Homework Statement
Problem:
Find the volume of the solid of revolution obtained by rotating the area bounded by the curves y = x^2 – 2 and y = 0 about the line y = -1. Consider only that part above y = -1.
Solution:
The solution is attached as TheSolution.jpeg.
Homework Equations...
Homework Statement
A solid sphere of mass M and radius R is rolling,without slipping, down a curved rail. The sphere is initially at rest at a height of h1. Find the angular velocity ω2 and the center of mass velocity of the sphere vcm at the end of the rail of height h2. You may assume that...
Solid State Physics
Quantum mechanics and quantum nature of solids, properties of materials. Band theory in metals and semiconductors. Conduction processes, the p-n junction, transistors and other solid state devices.
Field Theory
Review of vector analysis and coordinate systems...
How do water molecules behave in the presence of a static electric field?
If I apply an electric field on water molecules, would they apply pressure to a solid surface (let's say a noble metal), and if so, what would happen? Could the oxygen wedge in between the atomic gaps on the surface of...
Homework Statement
Consider a right circular cylinder with radius R and height L oriented along the z-axis. The center of the cylinder coincides with the origin. Inside the cylinder the volume charge density is given by \rho(z)=\rho_0+\beta z. Find the electric field at the origin (in terms...
1. Use a triple integral to find the volume of the given solid.
The solid enclosed by the cylinder x^2 + z^2 = 4 and the planes y = -1 and y + z = 4
This looked like a cylindrical coordinate system to me, except for the fact that it is not cylindrical around the z-axis but the y-axis. I...
Hi
I am very confused at determining the type of elastic wave in a vibrating body. For example, an elastic solid is flexuraly vibrating in one of its resonant mode. There should be elastic wave excited from this vibration. But, my question is which wave will be excited through it...
Homework Statement
Find the energy stored in a uniformly charged sphere of charge q, radius R
Homework Equations
The Attempt at a Solution
Ein=\frac{qr}{4\pi\epsilon o R^3}, Eout=\frac{q}{4\pi\epsilon o r^2}... W=\int_{0}^ {R}\int_{0}^{2\pi}\int_{0}^{\pi}[\frac{qr}{4\pi\epsilon...
Hello!
I had this doubt when I was 14-15 years old, and I waited for many years (I'm 49 now) to ask about it, as I always thought this to be a silly question.
In case someone can help with this, that's a thought experiment. It starts with this: if you have a sphere of gas, and then apply...
Homework Statement
The base of S is the triangular region with vertices (0, 0), (5, 0), and (0, 5). Cross-sections perpendicular to the y-axis are equilateral triangles.
Find V of described triangle.
Homework Equations
The Attempt at a Solution
I first wrote the equation of the...
Q: Consider the solid that lies above the cone z=√(3x^2+3y^2) and below the sphere X^2+y^2+Z^2=36. It looks somewhat like an ice cream cone. Use spherical coordinates to write inequalities that describe this solid.
What I tried to do:
I started by graphing this on a 3D graph at...
Homework Statement
The lab is attached. I've also attached the pre-lab just for the diagram.
Homework Equations
The Attempt at a Solution
Can anyone think of some good errors for this lab?
We ended up with ~80% error.
I've thought of two:
1. Adjusting the potentiometer so...
Hi forum goersI'm reviewing some coursework for my General Chemistry class and cannot seem to find a reasonable explanation of why amino acids exist as zwitterons in solid state and ph7 solutions. I'm fairly certain the explanation has to do with its solubility in water, but I am not sure.
Here...
Hello MHB,
As students of calculus, we are taught to find the volumes of solids of rotation obtained by revolving given regions about horizontal and vertical axes of rotation. But, what if the axis of rotation is neither horizontal nor vertical? Please consider the following diagram:
We wish...
Homework Statement
Find the volume of the region bounded by the curve y=x^(1/3) and y=x rotated about the line y=1.
Homework Equations
The Attempt at a Solution
My teacher's solution is 4∏/15 . I got 11∏/210.
http://imageshack.us/a/img443/426/0zhs.jpg...
hello
please see attached snapshot from the book of Ligthmann & al. (problem book in relativity and gravitation).
Can somebody please explain the expression for the derivative of the solid angle ?
here it is given as dvxdvy where the v's are speeds !
How come this is so ?
Thanks,
[solved]Find volume of solid generated (Calc 2)
Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y=e^x, and the line x = ln 2 about the line x= ln 2.
So I tried graphing it to see visually, and the expression I got...
It should for nitpicky convenience's sake, be pointed out that unless the point we choose to calculate the moments around is the C.M of the rigid body, or that the the point moves parallell (including being at rest) to the motion of the C.M, we get an additional term on the RHS.
Homework Statement
Show for a solid spherical ball of mass m rotating through its centre with a charge q uniformly distributed on the surface of the ball that the magnetic moment μ is related to the angular momentum L by the relation:
\textbf{μ} = \frac{5q}{6mc}\textbf{L}Homework Equations
μ...
reference to Feyman lectures vol.1 topic 19.2 locating centre of mass
Feyman gives us the law of pappus to find the centre of mass ,which he proves for semicircular disc and ring.
But when i am trying to extend it to finding the centre of mass of a solid semi-circular solid hemisphere ,i...
Question,
If I make a rocket engine using KNO3 fuel and bentonite clay for the nozzle, shouldn't the ISP of the engine be slightly higher due to the radiation?
It would be nearly Immeasurable but nevertheless there.
Kind of like the way a NERVA engine works.
Homework Statement
A spherical conductor has a spherical cavity in its interior. The cavity is not centered on the center of the conductor. If a positive charge is placed on the conductor, the electric field in the cavity
A. points generally toward the outer surface of the conductor.
B...
A spherical shell and a conducting sphere each of radius R are charged to maximum potential. Which of the two has more charge?
My attempt:
Since in a conductor, no charge can reside inside the conductor so all charge is on the surface of the conductor just like the spherical shell. Now ...
Homework Statement
The question is "Use double integration to find the volume of the solid bounded by the cylinder x2+y2=9 and the planes z=1 and x+z=5"
Homework Equations
The Attempt at a Solution
I tried to draw the curves and the solid that i formed is a cylinder with a...
Hello,
Quick run-down: I am attempting to model thin film materials (e.g. Ti-Al-N) for thermal analysis. I am confused on how to figure out the number density of Nitrogen for a ceramic. All the tables I have in school textbooks are for gas (~0.0013 g/cm3). I can find density of...
In an Engineering course I was used to being rewarded for proving a good understanding of theory. For example, if I explained a basis of the following solution, it would still give some rewards, even if the solution itself had major computing errors or even if it was partially mathematically...
Hello,
I'm working on a poster and senior thesis in materials science research and need to draw schematic diagrams of a few objects including:
-a PLD chamber
-Thin films
-XRD
-SEM
-energy diagrams
-a sin wave
I've downloads inkscape and have tried to draw in powerpoint so far. Are...
Confusing Solid And Plane Angles !
Supplementary Quantities -
1.Solid Angle - Steradian
2.Plane Angle - Radian
Doubts -
1.What Is The Use Of Supplementary Quantities ? Physical Quantities Are Used To Measure For Example .. To Measure
Length - m Current - ampere Etc... What Can I...
Hi everyone - quick question on something that's been bugging me. So, train wheels, which are solid steel, have incredibly low rolling resistance, an order of magnitude less than average car tires. This is because they don't bend significantly, so you're not wasting energy to heat as in the...
https://www.physicsforums.com/attachments/1012
Let f(x)=\sqrt{x}, Line L is the normal to the graph of f and point (4,2)
(a) show that the equation of L is y=-4x+18
f'=\frac{1}{2\sqrt{x}} so f'(4)=\frac{1}{4} so normal would be -4
then L is y-2=-4(x-4) or y= -4x+18
(b) Point A is the...
Has anyone ever built an internal combustion engine which runs on solid fuel? A system would have to use waste heat or a mechanical friction device or whatever to heat the fuel and produce vapor which would be burnt in the cylinder (similar to the way coal gas was produced). Of course the vapor...
how does letting the electrons diffuse to the P material/region lead to a "depletion" region in the center where the N and P material meet? please go into detail
Homework Statement
See the image.
Homework Equations
T=Iα, F=ma, I=0.5*m*r^2, Friction=u*N
The Attempt at a Solution
I used the torque equation to get Tension = mcylinder*a/2, and then plugged that into a force equation for the block.
mblockgsin(30)-Tension-Friction=mblock*a
so...
Homework Statement
Given a solid hemisphere with radius R and uniform charge density ##/rho##, find the electric field at the center.
Homework Equations
##E = \frac{1}{4 \pi \epsilon_{0}} \frac{Q}{r^{2}}##
##E = \frac{1}{4 \pi \epsilon_{0}} \int \frac{\rho (x',y',z') \hat{r} dx' dy'...
Hi folks, can someone help explain this in words of one syllable or less? I am looking at a text that compares flux and intensity of a distant source, and it states that
∫∫dΩ = ∏
I know that
dΩ = sinθ dθ d∅
but I don't understand where the given result comes from. What are the...
Hello,
I have found several references (I can send you the links if you want) that point to the fact that the enthalpy under uniaxial compression along z of a solid is simply given by:
H=U+PzV
This appears to make sense as during uniaxial compression the Pz pressure component is the...
I am trying to find the minimum thickness that a sleeve (without relief) needs to be in order to not fail when assembled by interference fit. I know the interference value and the outer diameter of the shaft, but that's all...
How do I solve for pressure, stresses, and ultimately the minimum...
A small solid sphere of mass M0, of radius R0, and of uniform density ρ0 is placed in a large bowl containing water. It floats and the level of the water in the dish is L. Given the information below, determine the possible effects on the water level L, (R-Rises, F-Falls, U-Unchanged), when that...
I hope this isn't a common question, and that I'm not breaking any rules of posting - please let me know if I am, as I'm new here.
So, to describe what I'm trying to ask: Picture a very long rod, say, one light-year long. Imagine it's in space, and is free of gravitational interactions (and...
Homework Statement
Referring to the parallelepiped in Question 3 in which vertices E,F,G,H are respectively the diametrically opposite corners to A,B,C,D . Find the volume, in cubic units of the solid with seven plane faces BGD,BCD,GFD,BHG,GHEF,EFGC,BHEC
Homework Equations
The...
1.Determine the volume of the solid obtained by rotating the area between the x-axis and the graph of the function given by f(x) = cos(x^2) with x between (pi/2)^0.5 and (3pi/2)^0.5 ,about the y-axis.
2.What is the volume if the above area is rotated about the line given by x=4.
Thank you in...