\;d\phi)\;\hbox { so if }\; \Omega = \frac S {R^2}...

Homework Statement y= -(x/6) + b, find the volume as this solid is rotated 360 degrees around the Y axis Homework Equations If I were given the interval at which I needed to find the volume and/or the value of B I could easily do this using the formula: [pi] Integrate: (R(y))2 dx...

So, I was trying to find a rigorous mathematical derivation of gauss's law(please I don't want to hear again any field lines nonsense) and I stumbled upon jackson's proof which uses the solid angle concept and seems a solid enough proof(stupid joke:smile:).The problem is that it's the first time...

186000 miles long with zero flex or give. You have an observer at both ends. Observer A has a machine strong enough to turn the bar in either direction. Observer B does not know which way its going to turn. Mr.A turns on the machine and the bar turns to the left. Mr. B sees its direction...

Homework Statement Homework Equations The Attempt at a Solution What is the relation between a shell and a solid sphere? Can you give me some hints?

Homework Statement Been awhile since I've done them and my memory/reasoning isn't so great apparently... Use the triple integral to find the volume of the given solid: The solid enclosed by the cylinder x^{2} + y^{2} = 9 and the planes y + z = 16 and z = 1. 2. The attempt at a solution...

Find the volume of the solid that lies under the paraboloid z = x^2 + y^2, above xy plane, and inside the cylinder x^2 + y^2 = 2y First, i try to find the range.. i transfer it to cylindrical coordinates.. sqrt(y^2)=<z<=r^2 i don't know how to find r i know that phi is from 0 to 2pi...

Hello guys, I will soon be stepping into the IB1 program and before I start school in late august, I wish to properly* review my maths (including but not limited to algebra, geometry, functions, graphs, etc). * I really need to strengthen my mathematical foundation. I'm looking forward to...

Homework Statement A sphere is floating in water. It is pushed just under the water level and released. I'm asked to write the equation of motion for the sphere, not assuming small oscillations. Is it just: my''=\rho V g - mg ? Or do I have to include that the buoyant force is changing...

how close are the atoms in any solid, is all the space possible in a solid is filled up by its atom finally can we consider an atom an isolated body ,or can size of strings pass between inter atomic spaces.i believe atoms in the solid is not actually in contact but there exists infinitsimally...