Surface Definition and 1000 Threads

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...

Charles Link submitted a new PF Insights post Permanent Magnets Explained by Magnetic Surface Currents Continue reading the Original PF Insights Post.

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)...

Homework Statement It's open container with water which moves horizontally. It moves with some acceleration. Angle of incidence (α) and angle of reflection(β) on water are given (α=40 deg., β=20 deg.). We need to find container's acceleration. Homework Equations a=(v2-v1)/t (?) The Attempt at...

I know that the surface roughness plays an role in the Magnus force exerted of a rotating cylinder. But, i cannot find an equation that includes the surface roughness in the equation of the Magnus force. If someone could state the formula (and preferably a source to read up more on it) it would...

Homework Statement [/B] Water rises in a capillary tube to certain height such that the upward surface due to surface tension is balanced by 7.5 X 10-4N Force due to weight of the liquid. If the surface tension of water is 6 X 10-2Nm-1,the inner circumference of the capillary must be Homework...

HELP I can't find the surface of revolution! By donuts I mean a circle that doesn't touch the axes (tore in french) y^2+(x-4)^2=2^2 is my function ( y^2+x^2=r^2) and the axe of rotation is y so y= sqrt(r^2-x^2) the formula I know : 2* pi (Integral from a to b (F(x)*sqrt( 1+ (f``(x))^2))...

Homework Statement We have an infinite cylinder that, from radius 0 to a, has a volume current density ##\vec{J(r)}=J_{0}(r/a) \hat{z}## , then from a to 2a, it has a material with uniform linear magnetic permeability ##\mu=(3/2)\mu_0## , and at the surface, it has surface current...

How do I find the surface area of a f(x) rotated around the y axis?

Homework Statement Find the centroid of solid enclosed by surface z= y^2 , plane x=0 , x = 1 and z =1 . The density is 1 Homework EquationsThe Attempt at a Solution Here's my working . Centoird = mass of inertia / mass So , i find the mass first . It's clear that the circle is on zx...

Homework Statement Find the surface portion bounded by plane 2x +5y + z = 10 that lies in cylinder (x^2) +(y^2) = 9 ... I have skteched out the diagram and my ans is 5sqrt(30) instead of 9sqrt (30) as given by the author ... Anything wrong with my working ? Homework EquationsThe Attempt at a...

Homework Statement Find the surface area of portion of plane x + y + z = 3 that lies above the disc (x^2) + (y^2) < 2 in the first octant ... Homework EquationsThe Attempt at a Solution Here's the solution provided by the author ... I think it's wrong ... I think it should be the green...

Homework Statement [/B] Question :- Find the acceleration of block of mass ##M##. The coefficient of friction between blocks is ##\mu_1## and between block and ground is ##\mu_2##. free body diagram at the end. Variables :- ##f_1## - friction between blocks. ##f_2## - friction between block...

Homework Statement Consider the metal-vacuum interface located at z = 0,the metal filling the entire half-space z ≥ 0, vacuum filling (!?) the half-space z < 0. The dielectric function in the metal in the long-wavelength limit is given by: where ε0 is the vacuum permittivity. In the metal a...

Homework Statement I'm just required to setup the integral for the question posted below Homework EquationsThe Attempt at a Solution So solving for phi @ the intersection of the sphere and the plane z=2: z = pcos(phi) 2 = 3cos(phi) phi = arccos(2/3) so my limits for phi would go from 0 to...

Homework Statement find the slope of tangent line to curves cut from surface z = (3x^2) +(4y^2) - 6 by planes thru the point (1,1,1) and parallel to xz planes and yz planes ... Homework EquationsThe Attempt at a Solution slope of tnagent that parallel to xz planes is dz/dy , while the slope of...