hi,could some one please help me to understand how to find the density of water using a specific gravity bottle?and also a solid material..:cry:
many thanks.
Homework Statement
Find the volume of the solid generated by revolving the region bounded by the parabola y=x^2 and the line y=1 about the line y=1
Homework Equations
V= integral of pi*r^2 from a to b with respect to variable "x"
The Attempt at a Solution
pi(integral of 1-(x^2-1)^2...
Supposing that some solid can exist at 2 different phases (had 2 different crystalline structure) at some temperature and pressure. Can we define the same reference entropy or chemical potential for these two states (knowing that we are talking about the same solid)?
Homework Statement
Find the volume of the solid formed by revolving the region bounded by f(x) = 2-x^2 and g(x) = 1 about the line y = 1.
Homework Equations
V = ∏∫(1-f(x))^2dx - ∏∫(1-g(x))^2dx
The Attempt at a Solution
I keep ending up with ∏∫(1-(2-x^2))^2dx - ∏∫(1-1)^2dx, on...
Homework Statement
The atomic mass of Niquel is 58.7 amu (atomic mass unit), and it's density (at 90ºC) is 8.86 g/cm³.
(a) Find the distance from one atom to the closest one from him.Homework Equations
1 amu = 1.66053*19⁻²⁷
The Attempt at a Solution
I started by finding the number of atoms...
Homework Statement
Find the volume of the solid bounded above by the surface z = x^2 + y^2 and below by the
triangular region in the xy-plane enclosed by the lines x = 0 , y = x , and x + y = 8.
Homework Equations
V = ∫∫ Height
Base
The Attempt at a Solution
I first found...
Homework Statement
Find the volume of an object bounded by x2 + y2 ≤ 1, x2 + z2 ≤ 1 and y2 + z2 ≤ 1.
Homework Equations
The Attempt at a Solution
This stuff is very new to me (multiple integrals to find volume) so I am not entirely familiar with it. My first thought was to put...
I have the following homework question I am working on.
I am given three scattering angles: 42.8, 73.2, 89. (in degrees) without the wavelength of the light used. I am to show that these are consistent with a diamond lattice.
I started with Laue's Law: delta(k) = G and according to the...
Homework Statement
Question is attached in this post.
Homework Equations
Question is attached in this post.
The Attempt at a Solution
Disk Method with the radius equal to 1/(x^2+5x+6)
∫A/(x+2) + B/(x+2)^2 + C/(x+3) + D/(x+3)^2 from 0 to 3
I've used algebra to solve for...
Homework Statement
A metal sphere with radius a is supported on an insulating stand at the center of a hollow, metal spherical shell with radius b. There is charge +Q on the inner sphere and charge -Q on the outer shell. Take the potential V to be zero at infinite separation.
Calculate...
Homework Statement
Find the volume of the solid of revolution obtained by rotating the area bounded by the curves about the line indicated.
y=x2-2, y=0 about y=-1. Need only consider part above y=-1
Homework Equations
V=∏a∫b[f(x)]2dx
The Attempt at a Solution
I'm mainly unsure of...
The way I understand plasma is that is almost a gas except some of the electrons of separated from the nuclei entirely making positively charged. Is there a temperature in which Iron is by definition a gas, and not a plasma?
Also, can something like a noble gas become a solid?
Atoms in solid are more closedly packed as compared to liquid and gases. But we exert more force, some solid gets compressed but liquid doesn't, why? If atoms are loosely packed in liquid than solids, liquids should get compressed...
A colleague and I want to model how a slab of PCM (wax) solidifies as it cools off. What I have noticed in my experiments is that temperature sensors on the top and bottom of the slab say it should be solid, as they read well below the melting point. But when I peek at the sample, the center...
Homework Statement
The problem is attached in this post.
Homework Equations
The problem is attached in this post.
The Attempt at a Solution
I've set up the integral via disk method: π∫(e^√x)^2 dx from 0 to 1
I've done integration by parts by don't know how to integrate the...
Homework Statement
NaCl (a0 = 5.64A° ), NaBr (a0 = 5.98A° ) and KCl (a0 = 6.30A° ) all have the same structure, which
is the NaCl structure.
(a) Assuming the spacings are determined by the ionic radii of the relevant ions, what would value
would you expect for the lattice constant of...
Homework Statement
The problem is attached in this post.
Homework Equations
The problem is attached in this post.
The Attempt at a Solution
I used washer method and set my outer radius as 2+2+√(x-1) and my inner radius as 2. I set my upper limit as 5 and my lower limit as 2...
Homework Statement
The problem is attached in this post. Homework Equations
The problem is attached in this post. The Attempt at a Solution
I used shell's method and set up my integral as 2π∫(4-x)(x^2)dx, from -2 to 2 and got an answer of 128π/3 which is incorrect. The actual answer is...
Homework Statement
Find the volume of the solid using cylindrical shells:
y=e-x^2 y=0, x=0, x=1, about y-axis.
Homework Equations
How do I integrate xe^(-x^2)?
The Attempt at a Solution
2∏x∫0 to 1 xe^(-x^2) dx
2∏*-(e^(-1))/2)
Homework Statement
See the attached problem. Homework Equations
See the attached problem. The Attempt at a Solution
I used washer method and got an inner radius of x=y^2 and an outer radius of x=y+2, I calculated my upper limit as being 4 and my lower limit as being 0. The answer is 72π/5...
Homework Statement
I don't have the exact wordings of the problem statement. I hope the following is enough to understand the problem.
A solid hemisphere is kept on a plane horizontal frictionless surface. The hemisphere is made to tumble (or toss, I am not sure about the correct word)...
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 y-axis.
2. The attempt at a solution
v=∏ ∫ from 0 to 1 of (y-y^3)^2 dy
and doing this, I got the answer to be 8∏/105.
Did I set up that integral...
Homework Statement
It asks to find the volume of the solid given these planes:
z = x
y = x
x + y = 2
z = 0
It also asks to find the volume using 2 iterated integrals with different orders of x and y integration.
Homework Equations
The Attempt at a Solution
I found...
Find the Volume of a Solid by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.
x = y^2, x = 1 - y^2, about x = 3
So here is how far I've gotten with this problem. I need help though. Any guidance will be...
I've been reading Kittel's book on Solid state physics and while it's been mostly smooth sailing, the abrupt loss of rigour in places in unsettling. In particular, the bits about scattering seem to be just thrown in here and there without any rigourous mathematical treatment at all.
He talks...
Hi,
It's surprising how little information is available on this topic, considering it seems like such a fundamental problem. The only tutorial I have found is http://www.umich.edu/~ners312/Course%20Library/SolidAngleOfADiskOffAxis.pdf, and my university does not have access to the other papers...
A uniform sphere of mass M and radius R has a point on its surface fixed at the origin. Its centre lies along a line in the direction of the position vector r = i + 2k + 3k at length R. Find the components of the torque acting on it due to gravity if the z-direction is upwards and gravity acts...
Homework Statement
a light string is wrapped around a solid cylinder and a 300 g mass hangs from the free end of the string. When released, the max falls a distance 54 cm in 3.0s.
b) calculate tension in string
c) calculate mass of cylinder
Homework Equations
F=ma
I=1/2(mr^2)...
Homework Statement
Set up a double integral to find the volume of the solid bounded by the graphs y=4-x2 and z=4-x2
The attempt at a solution
I drew myself a 3d graph but it's just a parabloid in the xy plane and a parabloid in the xz plane right? so I'm unsure how to set up my...
Hi,
Could someone explain how to calculate the probability that two substitutional dopants will reside in adjacent lattice sites.
For example, given a dopant concentration of 5% and a crystal structure in which each lattice site/atom is coordinated to 8 others what is the probability of...
Homework Statement
) Two uniform, solid cylinders of radius R and total mass M are connected along their common axis by a short, massless rod. They are attached to a spring with force constant k using a frictionless ring around the axle. If the spring is pulled out and released, the cylinders...
The problem is :
a) Find Helmholtz free energy F(V, T) of a simple solid.
b) Use the result of part a) to verify that (∂F/∂T)v and (∂F/∂V)T are consistent with S(T, V) and P(V, T) in equation P=a0T-b0ln(V/V0)
I know:
Helmholtz free energy is F=U-TS
and dF=-SdT-PdV
S=-((∂F/∂T)v)...
Homework Statement
The Question originally is to find the m of a solid uniformly charged solid sphere which is rotating uniformly with ω
Now
Homework Equations
Now my question to you is how to take the small element?
The Attempt at a Solution
i take a small disc with...
The problem is :
a) Find Helmholtz free energy F(V, T) of a simple solid.
b) Use the result of part a) to verify that (∂F/∂T)v and (∂F/∂V)T are consistent with S(T, V) and P(V, T) in equation P=a0T-b0ln(V/V0)
I know:
Helmholtz free energy is F=U-TS
and dF=-SdT-PdV
S=-((∂F/∂T)v)...
how would i go about calculating the peak force of an impact between two solids
i assume it has to do with the how readily the structure compresses but I am not sure what else might complicate it from there
also what if one of the objects fractures and what about granular impacts
Homework Statement
Find the volume of the solid of revolution when we rotate the area limited by the x-axis and the function f(x) = 1 - cosx where x e [0, 2∏] once around the y-axis?
The Attempt at a Solution
In my notes I have the following equation:
V = ∫ 2∏x f(x) dx
If I put...
1. The problem statement
The potential energy between two ions is
u(r) = -α/r2 + β/r8
Determine:
(i) The intermolecular distance ro for which the potential energy is minimum
(ii) The inter-atomic distance for which the potential energy is zero is
R= (2)-1/6ro...
I'm a mechanical engineer and I am more specialized in structural calculations than dynamic calculations and now I'm faced with a basic dynamic problem and would need some help.
I have a solid cylinder (shaft) that I want to rotate around its axis. The cylinder is supported by two bearings at...
I have an interesting question that I'm not sure how to go about solving. This question has a little general relativity and (maybe) a little QM, but I wasn't sure where to post it.
Question:
Imagine that a \pi0 meson traveling along the z-axis (velocity v=0.99c, rest mass M) decays into two...
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...