Hemisphere Definition and 160 Threads

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...

Hi gang, I was given this question, but I can't quite seem to get it all the way... 1.Determine the coordinates of the centroid of the surface of a hemisphere, the radius of which is r, with respect to its base. Homework Equations A=2\pi r^{2} A: Surface Area of the Hemisphere...

Homework Statement A nonconducting hemispherical cup of inner Radius R has a total charge Q spread uniformly over its inner surface. Find the electric field at the center of curvature. Homework Equations \sigma = \frac{Q}{2piR^{2}} dq = \sigma dA = \sigma R^{2}Sin\thetad\thetad\phi k =...

As part of a problem I need to find the center of mass of a hollow hemisphere. I did it in the following way. I considered the lower hemisphere ( around negative z axis ) First by definition, the position vector of the center of mass is obtained as \vec{R}=...

Homework Statement i am trying to apprixmate the surface area of a hemisphere. i am approximating by cutting the sphere into cylinders of different radius, and using their curved surface area to approximate. each cylinder will have a height of r.cos.theta and radius of r.sin.theta...

Homework Statement A ball with initial velocity 0 and mass m starts at the top of a hemisphere and begins to slid down the frictionless side. The radius of the hemisphere is r. At what angle does the ball fall off the hemisphere?Homework Equations mgsintheta, mgcostheta, fn mv^2/rThe Attempt at...

Homework Statement Hi all! I am an undergraduate who is currently doing a design on amusement ride. MY amusement ride would have a hollow hemisphere that is being rotated by a shaft. I need to determine the stresses acting on the hemisphere in order to know the material to use to build this...

EDIT: Problem solved, the mistake was in the statement that the point of contact traces out an arc of length \theta r on the hemisphere. This statement neglects the change in orientation of the sphere relative to the hemisphere. An object with cylindrical symmetry (Full/hollow sphere, cylinder...

Homework Statement A solid glass sphere of radius R is silvered over one hemisphere. Small object is located a radial distance 2R from the pole of the unsilvered side of the sphere. Find the position of the final image after refraction and reflection. Homework Equations Refraction at...

Homework Statement A hemisphere of radius R, covering +/- R in the x and y directions and 0 to R in the Z direction (only the top half of a sphere centered at the origin) Find the center of mass. Homework Equations Cm=(1/m)\int(z dm)The Attempt at a Solution dm is sigma dA, and dA is x dz...

I am not sure about how the integrations are initiated at the question below. http://img4.imageshack.us/img4/2831/123io.png Uploaded with ImageShack.us How does dA differ from dV and how are boundaries for integrations are done?

Homework Statement Find the area of the portion of the cylinder x^2 + y^2 = 2x that lies inside the hemisphere x^2 + y^2 + z^2 = 4, z \geq 0. Hint: Project onto the xz-plane. Homework Equations I want to use the formula for surface area \int\int\frac{|\nabla f|}{|\nabla...

There is a small object, which mass is m on the top of hemisphere, with the mass of M. the size of the object is neglectable. Also, the radius of hemisphere is R. There is no friction between the hemisphere and the object, and the hemisphere and the surface. What if we slightly hit the...

PREVIOUS POST ----https://www.physicsforums.com/showthread.php?t=165844 THIS POST HELP ME OUT TO SOME EXTENT BUT I AM STILL MESSED UP... I am messed up with the concept of projection of area of different surfaces and flux through different surfaces... Please someone explain it with some...

Homework Statement Seawater has density 1025 kg/m^3 and flows in a velocity field v=yi+xj, where x, y, and z are measured in meters and the components of v in meters per second. Find the rate of flow outward through the hemisphere x^2+y^2+z^2=9, z≥0Homework Equations Surface integral of F over...

Homework Statement Symbolic question: Consider the hemispherical closed surface in Figure P30.34. The hemisphere is in a uniform magnetic field that makes an angle θ with the vertical. (a) Calculate the magnetic flux through the flat surface (S1), using pi for π, theta for θ, B, and R as...

Homework Statement There is a hemisphere of radius R metres on the ground. You are standing at the very top of the hemisphere and you kick a ball out such that it travels outwards horizontally with speed v metres per second. During the trajectory of the ball, it does not come into contact...

Homework Statement Parallel light rays travel from air towards a glass hemisphere with radius R and index of refraction ng > nair. A top view is shown in the figure. http://img8.imageshack.us/img8/6380/parallellightrays.jpg (a) Determine where the light rays come to a focus relative to the...

[/tex]Homework Statement http://emweb.unl.edu/negahban/em223/sexam3/sexam3.htm" number 3...the one about the semicylinder on a ramp Homework Equations \Sigma F_x = 0 \Sigma F_y = 0 \Sigma M=0 f = \mu * N The Attempt at a Solution I got the first part to be 16.7 degrees. However...

Homework Statement 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 the summer, when the temperature is 30? Homework...

I have heard a couple of different explations from the jet stream moving south to the alantic dipole shifting. Others are saying that the gulf stream has temporarily shifted towards greenland. Does anyone have a clear idea of what is going on and more important why there has been this shift...

Homework Statement I'm currently working on this question: A particle moves on the smooth inside surface of the hemisphere z = -(a^2 - r^2)^(1/2), r <= a, where (r, theta, z) denote cylindrical polar coordinates, with the z-axis vertically upward. Initially the particle is at z =...

1. Seawater has density 1025 kg/m3 and flows in a velocity field v=yi+xj, where x, y, and z are measured in meters and the components of v in meters per second. Find the rate of flow outward through the hemisphere x2+y2+z2=9, z≥0 2. surface integral of F over S is ∫∫ F • dS 3. I parameterized...

Homework Statement I need help proving how you could use evaluation of the surface integral \oint\oint f(x,y,z)dS to show that the surface area of the upper hemisphere of radius a is 2\pi a2. So any ideas? Homework Equations The teacher mentioned that the divergence theorem would be...

Homework Statement "Two identical beads each have a mass m and charge q. When placed in a hemispherical bowl of radius R with frictionless, nonconducting walls, the beads move, and at equilibrium they are a distance R apart. Determine the charge on each bead. (Use k_e for ke, g for the...

Homework Statement A small mass m slides on a hemisphere of mass M and radius R is also free to slide horizontally on a frictionless table. An imaginary vertical line is drawn from the center of the hemisphere to its highest point, where the small mass is originally placed at rest. The angle A...

Hi, I was wondering if anyone could point me to physics labs or really any place to do with physics (not engineering) that take on students in the summer holidays. I am currently in my 2nd year of a B Eng / B Adv. Science degree in Australia. I've looked up places to do with engineering but...

Homework Statement Show that total mass of half solid hemisphere radius a given as x^2 + y^2 + z^2 = a^2 and z>=0 and having variable density ρ=1+(r^2)z where r is the distance of any point from the origin is given by: M = (2π(a^3))(6+3(a^3)/18 where M is total mass. Homework Equations -The...

Homework Statement Charge Q is distributed uniformly over surface of a hemisphere of radius r. Calculate electric field at centre of curvature of hemisphere. Homework Equations I realize that this should be quite straightforward but I am a bit confused. The total charge Q is...

imagine a hemisphere of radius a with the circle lying in the x-y plane and so the axis of the hemisphere is the z axis. if z=0 is at the centre of our circle, what value of z corresponds to the centre of the hemisphere? i used z=a/2 but have a sneaky feeling its' meant to be...

Can the surface of a hemisphere be distinguished from a disk without introducing a metric? What is the minimum amount of info we need to know to identify one space as a disk and the other as the surface of hemisphere? Both can have the same coordinate chart. For example, distance from...

Homework Statement Hi, I'm wondering if this is the proper way to approach this problem. The question says to: a)find the electric field at the center of curvature of the hemisphere (center of the flat bottom). Homework Equations Gauss's law: integral E*da = Qencl/epsilon...

Homework Statement A hemisphere of radius R and mass M, curved side down, is pulled along a plane at a constant velocity by means of a horizontal force F. The coefficient of sliding friction is mu. Find the the angle at which the hemisphere is inclined as it is pulled. C.M. of the...

Hi there, I can't get my head round how to do the math for this problem. I'm sure it's not as hard as I think... Homework Statement Show that the CoM of a uniform solid hemisphere of radius r lies at a distance (3/8)r from the centre of the flat face. You may find it convenient to regard the...

Hello, Thank you very much for takign the time to help me out. This is an applied calculus 3 (multivariable calc) level problem. I have an answer, but it is nonsensical as the units are not in accordance with units of charge, C. Homework Statement Instructions: Use Gauss' Law for...

I was told this problem could be done with divergence theorem, instead of as a surface integral, by adding the unit disc on the bottom, doing the calculation, then subtracting it again. Homework Statement Homework Equations The Attempt at a Solution for del . f I get i + j =...

Hello I wanted to ask why at the south hemisphere the sun rises from the west? We know that Earth rotates reversely than the watch pointers(this happeness to both hemispheres),so all the "sky" (the stars etc..) goes to the opposite direction. If someone could explain me.. Thank you!

Homework Statement The moment of inertia of a uniform sphere of mass m and radius r about an axis passing through its center of mass is (2/5) mr^2. If half of the sphere is removed, what is the moment of inertia about the same axis? Homework Equations integral of r^2 dm The Attempt at a...

Homework Statement Determine the x-coordinate of the mass center of the homogeneous hemisphere with the smaller hemispherical portion removed? I know what the answer should be it's Xcm = 45/112 R Homework Equations The center of mass R of a system of particles is defined as the average...

Homework Statement Center of Mass of a hemisphere http://www.goiit.com/templates/default/images/chapters/center_mass/image064.gif http://www.goiit.com/templates/default/images/chapters/center_mass/image068.gif Why is volume of elemental disc = Rd\theta (cos \theta) (\pi R^{2}cos^{2}...

Homework Statement A person standing at 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 Vi. What must be its minimum initial speed if the ball is never to hit the rock after it is kicked? With this initial...

The problem concerns with the work done by the Gravitational Feild force exerted on a mass 'm' kept on the center of the base of a hemisphere of mass "M" radius "R". The way I did it was, first I found the Center of Mass of the hemisphere which is 3R/8. Next I used the concept => Work done=...

Where to look? When I see a news story about when to see celestial events (in this case an alignment) how much to I have to adjust for my geographic position on the Earth?? I am reading a story directed at those in the United States, but as I am currently in a different hemisphere how would I...

I'm not much of a historian, but I believe that if you take a good look at history, most initial technological advances, understandings in science, formation of governments, religions, most everything we associate with the so-called "modern day world", including civilizations themselves, have...

Homework Statement "A boy is initially seated on the top of a hemispherical ice mound of radius R = 13.8m. He begins to slide down the ice, with a negligible initial speed. Approximate the ice as being frictionless. At what height does the boy loose contact with the ice?" Homework...

Does it snow in places like southern south America or southern Africa durring their winter seasons? If not, why?

Homework Statement "What is the flux through the hemispherical open surface of radius R? The uniform field has magnitude E. Hint: Don't use a messy integral!" \mid \vec{E} \mid= E radius = R Homework Equations Electric Flux over a surface (in general) \Phi = \int \vec{E} \cdot \,dA...

I am supprised and puzzled when my nephew, a 14 year old boy asked me : 'Why most of the continents are on the Northern hemisphere ?'. I answered him it is just a coincidence. Could anybody explain if there are any real reasons for that? Thanks

How would i calculate an equation for the velocity of a ball inside a hemisphere ( the ball is orbiting in a horizontal circle inside the hemisphere)

Imagine viewing a hemisphere normal to the equator such that it looks like a circile with the full radius of the hemisphere. Now randomly section or cut the hemisphere in a manner a tomato is sliced. If we only consider the portion of the hemisphere that contains the pole we should be...