Surface Definition and 1000 Threads

Homework Statement So the equipotential surface of a point charge is sphere with the charge in the center, and the equipotential surface of a infinite line is a cylinder with the line of charge as the axis. I was wondering what is the shape of the equipotential surface of a infinite plane...

Homework Statement [/B]Homework EquationsThe Attempt at a Solution [/B] Honestly, I don't even know how to begin this problem. I've drawn myself some free body diagrams, but I'm uncertain of all of them. The weight of the bar is just (0,-mg) at .9r from the pivot point. But I don't know how...

Homework Statement [/B] Find the coordinates of the point P on the surface of the paraboloid z=6x2+6y2-(35/6) where the normal line to the surface passes through the point (25/6, (25√22)/6, -4). Note that a graphing calculator may be used to solve the resulting cubic equation. Homework...

Homework Statement Express f(x,y) = \frac{1}{\sqrt{x^{2} + y^{2}}}\frac{y}{\sqrt{x^{2} + y^{2}}}e^{-2\sqrt{x^2 + y^2}} in terms of the polar coordinates \rho and \phi and then evaluate the integral of f(x,y) over a circle of radius 1 centered at the origin. Homework Equations y = \rho...

Homework Statement Its more of a general issue of understanding than a specific problem I have to evaluate a few surface integrals and I am not sure about the geometric significance of what I am evaluating or even of what to evaluate. Examples. If n is the unit normal to the surface S...

If I crumple and unfold a piece of foil, am I increasing it's surface area? Since it's malleable, if I step on it with golf spikes, without completely piercing it, will it gain surface area?

Homework Statement Electric charge resides on a spherical surface of radius 0.3 centered at the origin with charge density specified in spherical polar coordinates by f(r,\phi, \theta) = 3 × 10^{-12} cos(\theta). Determine the total amount of electric charge on the sphere. Homework Equations...

What is the simplest way to calculate the surface area of a region of a torus? Please see this diagram: https://www.dropbox.com/s/73eics7x43bgiwm/surface-area-torus.png?dl=0 This is a cross section through a torus, the dashed line is the central axis. I am interested in the external surface...

I'm building an frame out of solid 5/8 inch thick aluminum square bars. this frame will be around a fire temps close to melting points but there will be insulation in make sure it won't melt. I was thinking about drilling holes in the free space of the aluminum to reduce it's weight and if you...

Hi PF! Simple question here, but if we have some fluid in, say a cylinder container, with a specified surface tension, to get force would we multiply the surface tension by the height of the cylinder (if it's standing up on a circular side)? I know we multiply it by some length, but I don't...

Hi, I am a student interested in wetting and super-hydrophobic surfaces. I am very new to this field and am a software engineer, and as such do not have strong mechanical or chemical background. I am trying to model contact angle and surface energy for super-hydrophobic surfaces. However my...

How is 3-sphere curvature measured? If a 2-D being living "in" the surface of a sphere tried to measure the 3-D curvature of the sphere, how would they go about it? They couldn't detect the curvature by looking for curvature in the paths of signals, because if the surface of their sphere was as...

Homework Statement A man of mass 70[kg] pules a box at an angle 100. the static coefficient of friction between his legs and the floor is 0.6 and the kinetic coefficient between the box and the floor is 0.3 What's the maximum's box's mass Homework Equations Friction: f=μN The Attempt at a...

Homework Statement For a 0.90km radius cylinder, find the time for one revolution if "gravity" at the surface is to be 9.8 m/s2. Homework Equations rω^2=a The Attempt at a Solution i tried solving for omega but i couldn't find a solution that i only had 1 variable in it.

- You are driving car with 100 mile/hour - You are pressing brake pedal. - The speed of car is suddenly gone down. Decelerated. - However, Wheel is rolling on road without sliding and car stopped smoothly finally.In this case, - the tangent force acting on road surface is related with...

Homework Statement The drawing shows an edge-on view of two planar surfaces that intersect and are mutually perpendicular. Surface (1) has an area of 2.20 m², while surface (2) has an area of 3.90 m². The electric field in the drawing is uniform and has a magnitude of 200 N/C. Find the...

Homework Statement I am not asking you to help me solve this, so i won't put in any usefull relevant equations or attempts at a solution. The nature of my problem is more of an understanding this collision - it is more of a thinking thing to process here. The problem goes like this. Ball is...

I have also posted this question here: Relationship between surface area of electrode and reaction rate of hydrogen in fuel cells, but I really need an answer before tomorrow morning so I hope you don't mind me posting it here as well! I am looking at the effects of increasing the surface area...

Hi! Here is my task: Calculate surface area of sphere $$x^{2}+y^{2}+z^{2}=16$$ between $$z=2$$ and $$z=-2\sqrt{3}$$. Here are 3D graphs of our surfaces: Surface area of interest is P3. It would be P-(P1+P2), where P is surface area of whole sphere. Is it correct? Here is how I calculated...

When I learned Integrals in Calc III, the formula looked like this ∫∫ F(r(s,t))⋅(rs x rt)*dA but in physics for Gauss's law it is ∫∫E⋅nhat dA How are these the same basic formula? I know that nhat is a unit vector, so it is n/|n|, but in the actual equation, it is a dot between the cross...

Homework Statement I have a coordinate system, (x,y,z). There is a uniform-magnetic-field of 2.0 T that exists along the direction of the y-axis. There is a rectangular plane bounded by the points (3,0,0),(0,1,0),(0,1,1),(3,0,1). Calculate how much flux is traveling through the rectangular...

Homework Statement find the values of the integral \int_{S} \vec A\cdot\ d\vec a where, \vec A\ = (x^2+y^2+z^2)(x\hat e_{1}+y\hat e_{2}+z\hat e_{3}) and the surface S is defined by the sphere R^2=x^2+y^2+z^2 Homework Equations first i must evaluate the integral directly, so i don't...

Let us suppose that a cylindrical bottle is on the surface of the water (filled with air for simplicity). A little spin is given to the bottle makes it rotating around the symmetry axis of the cylinder. After a while the bottle stops rotating. How to calculate the time duration of spinning?

Homework Statement Homework Equations The sphere is positively charged and appears to have its charge concentrated at its centre. Potential V is calculate to be 285V The Attempt at a Solution The charge induced on inside of box is negative. THe potential is less. It is said that it's being...

Homework Statement A small ball of m=1kg at height hp = 8m at point p, is given an initial horizontal speed vp = 10 m/s. It slides over an uneven frictionless surface. What is speed vq of the ball at height hq = 3m at point q? Homework Equations Ui + KEi = Uf + KEf The Attempt at a Solution...

I am trying to understand in more detail the answer to: http://math.stackexchange.com/questions/673187/universal-cover-of-a-surface-with-boundary It is mentioned that the universal cover of a hyperbolic surface ##S## with geodesic boundary is a closed disk ##D^2## with a Cantor set removed from...

I'm going through Kerr metric, and following the 'Relativist's toolkit' derivation of the surface gravity, I've come to a part that I don't understand. Firstly, the metric is given by...

we say the surface element of x(u,v),y(u,v),z(u,v) is absolute value of the cross product or i don't understand why this is. i know that the absolute value of the cross product is the area of a parallelogram formed by a,b,a+b, but i get lost after that im guessing something happens where dudv...

So i am working on a program that models the movement of a rocket through different planets. and i sm starting to get teach my self fluid dynamics. As i was reading a presentation by NASA about the forces that act on a rocket they got into shape effects on drag, i noticed from their equation Cd...

Hello every one . What is the Surface Area vector form in exterior algebra ,I mean by that the Surface Area vector as an exterior form in 3D , just like the volume form .THANKS

So I have a physics midterm tomorrow that will have a five part, 10 point question about the following "an object pushed across a horizontal surface. You should be able to calculate net force, frictional forces from the coefficient of friction, acceleration, velocity, momentum, impulse, and...

Stephen hawking came to know of a study that stated that surface area of an event horizon increases. So he said that since area has increased Entropy also had increased. But why does surface area of an Event Horizon increase?

A block is at rest at the top of a frictionless hemisphere of radius r. It is slightly disturbed at starts sliding down. I already know where it will leave the surface (height = 2r/3). My question is, WHEN will it leave the surface?

Homework Statement http://ocw.mit.edu/courses/mechanical-engineering/2-06-fluid-dynamics-spring-2013/assignments/MIT2_06S13_ps2.pdf Problem 7[/B]Homework Equations ##F=2*V/(a^2)*\sigma*cos(180-\theta)## The Attempt at a Solution With the problem statement given, it seems like the component of...

Homework Statement A uniform rod of mass M and length L can rotate around point P which is at position x from one end of the rod as shown in the figure. The rod is gently placed on a rough horizontal surface that has a friction coefficient μ. and at t=0 starts rotating with angular velocity...

The event horizon is a null surface in spacetime separating events that are causally connected to an observer from those that are not. Does anyone have a good, simple argument on why it must be a null surface?

Im having trouble convincing myself that a charge located anywhere inside a conducting sphere will create an induced charge on the surface of the sphere with an electric field that is completely uniform. This doesn't make much sense to me. Also same with how the electric field inside solid...

Homework Statement The problem and its solution are attached in TheProblemAndSolution.jpg. Homework Equations Stoke's theorem: ∮_C F ⋅ dr = ∮_C (F ⋅ T^) dS = ∫∫_S (curl F) ⋅ n^ dS The Attempt at a Solution In the solution attached in the TheProblemAndSolution.jpg file, I don't understand...

If I have a U-shape wire frame and it contains a straight sliding wire and I dip this in soap, a film forms between the sliding wire and the boundary of U shape frame. Why is the force due to surface tension F = 2Tl where l is length of sliding wire? They say there are 2 layers in contact...

Homework Statement What exactly does it mean for a surface to span a contour/curve? For example, which surface(s) span the contour/curve defined by the equations x^2 + y^2 = 1 and z = y^2? Homework Equations N/A The Attempt at a Solution I'm not sure if I'm saying something nonsensical, but...

I had this problem in my exam. It required me to calculate relative permittivity of a dielectric slab which acquires a surface charge density of 800micro Coulomb/m^2 when subjected to an electric field of 10^8 V/m. Applying E=sigma/(2epsilon), I got relative permittivity as 0.45 which is less...

Homework Statement A spherical air bubble in a lake expands as it rises slowly to the surface. At the point it starts to rise, the pressure is 2.00 atm, the temperature of the water is 10.0 ∘C, and the radius of the bubble is 5.00 × 10^−3 m. At the surface, the pressure is 1.00 atm and the...

Homework Statement ##\iint_S (x^2+y^2)dS##, ##S##is the surface with vector equation ##r(u, v)## = ##(2uv, u^2-v^2, u^2+v^2)##, ##u^2+v^2 \leq 1## Homework Equations Surface Integral. ##\iint_S f(x, y, z)dS = \iint f(r(u, v))\left | r_u \times r_v \right |dA##, The Attempt at a Solution...

Hi, I have a simple problem. A Lambertian emitter has the shape of a square planar surface, with area Ae=4mm2, total power P=1mW, and is located in yz plane. Another square planar surface, with area Ad=6mm2, is located in the xy plane, at a distance d=10cm to the Ae, and is tilted 20 Degrees...

For the following three-dimensional surface, z = -4.53 + 2.67x + 2.78y - 1.09xy, I would like to calculate the area for each of three subsections of this surface: (1) for which z is in between the corresponding x and y values (i.e., x < z < y OR y < z < x); (2) for which x is in between the...

If you increase the surface tension of a liquid, does it change the average bond strength of the liquid?

What's the difference between surface tension and capillary force? Surface tension, a tensor, is the force per unit length. Again surface energy is the energy required to increase the surface area by one unit. Is the surface tension a capillary force?

I am writing a simulation in MATLAB of particles that perfectly reflect off of a surface. However, my question is physics based, not code based. So here is my issue. A particle is traveling towards a flat plane in space at z=1 with a velocity vector of [0,0,1]. The normal vector of the...

If the magnetization vector is in the z direction, is the bound surface current of a cube always 0, since z cross z is 0, and x and -x cancels and y and -y cancels out?

Hi How is circular surface area values square rooted ??. I am using this formula r2Xπ=mm2 to calculate the surface area of a circle but i want to know if there is a formula to get back to the diameter or the radius of the circle ?. example i have a circular surface area of 5.26mm2 and i want...