Surface Definition and 1000 Threads

Hi, if I have a block of metal with a quarter circle curve cut out of it, and a metal roller of matching radius that contacts this curved piece, what are some ways I could go about measuring the friction between these two surfaces? The roller is fixed and the block is pushed into it with a...

Homework Statement Use a line integral to find the area of the surface that extends upward from the semicircle ##y=\sqrt{9-x^2}## in the ##xy##-plane to the surface ##z=3x^4y## Homework Equations Parametric Equation for Circle: ## x = rcos(t) ## ## y = rsin(t) ## Line Integral: ## \int_c...

Suppose a cylindrical rod is given a push such that it rolls without slipping on a horizontal plane. Am I right to say that rolling friction is only required at the start when the push is applied to initiate the rolling motion? Once the push is removed, the only forces acting on the rod are its...

Homework Statement A body moves down along an inclined plane from A(top) to B(bottom), and then moves on the floor in continuation to some point C. (All surfaces are frictionless) After reaching B, body is having some acceleration. But while moving from B to C, a) will it keep on...

I think its a defination to have infinite longitudnal lines , if line are not perpendicular than the infinite point will not add up to give the circumferance of equator, please help

Hello Forum, In the case of an ideal, thin lens (free from any aberration), it does not matter which face of the lens is facing the object. The results will be identical. What if the lens was an ideal (no aberration) thick less with the H planes, etc...? Would it matter which lens surface is...

Homework Statement Problem is in image uploaded Homework Equations n/a The Attempt at a Solution x = u, y = v and z = 1 - u - v ∂r/∂u × ∂r/∂v = i + j + k F dot N = u^2 + 3v^2 ∫∫(u^2 + 3v^2 )dudv My problem is I'm not sure what I should take as the limits? Should I flip around the order of...

Homework Statement Two blocks, A and B , are being pushed on a frictionless surface by a froce of 30 N to the right, .Block A has a mass of 2.0kg, Block B, being pushed by Block A is 4.0kg. Calculate the magnitude of the force that block B exerts on Block A. Homework Equations f=ma The...

Hello, This problem is about cooper pair formation and what happens with the calculations if there is an attractive potential between electrons but it is not in the presence of a filled fermi surface. 1. Homework Statement Two electrons just above the filled Fermi Surface of a material can...

Homework Statement Sorry- I've figured it out, but I am afraid I don't know how to delete the thread. Thank you though :) Homework Equations Below The Attempt at a Solution Photo below- I promise its coming! I've started by using cylindrical coordinates, but I wasn't sure if spherical...

Homework Statement 1) Calculate the angular diameter distance to the last scattering surface in the following cosmological models: i) Open universe, ΩΛ= 0.65, Ωm = 0.30 ii) Closed universe, ΩΛ = 0.75, Ωm = 0.30 ii) Flat universe, ΩΛ = 0.75, Ωm = 0.25 Describe how the CMB power spectrum...

Homework Statement a) A charge q is released a distance d above a grounded infinite conducting plane. It's non relativistic velocity is v. Find the induced surface current density on the plane. b) Show that the above current density produces a vanishing magnetic force on the charge. Homework...

Homework Statement 1) Calculate the angular diameter distance to the last scattering surface in the following cosmological models: i) Open universe, ΩΛ= 0.65, Ωm = 0.30 ii) Closed universe, ΩΛ = 0.75, Ωm = 0.30 ii) Flat universe, ΩΛ = 0.75, Ωm = 0.25 Describe how the CMB power spectrum...

Hey guys! The question is related to problem 2.26 from Electrodynamics by Griffiths (3ed). 1. Homework Statement A conical surface (an empty ice-cream cone) carries a uniform surface charge σ. The height of the cone is h, as the radius of the top. Find the potential difference between points a...

Homework Statement Find the surface area S of the portion of the hyperbolic paraboloid: ## r(u,v) = \langle (u+v),(u-v),uv \rangle ## for which: ## u^2 + v^2 <= 225 ##Homework Equations (Surface Area for Parameterized Region:) ##\int \int ||\frac {\partial r} {\partial u} \times \frac...

An area A in the (x,y) plane is limited by the y-axis and a parabola with the equation x=6-y^2. Further, is a surface F given by the part of the graph for the function h(x,y)=6-x-y^2 which satisfies the conditions x>=0 and z>=0. Determine a parametrization for A and for F. So far I've got the...

Dear Member, Respected Members, I am working on the behaviour of hydrogen at the Cu/Ni (111)-graphene interface. In case of Ni (111), the atomic H on the interface diffuse inside the the surface. While in case of Cu (111), the H atom stays at the Cu(111)-graphene interface. It seems that H...

I'm given that: S is the surface z =√(x² + y²) and (x − 2)² + 4y² ≤ 1 I tried parametrizing it using polar coordinates setting x = 2 + rcos(θ) y = 2rsin(θ) 0≤θ≤2π, 0≤r≤1 But I'm not getting the ellipse that the original equation for the domain describes So far I've tried dividing everything...

Homework Statement The Earth receives on average about 390 W m−2 of radiant thermal energy from the Sun, averaged over the whole of the Earth. It radiates an equal amount back into space, maintaining a thermal equilibrium that keeps the average temperature on Earth the same. Assuming the Earth...

Homework Statement This is problem 3.4 from Prucell and Morin if you have the book. Homework Equations None The Attempt at a Solution Electric field inside a conducting sphere is zero. Let P be a point on one of its equatorial plane. The field along the plane is zero. So I know the charge...

Hi , I came across a problem ,I've search a lot but couldn't exactly find the solution. here is my problem: suppose there is an image ( I call it IMG_A),place IMG_A in the X-Y plane , put a mirror cylinder at the center of IMG_A. what we see in the cylinder mirror is a deform image (I call it...

Hey all, Interestingly enough, I was actually recently feeding some ducks at a nearby pond when I noticed a cool phenomenon that I couldn't explain myself, so I was hoping you guys could assist in that. When you have two air bubbles over a liquid surface, like water, they seem to accelerate...

From a textbook: I don't quite understand the part where the difference of densities is taken, could someone explain that for me? Thanks.

The motivation for this thread comes from physics, but I'm posting it in the maths section as the question is more of a mathematical one and less concerned with the underlying physics. In cosmology, they often talk about closed universes with positive curvature, or non-Euclidean elliptic...

Homework Statement By finding the Lagrangian and using the metric: \left(\begin{array}{cc}R^2&0\\0&R^2sin^2(\theta)\end{array}\right) show that: \theta (t)=arccos(\sqrt{1-\frac{A^2}{\omega^2}}cos(\omega t +\theta_o)) Homework EquationsThe Attempt at a Solution So I got the lagrangian to be...

Homework Statement Electric current of I amperes flows along the z-axis from (0, 0,-∞) to (0, 0, -a) and from there it spreads over a conducting sphere r = a in the -aθ direction, comes to the point (0; 0; a) and goes to (0, 0, ∞) again along the z-axis. What is the surface current density at...

I have a free particle moving on the surface of a sphere of fixed radius R. Gravity is ignored and m/2 is left out since its constant. The lagrangian is L = R^2 \dot{\theta^2} + R^2 sin^2{\theta} \dot{\phi^2} Using the Euler Lagrange equations I obtain sin^2{\theta} \dot{\phi} = A = const \...

Homework Statement The free fall acceleration of a mass ##m## above the Earth's surface in one dimension can be represented by ##m\ddot{y}=-\frac{mMG}{y^2}## where ##M## is the mass of the Earth and ##G## is the gravitational constant. With ##\dot{y}(t=0)=0## and ##y(t=0)=y_0##.. (1) Find an...

Hello all, new here but plan to stick around for a while. I am currently trying to make a sensor that can detect if a material below it is paramagnetic. I believe paramagnetic is the proper term, but it needs to detect if the force exerted by permanent magnet is above a certain threshold. The...

Homework Statement Ball strikes inclined plane of infinite mass with velocity v vertically. Elastic collisions. Velocity and direction after collision? One way of solving is take components along and perpendicular to inclined plane and then solve easily. Is there any way to solve is using...

Homework Statement i don't understand the statement 1 and 2 , can someone help to explain ? for 1 , does the author mean Fh= Fv ?? for 2 , does the author mean Fv = Fh + W ? but in statement 1 , Fh already = Fv Homework EquationsThe Attempt at a Solution

Homework Statement An infinitely long, cylindrical, conducting shell of inner radius b and outer radius c has a total charge Q. A line of uniform charge distribution Λ is placed along the axis of the shell. Using Gauss's Law and justifying each step, determine. A) The Electric Field for r>a...

Hello If we have a gaussian surface that is placed in a uniform electric field E and encloses 0 charge, what would the E-field at the gaussian surface be? I have assumed the gaussian surface to be cubic surface, and then I have found from Gauss's law that the electric field is zero at the...

https://www.google.ca/search?q=stress&biw=1366&bih=629&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjA9u3S5_jKAhXCJx4KHfN8DmYQ_AUIBigB#tbm=isch&q=stress+tensor&imgrc=xK8-tGSPxXha7M%3 This is a simple question. -why stress is defined on 3 surfaces only instead of the entire 6 surfaces? I believe 3...

Homework Statement f(z)=z^\frac{3}{2} find the branch points, branch cuts, and Riemann sheet structure. Homework Equations none The Attempt at a Solution So, I converted this to complex exponential form r^\frac{3}{2} e^\frac{i*3*\Theta}{2} From here I mapped around a circle that was...

Namely, are the wave functions of electrons near the Fermi surface spatially distributed in the so-called "active blocks" (CuO2 layers and etc.) or in the so-called "charge reservoir blocks" ? Or any other case? ( EO/(AOx)m/EO with m =1, 2 monolayers of a quite arbitrary oxide AOx(A = Bi, Pb...

Homework Statement A closed surface with dimensions a = b = 0.302m and c=0.604m is located as in the figure. The electric field throughout the region is nonuniform and defined by E⃗ = (α+βx2)ˆı where x is in meters,α=4N/C, andβ=4N/(C·m2).? What is the magnitude of the net charge enclosed by the...

Homework Statement I have this problem in an online assignment. Someone told me the answer, so I already got it right, but I don't know why my logic leads me to the wrong answer. The problem: The temperature u of a star of conductivity 1 is defined by u = \frac{1}{sqrt(x^2+y^2+z^2)}. If the...

Homework Statement Assuming that the average surface brightness within the effective radius is 19 mag/arcsec2, use the definition of the effective radius to estimate what the effective radius in kpc would be for NGC 4216 if it was an elliptical galaxy. Homework Equations All the logs are base...

Homework Statement A Ti Rod is to be put into a furnace to try and increase the carbon content of the rod. Initially, the carbon content of the rod is 0.2%wt. The carbon content of the furnace is 1.0%wt. What would the temperature have to be in order to get a final carbon content in the Ti rod...

Why he did not consider parallel force?Will parallel component of electric field not produce electric pressure on the surface?

Homework Statement [/B]Homework Equations Poynting's Theorem S = 1/μ0 (E x B) Momentum = p = μ0ε0 ∫ S dτ The Attempt at a Solution My strategy was to treat the hollow sphere as a point charge (by Gauss' Law), so E = 1/4πε0 Q/a2. I believe the magnetic field would be B = 2/3μ0M (where M is the...

In my physics textbook, I see Gauss' Law as https://upload.wikimedia.org/math/0/3/5/035b153014908c0431f00b5ddb60c999.png\ointE dA but in other places I see it as...

Old article: http://edition.cnn.com/2009/TECH/science/08/28/hurricanes.gates.gray/ What do you guys think? Where do you see this project going? The official word is that it's not being publicly funded. But if there was even a 10% chance it would work, I see governments lining up at the...

Homework Statement Evaluate integral A.n dS for A=(y,2x,-z) and S is the surface of the plane 2x+y=6 in the first octant of the plane cut off by z=4 Homework Equations Integral A.n dS The Attempt at a Solution The normal to the plane is (2,1,0) so the unit normal vector is 1/sqrt3 (2,1,0)...

hi guys, i have a question. i saw this picture, and i don't really understand how they derived with the formula. The aim is basically to find the formula for the surface area of a spherical cap. why do you differentiate the x=sqrt(rˆ2-yˆ2)? how does that help to find the surface? and then...

Hey! :o I want to calculate the surface integral of $$F(x,y,z)=(0,0,z)$$ on the unit sphere with parametrization $$x=\sin u \cos v, \ y=\sin u \sin v , \ z=\cos u \\ 0\leq u\leq \pi, \ 0\leq v\leq 2\pi$$ with positive direction the direction of $T_u\times T_v$. Could you give some hints how...

Hi PF! I have been reading and reading for a clean explanation for the hydrostatic force of a curved submerged 2-D (or 3-D if you're up to it) surface. I really don't care what the curve looks like: quadratic, circular, partway sinusoidal, etc. All articles I read involve the centroid, but...

Take two lasers of the same intensity and wavelength and aim them at 30 degrees at the same spot on a mirror, so that at the surface the waves cancel perfectly. What happens? How can the wave be reflected if there is no field present?

So I'm reading that ice (solid) always has a liquid surface if it's surrounded by a gas. Does this mean every solid (e.g., my dining room table) also has a liquid surface because it's surrounded by gas? It doesn't seem to have a liquid surface. :-/ If something sublimes it skips this phase so I...