Hemisphere Definition and 157 Threads

Homework Statement A particle of mass m rests atop a frictionless hemisphere of radius R. A force F = -mkyα acts in the y direction. After an initial small displacement, the particle slides down the sphere under the action of the force. Find a) the height above the equator and b) the speed of...

Homework Statement The figure shows a charge q placed at the centre of a hemisphere. A second charge Q is placed at one of the positions A,B,C and D .in which position(s) of this second charge , the flux of the electric field through the hemisphere remains unchanged ? 2. Relevant Point: My...

Homework Statement Basically, I am being asked to calculate the electric flux through the top of a hemisphere centered on the z-axis using "brute force integration" of the surface area. Homework Equations Gauss' Law The Attempt at a Solution Using intuition and Gauss' law, I know that the...

Homework Statement Find the center of mass of a hemisphere of radius R. Homework Equations R_cm = (rho/M) Integral[ (vector r) dv] dv = r^2 Sin[theta] dr d[theta] d[phi] The Attempt at a Solution [/B] In spherical polar coordinates, vector r = r r-hat, so the argument of the integral should...

I am preparing my AOSS class next semester, and I found it is interesting that there is a seasonal cycle of CO2. I looked for some information on the Internet, and this seems to do with the plants. They awake in the spring and summer, absorbing a lot of CO2 by photosynthesis and die in the...

Homework Statement Calculate the Electric Field generated by a hemisphere of radius ##R## (and uniform charge density ##\sigma##) at its center. Homework Equations ##\displaystyle E = \frac{Q}{4\pi \varepsilon_0 r^2}## The Attempt at a Solution I think I'm doing some mistakes with the...

I have to calculate the centre of mass of the drawn hemisphere. I don't understand where I make mistakes. The process I followed on the above image is the following: (I) Here I simply translated position vector components from cartesian to polar coordinates. (II) Formula of x-component of...

Homework Statement I'm looking for a good explanation, not interested in the answer. A geodesic dome constructed with an aluminum framework is a nearly perfect hemisphere; its diameter measures 55.0 on a winter day at a temperature of -18 C. How much more interior space does the dome have in...

Homework Statement find the acceleration due to gravity at the centre of a solid hemisphere. Homework Equations ##F=\frac{GMm}{r^2}## The Attempt at a Solution i decided to go for cylindrical coordinayes (which is way beyond my syllabus). I did some research though. let me take a point...

Homework Statement My English of influid meachanics is poor, so I only can hope that you can understand the figure (please forgive me!) Please find the force Fz which the hemisphere endures Homework Equations My way: "on" the hemisphere, I want to use triple integral（but I'm not sure...

Homework Statement Consider a solid hemisphere of uniform density with radius R. Where is the center of mass? z=0 0zR2 z=R2 R2zr z=R Image is provided. Homework EquationsNoneThe Attempt at a Solution Answer A and E do not seem logical. I thought it was answer C from my eyes. Center of...

Homework Statement A solid uniform hemisphere rests in equilibrium with its curved surface in contact with a rough inclined plane which is elavated by an angle α where sin(α) = 3/16. Find the angle between the symmetry axis of the hemisphere and the vertical.[/B]Homework Equations Sine rule...

Homework Statement I am trying to understand a substitution used to solve for the center of mass of a solid uniform hemisphere as in this post: https://www.physicsforums.com/threads/solid-hemisphere-center-of-mass-in-spherical-coordinates.650663/#post-4151797[1] I completely understand the...

Homework Statement A particle slides on the outer surface of an inverted hemisphere. Using Lagrangian multipliers, determine the reaction force on the particle. Where does the particle leave the hemispherical surface? L - Lagrangian qi - Generalized ith coordinate f(r) - Holonomic constraint...

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 A charge distribution is given by ##\rho(r,\theta,phi)=\gamma r^3cos\theta,a<r,b,0\leq\theta\leq\pi/2## and is zero everywhere else. The distance from the origin ##r=\sqrt{x^2+y^2+z^2}## and ##\gamma## is a constant. Write out the electric field P along the z-axis a distance...

Can anyone guide me how to mesh solid and shell 3d hemisphere with hex dominant approach in ansys mechanical APDL? I found no such verification manual for 3d hemispherical meshing in ansys. What method should be applied and what element should be chosen appropriately to mesh this structure? I...

Homework Statement A block of mass m slides down a hemisphere of mass M. What are the accelerations of each mass? Assume friction is negligible. (See attatchment) Homework Equations a_M = Acceleration of hemisphere N_m = Normal force of M onto m N_M = Normal force of ground onto M...

Integrating a hemisphere Homework Statement I am self-teaching calculus. I'd like to integrate a hemisphere G (http://en.wikipedia.org/wiki/Spherical_cap), where the points of each circle have a given property (k=100x/(√20x)3 the radius of G r = 10, A = 628.3, h = x the top point is A...

I noticed this intriguing phenomena whilst messing about in work with a perfect glass hemisphere the other day: Place the hemisphere on a surface, with the flat surface facing upwards. (Looks like a 'D' rotated 90 degrees clockwise). When I spin the hemisphere fast enough, it will spin...

Homework Statement hi all, why the wave is reflected back form the centre when it is at the distance of 200mm? why the wave can't go beyond 200mm to reach 250mm from the side of bowl? Homework Equations The Attempt at a Solution

During my physics lecture, the professor said that flux on a closed surface is equal to zero. What exactly is a closed surface defined as? This problem also requires the use of the Flux = Field * Area formula. In relation to the direction of the electric field, what is the area for Part B...

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)...

I was woundering if the terms "Northern Hemisphere" and "Southern Hemisphere" (of the universe) are used a lot in either an astronomy or astrophysics concepts? Because i have see both those terms being used to describe some ideas for the universe, and i was woundering if anyone could give me...

In case the context, which this question is based needs to be provided, the context follows. A sub-project was being done on using sphere or hemisphere "scatterers" on TFSC (Thin-Film Solar Cells). These "scatterers" can be applied on the top of a TFSC in order so that the solar cells can...

We have a frictionless hemisphere M,of a radius R and a body m on the top of it.We give to the hemisphere a horizontal constant acceleration W and consequently the body begins to slide down the accelerating hemisphere.What is the relative velocity of the body in respect to the hemisphere when...

I was thinking about this when I was trying to work out a simpler way of finding the volume of a sphere. Suppose we cover a hemisphere with a piece of pliable thin cover. Stretching the cover flat would make a circle. The circumference of the sphere is 2*pi*r. The distance along the surface of...

reference to Feyman lectures vol.1 topic 19.2 locating centre of mass Feyman gives us the law of pappus to find the centre of mass ,which he proves for semicircular disc and ring. But when i am trying to extend it to finding the centre of mass of a solid semi-circular solid hemisphere ,i...

Homework Statement [See image] https://www.physicsforums.com/attachments/61123 Homework Equations Electric force \vec{F}_{e}=k_{e}\frac{q^{2}}{d^{2}}\hat{r} Gravitational force = -mg\hat{j} Normal force = \vec{n} |\vec{n}|cos(θ) = |\vec{F}_{e}| |\vec{n}|sin(θ) = mg ... where θ is the...

Homework Statement A Gaussian surface in the form of a hemisphere of radius R = 6.08 cm lies in a uniform electric field of magnitude E = 9.35 N/C. The surface encloses no net charge. At the (flat) base of the surface, the field is perpendicular to the surface and directed into the surface...

Homework Statement Given a solid hemisphere with radius R and uniform charge density ##/rho##, find the electric field at the center. Homework Equations ##E = \frac{1}{4 \pi \epsilon_{0}} \frac{Q}{r^{2}}## ##E = \frac{1}{4 \pi \epsilon_{0}} \int \frac{\rho (x',y',z') \hat{r} dx' dy'...

Homework Statement A non-conducting hemisphere of radius R centered at the origin has a total charge Q spread uniformly over its surface. The hemisphere is oriented such that its base is in the (y,z) plane. Find the electric field anywhere along the x-axis for x > 0. Give explicitly the value...

This paper critically examines the 'hemisphere of evil' CMB asymmetry reported by Planck - CMB Aberration and Doppler Effects as a Source of Hemispherical Asymmetries, http://arxiv.org/abs/1304.3506. Its worth a look if you find this aspect of Planck vaguely disturbing [as I did].

Homework Statement A thin walled hollow sphere of radius 16 cm is sliced in half. What is the moment of inertia of this hollow hemisphere about the x-axis if the areal density is 90 g/cm2? Homework Equations No idea The Attempt at a Solution I've had no luck with this. I've...

Hey all, I haven't been alive for that long, so I guess my data probably isn't as good as it should be, but in my experience there have been far more noteworthy comets appearing only to the southern hemisphere, and not to the northern one. In fact, I haven't ever seen a comet (since I was a...

Homework Statement The hemisphere is of radius R. Prove that the period equals that of a mathematical pendulum of length 4R/3 I have a solution, but i don't understand. Homework Equations Center of gravity: a=\frac{3}{8}R Moment of inertia round the center of mass...

Homework Statement Please evaluate the integral \oint d\vec{A}\cdot\vec{v}, where \vec{v} = 3\vec{r} and S is a hemisphere defined by |\vec{r}| \leqa and z ≥ 0, a) directly by surface integration. b) using the divergence theorem. Homework Equations -Divergence theorem in...

Exoplanet discoveries continue to be made using various sensitive techniques. Since there is no evidence to the contrary none of them are thought to harbor life forms. Here is a new set of maps showing where the exoplanets are located in both the Northern and Southern Hemispheres...

Hello, I am struggling with what was supposed to be the simplest calc problem in spherical coordinates. I am trying to fid the center of mass of a solid hemisphere with a constant density, and I get a weird result. First, I compute the mass, then apply the center of mass formula. I divide...

Homework Statement we put a dielectric hemishphere with radius (a) and dielectric coeeficient(k) on an infinite conducting plane.the system(hemsiphere and the plane) are in a constant electric field E0. find the surface charge distrubution on the plane as a function of (r). and explain what...

Suppose there's a hemisphere of radius R (say) and a right cone of same radius R but ht. R/2 is scooped out of it then i have to find the center of mass of the remaining part. Here's how i approached... clearly by symmetry, Xcm = 0 Now, Let M be the mass of the hemisphere so...

On finding the center of mass of a solid hemisphere i came up with some different result. Here's what i did... consider a small ring at a distance r from the center of the hemisphere and one more ring at a distance of r+dr from center of the ring. let, mass of the small element formed...

Find the gravitational attraction of a solid hemisphere of radius a anddensity1 on a unit point mass placed at its pole. My attempt: Obviously I figured that spherical coordinates would work nicely for this problem. I decided to invert the hemisphere thus placing the pole on the origin...

Homework Statement As shown in attached figure, a small object is in uniform circular motion in a horizontal plane, on the smooth of a hemisphere (radius:r). The distance between the object's plane of motion and the hemisphere's lowest point is \frac{r}{5} What is the speed of the object...

Homework Statement The vector field F is defined in 3-D Cartesian space as F = y(z^2−a^2)i + x(a^2− z^2)j, where i and j are unit vectors in the x and y directions respectively, and a is a real constant. Evaluate the integral  Integral:(∇ ×F)·dS, where S is the open surface of the...

I need to find the total surface area of the hollowed out hemisphere (picture attached), with an inner diameter of 1.86 cm and what looks like an outer radius (also what I am assuming as height) of 1.25 cm. Surface area of a sphere is 4∏r2, so half the sphere is 2∏r2. Since the outer...

Homework Statement A person standing on the top of a hemispherical rock of radius R kicks a ball (initially at rest on the top of the rock) to give it horizontal velocity v_i What must be it's minimum initial speed if the ball is never to hit the rock after it is kicked? Homework...

Homework Statement For upper hemisphere S: x^2 + y^2 + z^2 = 1 , with z≥0, find the area element dS and unit normal vector N. Compute the total area of the hemisphere, ∫∫dS over S. Homework Equations Unit normal to surface f(x,y,z) = const N(hat) = grad(f)/|grad(f)| Surface area...

Evaluate surface area of top hemisphere Homework Statement http://s1.ipicture.ru/uploads/20120106/jrHc5122.jpg The attempt at a solution This problem is new to me, in the sense that the integration is to be done against S, which is the same region S, over which the limits are defined...

Homework Statement I've just started with center of mass, and instead of the method in the book, I tried solving the center of mass for a solid hemisphere using angle as a variable, but the answer didn't match. A small disk of mass "dm" is taken, which subtends an angle "dθ" at the center.The...