A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is the portion with which other materials first interact. The surface of an object is more than "a mere geometric solid", but is "filled with, spread over by, or suffused with perceivable qualities such as color and warmth".The concept of surface has been abstracted and formalized in mathematics, specifically in geometry. Depending on the properties on which the emphasis is given, there are several non equivalent such formalizations, that are all called surface, sometimes with some qualifier, such as algebraic surface, smooth surface or fractal surface.
The concept of surface and its mathematical abstraction are both widely used in physics, engineering, computer graphics, and many other disciplines, primarily in representing the surfaces of physical objects. For example, in analyzing the aerodynamic properties of an airplane, the central consideration is the flow of air along its surface. The concept also raises certain philosophical questions—for example, how thick is the layer of atoms or molecules that can be considered part of the surface of an object (i.e., where does the "surface" end and the "interior" begin), and do objects really have a surface at all if, at the subatomic level, they never actually come in contact with other objects.
Hello! I am a bit confused about calculating the induced surface charge density on an infinite conducting plane, with 0 potential, in the presence of a charge, q, a distance d above it. Assuming that the plane is in xy plane and the charge in positive z region, in the book they use the method of...
$ \tiny{231.14.88}\\$
$\textsf{Identify and briefly describe the surface of the equation}\\$
\begin{align*}
S_{88}&=\frac{-x^2-y^2+z^2}{9+6x-8y}=26
\end{align*}
$\textit{this had no template example but on}\\$
$\textit{ W|A it looked like a torus?}\\$
$\textit{where is a good online 3d graphing...
I have never heard of a way to investigate this mathematically but I'm sure there is. How would you describe the surface area or volume of some 3-D surface formed by moving an enclosed area along a curved axis a certain distance? You could easily describe a torus by taking a circle and forming...
Homework Statement
The electric field strength just above one face of a copper penny is 2230 N/C. What is the surface charge density on this face of the penny?
Homework Equations
Electric field of an infinite plane of charge = η/(2*ε0)
The Attempt at a Solution
I used the above equation, and...
Homework Statement
Let n be the unit outward normal of a spherical surface of Radius R, let the surface of the sphere be denoted by S.
Evalute Surface integral of nndS
Homework EquationsThe Attempt at a Solution
I have evaluated the surface integral of ndS and found it to be 0. but am not...
Eventually the Sun will go through its phases and cool down. Is it possible to calculate how long it will take for the surface to cool to 75 degrees Fahrenheit?
Homework Statement
Problem:
A 12.0-kg block is pushed to the left across a rough horizontal surface by a force that is angled 30.0◦ below the horizontal. The magnitude of the force is 75.0 N and the acceleration of the block as it is pushed is 3.20 m/s^2 . What angle does the force exerted on...
Hi,
My textbook has a multiple choice question about which stellar object has the highest surface temperature and the answer was a white dwarf. However, one of the options was a neutron star. Neutron stars are much denser and have been crushed by gravity even more plus they are rotating at...
Homework Statement
A metal sphere of radius a is surrounded by a metal shell of inner radius b and outer radius R, as shown in the diagram below. The flux through a spherical Gaussian surface located between a and b is 1.20Q/εo and the flux through a spherical Gaussian surface just outside R is...
Homework Statement
Homework Equations
E=σ/(2Eo)
σ=2Eoma/e
a=Δv/Δt
The Attempt at a Solution
So doing my best to read the velocity over time graph I came up with
Δv/Δt=(-2E5m/s)/(10E-12s)=-2E17 m/s/s
σ=2Eoma/e
=2(8.99E-9C)(9.109E-31kg)(-2E17m/s/s)/(1.6022E-19)
=-0.020444 C/m^2
but by the...
I found it very interesting to see that surface charge and the Poynting vector are being used to describe how a simple DC circuit actually works. Chabay and Sherwood have made an outstanding contribution to physics and engineering in their texts and papers. Of course others jump on the...
Homework Statement
Calculate surface temp of heat exchanger when it's heating the room with the known power of P. Room temperature T is also known, as is the heater surface area A. ε ≈ 1.
Homework Equations
P = εσAT^4 is what I've been trying to use.
The Attempt at a Solution
I've been...
I will use an example:
-The surface is given by the intersection of the plane:
y+z=2
-And the infinite cilinder:
x2+y2<=1
We want to parametrize this surface, it could be done easily with:
x=r cosθ
y=r sin θ
z=2 - r cos θ
Then this surface could be written using vector notation:
S= r...
Homework Statement
There is a disk with mass 50 grams put on a slippy surface (no friction!). Its radius is 5 cm. Mass of the weight is 20 grams. At the beginning there is no motion. How far does the center of mass of the disk move in 10 seconds? (answer: 91 m) How many turns does the disk in...
Hi guys,
First of all, thank you for your help. I am new in Ansys and Fluent (less than a month), hoping to learn.
I am trying to model a simple and single surface reaction
CH4 (g) -> C(s) + 2H2 (g)
on a "CVD reactor" to grow C(s) (graphene, or graphite). The inlets are gases inyections of...
Homework Statement
Sketch the surface of a paraboloid z=9-x2 -92 in 3-dimensional xyz-space
Homework Equations
I assume partial derivatives are involved in some manner
The Attempt at a Solution
[/B]
I attempted to solve by making each variable equal to zero... That didn't work xD. I would...
Let V be the region bounded by the hemisphere z=1-sqrt(1-x^2-y^2) and the plane z=1, and let S be the surface enclosing V. consider the vector field $F= x(z-1)\hat{\imath}+y(z-1)\hat{\jmath}-xy\hat{k}$.
Homework Statement
The two blocks ##(m=16 kg)## and ##(M=88 kg )## , are not attached to each other.The coefficient of static friction between the blocks is ##μ=0.33##, but the surface beneath the larger block is frictionless.What is the minimum magnitude of the horizontal...
Homework Statement
A 1 500kg satellite is in orbit 250km above Earth's surface. What minimum additional energy is needed to place this satellite in a new stable orbit 800km above Earth's surface?
Homework Equations
W = delta Ep = -GMm(1/r2-1/r1)
Ep = -GMm/r
Ek = GMm/2r or 1/2mv^2
The...
Homework Statement
Will a frictionless body placed on the Earth move, and if so, describe it's path and acceleration.
Homework Equations
I was given no equations, but I believe that coriolis and centripetal forces would act on the body.The Attempt at a Solution
I assume that we have to assume...
Given that 1.34Tbit of information can fit on a square inch of average hard drive surface, how many 400 KB files could be written on a square millimeter? I did the math and came up with about 634. This seems unbelievably high and I wonder if someone would have time to check it. I kind of need...
Homework Statement
A hollow stirrer that has a diameter of 2.0 mm is inserted into a cup of water at 20∘C. The surface tension of water at that temperature is γ(surface tension) = 7.28×10−2 N/m.
What is the mass of the water supported by the surface tension in the stirrer?
Given:
d=2 mm...
Homework Statement
Consider the cardioid given by the equations:
##x = a(2\cos{t} - \cos{2t})##
##y = a(2\sin{t} - \sin{2t})##
I have to find the surface that the cardioid circumscribes, however, I don't know what limits for ##t## I have to take to integrate over. How can I know that, as I...
Homework Statement
A student looks at the sunlight reflected off a puddle of water. She puts a polarising (Polaroid) filter in front of her eye. As she rotates the filter the puddle appears darker then lighter.
Explain this observation
Homework EquationsThe Attempt at a Solution
Here's my...
Homework Statement
Is the solution provided by the author wrong ? Stokes theorem is used to calculate the line integral of vector filed , am i right ?
Homework EquationsThe Attempt at a Solution
To find the surface integral of many different planes in a solid , we need to use Gauss theorem ...
https://web.mst.edu/~numbere/CP/CHAPTER%203.htm
I have trouble understanding why the length used in 3.1.1 is pir^2. My notes don't explain what length we use either.
So if I drop an apple, we can consider the ground accelerating upwards and the apple still. And the radius of the Earth doesn't change due to space time being curved.
I'm having a hard time conceptualizing this.
Is it analogous to a classically orbiting object? Classically, under simplfying...
Hi everyone,
While studying surface tension I came across a(numerical example) problem which asks to find the force required to pull a circular glass plate of some given radius from the surface of water(assume plane of plate on water surface). Value of surface tension of water is also given in...
If you increase surface tension, the molecules at the surface are more strongly pulled into the center of mass due to the stronger attractive molecular forces.
-Why is it that when surface tension increases in a liquid, its surface decreases in area, but its volume does NOT change? (Volume...
Homework Statement
Hi,
Infinitely far away from a mass-->gravitational potential is zero.
As get closer-->becomes negative.
At surface-->it is the smallest value of r, i.e. the radius of the mass, hence the most negative value for gravitational potential.
But as you go below surface of Earth...
Homework Statement
A fish watcher at point P watches a fish through a glass wall of a fish tank. The watcher is level with the fish; the index of refraction of the glass is 8/5, and that of the water is 4/3. The distances are d1=8.0 cm, d2=3.0 cm, and d3=6.8 cm (a) To the fish, how far away...
Homework Statement
We are given a Banana, and asked to find the volume and surface area of the function, using calculus. So far, we have learned elementary calculus (derivatives, limits, and integrals) as well as volumes of revolutions. We traced the banana on graph paper, plotted points on the...
I am doing surface failure analysis for a ball bearing SKF 6025, , as an exercise, It has been used in the washing machine tub, after some time a noise has been reported and it is no longer rotating. When i got it I opened the seal and captured the attached photo. I had a feeling that it suffers...
Homework Statement
Calculate ##\iint { y+{ z }^{ 2 }ds } ## where the surface is the upper part of a hemisphere with radius a centered at the origin with ##x\ge 0##
Homework Equations
Parameterizations:
##\sigma =\left< asin\phi cos\theta ,asin\phi sin\theta ,acos\phi \right> ,0\le \phi \le...
we interest one V-Sorb 2800 BET surface area analyzer, using physical adsorption principle to test particles surface area data, if anyone knows this analyzer principle?
Homework Statement
A landing craft with mass 1.22×10^4 kg is in a circular orbit a distance 5.50×10^5 m above the surface of a planet. The period of the orbit is 5100 s . The astronauts in the lander measure the diameter of the planet to be 9.50×10^6 m . The lander sets down at the north pole...
Hey guys,
Desai Yield Surface:
I have a hard time understanding the parameters of the model for soils. If I have three principle stresses, σ1, σ2, σ3. And R is defined as the Tri-axial strength in tension, how would I define R.
Lastly can I just say that
I1 = σ1+σ2+σ3
J2= 1/6 * ((σ1-σ2)2...
Homework Statement
A 5-foot long cylindrical pipe has an inner diameter of 6 feet and an outer diameter of 8 feet. If the total surface area (inside and out, including the ends) is k*PI , what is the value of k?
Homework Equations
In my view the formula should be:
2* PI * radius * h + 2*PI *...
according coulomb force of friction is independant of contact surface
a tyre car grip goes in function of contact surface and grip is caused by friction
this seems contradictory with coulomb
is still coulomb view mainstream or has it been corrected?
This is schematic band structure for the dxz and dyz orbitals using a 2D square Fe lattice. What is the location in the Brillouin zone of the hole-like Fermi surface and the electron-like Fermi surface?
How exactly does hydrostatic pressure affect the shape and size of each Fermi surface in Figure 4B? How do you read this figure or what exactly is it showing?
an idea for my new project
construction - a cubical bowl of tap water , 2 sheet electrodes for 1 pair (y-axis pair)of opposite face(square wave 10Hz 10vpp), 2 sheet electrodes for the other pair (x-axis pair)(similar square wave lags by half cycle )
left hand touches adc pin. right hand touches...
I assume this is a simple summation of the normal components of the vector fields at the given points multiplied by dA which in this case would be 1/4.
This is not being accepted as the correct answer. Not sure where I am going wrong. My textbook doesn't discuss estimating surface integrals...
Homework Statement
A solid sphere rolls down a hemisphere from rest. Find the angle at which the sphere loses contact with the surface.
R = radius of hemisphere
a = radius of sphere
Homework Equations
ΣFr = Macm,r
N-mgcosθ = -mVcm2/(R+a)
N = mgcosθ - mvcm2/(R+a) eq. (1)
Conservation in...
Hi
I want to study the topic of surface tension for the purpose of solving problems. I have textbooks like Halliday Resnick and Young Freedman. But these books don't cover the topic of surface tension. If you know any free, open resources to study this topic, please let me know
thanks
Homework Statement
A 60 kg farmer ropes a 300 kg ox. Both are initially at rest, 24 m apart on a frictionless level surface. When farmer ends up pulling the ox towards him, the ox will move
A) 4m, B) 5m, C) 12m, D) 20m, E) 24m .
Can anyone help me solve this?
Homework EquationsThe Attempt at...
Hi everybody,
I’m trying to calculate the shape of a boundary line f(x) between two mediums that collimates rays from a point light source. This requires the rays to hit the boundary line under a certain angle, so I calculated the slope m(φ) of the boundary line for a ray with polar angle φ (φ...
Homework Statement
A very thin plane of length ##2a## is placed in the air at height ##a## above the conducting surface. The plane is charged on its surface and the expression for it's surface charge density (##ρ_s##) is given by ##ρ_s=ρ_{s0}*\frac{x}{a}## and ##ρ_{s0}## is some constant.
a)...