Solid Definition and 1000 Threads

Hi, I am doing a project for the math department and in it I would like to revolve this piecewise (3) function about the x axis. I have found programs like winplot which are pretty easy but it will only show the finished product. I am looking for something that I can either manipulate or it...

Homework Statement Here is the surface I need to parameterize. It is a solid of revolution. Homework Equations The Attempt at a Solution So since its a piecewise function, I can define it as follows (x-2)^2 + z^2 = 1, 1<x<2 z = -x+3, 2<x<3 z = x-3, 2<x<3 I know...

Homework Statement Find the volume of a solid created when the area between the function y=x^2+1 and the x-axis (for 0<x<2) is rotated about the line y=-2. Homework Equations Vs = ∏*r^2*h The Attempt at a Solution I can't seem to set this up correctly and am thrown by the inner radius...

Hi Everyone, I have a question about panel vs. solid rod structures. Assume a two cubes of equal dimension and weight. Cube 1 is made of panels, ie. a hollow cube. Cube 2 is made with solid rod Material is linear elastic Which would be stiffer? I think the panel...

Why do LEDs and other light emitting solid state devices have a definite lifespan?

Homework Statement A solid sphere of radius a rotates with angular velocity ω\hat{z} relative to an inertial frame K in which the sphere's center is at rest. In a frame K' located at the surface of the sphere, there is no electric field, and the magnetic field is a dipole field with M=M\hat{z}...

Homework Statement Find the volume of the first quadrant region bounded by x=y-y3, x=1 and y=1 that is revolved about the line x=1. The Attempt at a Solution dV=∏R2t where : t=dy R=1-(y-y3) =1-y+y3 so.. dV=∏(1-y+y3)2dy dV=∏(1-2y+y2+2y3-2y4+y6)dy V=∏∫ from 0 to 1 of...

find the volume of the solid generated by revolving the area bounded by the given curve about the indicated axis:y = 2x-x^2 and y = x; about the y-axis The attempt at a solution: so i assigned values for x and y, and the curve is a parabola that opens downward with a vertex of (1,1), i used...

Homework Statement Find the center of mass of the solid figure similar to a cone pointing upward with slope = 1 Note: the density varies with z^2 and the edge has a slope of 1. From symmetry we see that both Xc and Yc are equal to zero. Find the center of mass in the z direction as a function...

There are two sphere of same radius but one is solid and other is hollow. Both are heated to same temperature(greater than room temperature). which will cool at faster rate? I think both the spheres will cool at same rate since hollow sphere can't loose it's heat inside it (because internal...

Hello, Am working on a model that involves heat conduction in a semi-infinite solid. I have been using linspace() command for finite geometry, but now i need to create a 1-dimensional semi-infinite solid. Any suggestions? Thank you.

Homework Statement A solid cylinder is pivoted about a frictionless axle as shown. A rope wrapped around the outer radius of 2 m exerts a downward force of 3N. A rope wrapped around the inner radius of 0.7 m exerts a force of 8 N to the right. The moment of inertia of the cylinder is 8 kg m^2...

Homework Statement Find surface area of solid of revolution obtained by rotating the curve: y=x2/40-5lnx from x=5 to x=7, rotated about x=-4 The Attempt at a Solution The problem is I know how to do this if I rotated it about x-axis/y-axis, but I have no idea how to do it if the...

What is "kinetic capacitance" in superconductors or in solid state in general? Hi, I would appreciate it if anyone could explain to me what "kinetic capacitance" is, particularly in the context of superconductors or solids. I understand "kinetic inductance" which comes from the kinetic...

Is there a general level of vibration that describes most solid state matter that we can touch? Perhaps in hertz?

Hi So the reaction is below: Sodium thiosulfate + HCl = Sulfur + NaCl+ Water+ SO2 So if I wanted to say 'Increasing the conc. of Sodium thiosulfate has shifted the equilibrium to the left (reactants) and thus the system works to break down excess reactants and create more product by...

Homework Statement In the picture belowHomework Equations Stress=P/AThe Attempt at a Solution I equated stress AB=-stress BC p/pi=-(p-60 kips)/2.25pi P=18.4615kips This is not the right answer according to the book

Homework Statement A long, non conducting, solid cylinder of radius 4.2 cm has a nonuniform volume charge density ρ = Ar^2, a function of the radial distance r from the cylinder axis. A = 2.5 µC/m5. (a) What is the magnitude of the electric field at a radial distance of 3.2 cm from the axis...

Reading about einstein's model of a solid as being made up by quantum harmonic oscillators. Now while the idea is VERY interesting, I think my book's explanation of the multiplicity of an energy state is quite flawed. One can easily derive a simple formula using the binomial coefficient...

Question: A solid sphere of radius R has a non-uniform charge distribution of p=Ar^2, where A is constant. Find total charge Q within the volume of the sphere. p=roe p=Q/dV EdA=qenclosed/Enaught Can you use Gauss' Law for this problem when sphere is solid? If so, how? Since p...

Plasma, the fourth state of matter, is a gas that consists of ions and free electrons. If you cooled plasma would it become a liquid? A solid? What would be the properties of this plasma? would you be able to magnetically separate it?

Homework Statement As the title would lead you to believe I have to classify each solid as a covalent, ionic, metallic, or molecular solid. These are the given solids Calcium Fluoride Rhombic Sulfur Frozen Ethanol Pure Calcium Homework Equations n / a The Attempt at a...

Homework Statement Positive charge is distributed throughout a solid non-conducting cylinder of radius 'b ' and infinite length. The charge density increases with radius according to ρ = {ρ}_{o}({r}{^2}/{b}{^2}), where {ρ}_{o} is a constant (evidently equal to the charge density at the surface...

Homework Statement In my Chemistry lab, we made silver using copper and silver nitrate. We put a solution of silver nitrate, distilled water, and copper wire in a test tube and observed it. Then we took the copper out (the solution turned blue and the copper had crystals formed on it but we...

Use the shell method to find the volume of a solid generated by revolving the region bounded by the given curves and lines about the x-axis. x=2√y x=-2y y=1 So I drew a graph and then using the equation v=∫2πrh and I got the following v=∫(from 0 to 2) 2π(y-1)((2√y)-(-2y)) but...

Homework Statement Hey we have started solids of revolutions using disk, washer, and shell methods. But I came across a problem i cannot figure out. "The region of the graph of y=x^2 and the x-axis, for 0<x<2, rotated about the line y=4. Homework Equations Area of a circle = ∏r^2...

Homework Statement The Attempt at a Solution I dont' see why you don't take the antiderivative of pix^(1/2) which makes it (2pix^(3/2))/3

Hello, Thank you all for the help here. Here we go, I have a known solid weight start of the propellent. I know the PSI of a known volume chamber(After combustion) and Temperature, can I find density? So example Bullseye powder has a load of 0.336954332 grams (5.2 grains) The volume...

I know that particles in a solid are not fixed. They are constantly vibrating about their mean position. That is because of their kinetic energy. I was imagining a situation, lets say solid moves towards left of it's mean position. then the inter-molecular forces of attraction on the left...

Homework Statement A solid conducting sphere carrying charge q has radius a. What is the electric field when r<a. Homework Equations EA=Qenclosed/εo The Attempt at a Solution I found it using gauss law where Q=density*V. I ended up with qr/(4pi*a3*εo)HOWEVER, my friend told me it should be...

Homework Statement Tha band structure of a simple cubic lattice is given by, E = E_{0}-A(\cos k_{x}a+\cos k_{y}a+\cos k_{z}a) where a is the lattice constant and A is a positive constant. Find the effective mass for the electron at the values of k corresponding to the top and bottom...

---------------------------------------------------------------------------- I know about the shell theorem and that the force of gravity due to the mass of the spherical shell is zero inside. I have some questions that may easily be answered for other special cases using the shell theorm and...

I know about the shell theorem and that the force of gravity due to the mass of the shell is zero inside a spherical shell. I have some questions that may easily be answered. 1. Does this same conclusion hold for an ellipsoid and/or a disk with the shell on the exterior rim ? 2. How is...

Hi all Maybe a juvenile question but throw it out there anyways I know India is heavily vested in thorium due to the abudance in that region. I was wondering why current vendors are not looking to develop a thorium burning reactor to market to these guys or at least a modificaion to...

x 0 0.5 1.0 1.5 2.0 2.5 3.0 f(x) 2 1.3 0.9 0.6 0.7 1.1 1.9 Find a formula for the volume V of the solid whose base is the region bounded by y = f(x), the x-axis, and the line x = 3 and its cross-sections perpendicular to the x-axis are semicircles.** So, I...

Homework Statement I uploaded of a picture of the question so hopefully it comes up here. Homework Equations The Attempt at a Solution OK! so i am SO confused on where to start. I am imagining the solid flipped on its side with the x-axis going through its center. So all i...

Homework Statement Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 5x, y = 5\sqrt{x} about y = 5 Homework Equations A(x)=∏(R2-r2) The Attempt at a Solution A(x)=∏(5x)2-(5\sqrt{x})2) A(x)=∏(25 x2 -...

I'm looking for information about absorption of light per unit (atom, molecule, stoichiometric) in a liquid vs solid. For instance, imagine a unit cube filled with a saturated solution of, say, potassium permanganate, and shine a laser beam through it from bottom to top and measure the...

Homework Statement Question Assuming the torque and maximum shear stress values to be the same for both shafts, determine the size of a suitable soild shaft which could be used instead of the hollow shaft. Information/Data Known Firstly, a previous question - A ship's propellar...

Hello, I am not an electrical engineer but I do have a slight background in some electrical engineering concepts. My question is a general one about relays (more specifically solid state relays but I don't think that really changes my question). I understand that a relay gets a small input...

Homework Statement Solid slab with moment of inertia 2 kg m2 is given the forces as shown. Find the angular acceleration if θ = 37°, R1 = 10 cm, R2 = 25 cm Homework Equations τ = I . α The Attempt at a Solution This is what I've tried although I don't know it is correct or wrong; I tried to...

Homework Statement Find the volume obtained by rotating the solid about the specified line. y=2-(1/2)x, y=0, x=1, x=2, about the x-axis. Homework Equations I used the disk method The Attempt at a Solution I drew a sketch and used disk method. For the radius I used 2-(1/2)x...

Homework Statement Hi, We meet again PF, this time I am little stumped on the following question(link posted down). Homework Equations Link to the question "Question" The Attempt at a SolutionI think I get the gist of it for part (i) my calculated value for equlibirum separation is about...

Homework Statement I've just started with center of mass, and instead of the method in the book, I tried solving the center of mass for a solid hemisphere using angle as a variable, but the answer didn't match. A small disk of mass "dm" is taken, which subtends an angle "dθ" at the center.The...

Hi everyone I'd like to compute the solide angle defined by a cone whose angle θ is known. I tried with the definition but I probably mistook since it lead me to compute an integral worth...0. I then tried with a rule of three, but the result I get is clearly wrong too. Could you...

Homework Statement My problem is to calculate the Thermal stress of a Cylindric shell with inner radius a and outer radius b the inner surface is experiencing Temperature T1 and the outer surface is experiencing T2 with T1>T2 assuming that the linear thermal expansion coefficient is a, the...

Hello! I'm trying to derive the formula for the moment of inertia of a solid sphere, and I keep running into a strange solution. I set up the infinitesimally mass of an infinitesimally thin "shell" of the sphere: dm = 4\rho\pir2 dr And then solved for the moment of inertia: I = \intr2dm =...

Say we shoot a bullet that travels in the theta = 0 direction (we are in spherical coordinates). Say the bullet strikes and sticks to a half-infinite isotropic elastic solid that begins at the theta = 90 degrees plane. Is it true that longitudinal waves generated by the bullets impact will be of...

A solid sphere of mass m is released from rest from the rim of a hemispherical cup so that it rolls along the surface. If the rim of the hemisphere is kept horizontal, find the normal force exerted by the cup on the ball when the ball reaches the bottom of the cup.

Homework Statement I've just started with center of mass, and instead of the method in the book, I tried solving the center of mass for a solid hemisphere using angle as a variable, but the answer didn't match. A small disk of mass "dm" is taken, which subtends an angle "dθ" at the center.The...