Hemisphere Definition and 157 Threads

Hello everyone, I was trying to find volume of a sphere by doing some calculus, the area of a circle is ##{\pi}r^2## So I thought I would calculate the volume of one hemisphere and then multiply by two, but I got a different result than the standard formula, the standard formula is ##\frac 4 3...

My thought: First of all, I find the upper hemisphere (with a total charge +Q): ##ρ(\vec r)=\frac {V} {Q}## where V is the volume of the upper hemisphere = ## \frac {2} {3} \pi R^3##. Secondly, find the lower hemisphere (with a total charge −Q): ##ρ(\vec r)=\frac {V} {Q}## where V is the volume...

Problem: I have done part a) in spherical polar coordinates. For part b) I thought it would be just: $$\sigma = -\epsilon_0 \frac{\partial V}{\partial r}$$ But I got confused by "You may want to use different coordinate systems .." So I assume partial derivative w.r.t to r is the spherical...

TL;DR Summary: Astro Olympiad Problem determining the latitude of an observer from a picture taken. Well this question and answer are really confusing. There are no cardinal directions labelled on the picture. However because the Sun and the Moon should move on a circular path, the left side...

I tried approaching this question like this: F_N - mgcos(theta) = -mR(theta_dot)^2 and theta_dot = v/R since R is constant F_N = m(gcos(theta) - (v - v_0)^2/R) (with v being final velocity and v_0 being the initial velocity from the impulse) and then using energy conservation: at t = 0: E =...

I tried gauss law. And the fact that if alpha is less than pi/2 we can say that we have two parts with angle alpha and one other part which has a normal field at the center. But non of them helped me answer. The problem's solution says that we can use the fact that our section has longitudinal...

[FONT=times new roman]Problem statement :[FONT=times new roman] I draw the problem statement above. I hope I am correct in inferring that the bowl is hemispherical. Attempt : I could not attempt to the solve the problem. We are given that the rate of change (decrease) in volume is proportional...

Let the radius of the small sphere = r 3r = 1 → r = 1/3 ##x=\sqrt{4r^2-r^2}=r\sqrt{3}## Volume of pyramid: $$=\frac{1}{3} \times (2r\sqrt{3})^2 \times r$$ $$=\frac{4}{27}$$ So m + n = 31, but the answer is 29. I guess my mistake is assuming line AB is tangent to the top sphere. How to do...

a) From impulse-momentum theorem I have: ##J=mv## so ##v=\frac{J}{m}## and since the ball doesn't slip ##v=\Omega b## so ##\Omega=\frac{J}{mb}## and ##\dot{\theta}=\frac{v}{a+b}=\frac{\Omega b}{a+b}##. b) I considered the angular impulse: ##-J(a+b)=I_0 \Omega_0 \Rightarrow...

I recently learned how to calculate the centroid of a semi-circular ring of radius ##r## using Pappus's centroid theorem as ##\begin{align} &4 \pi r^2=(2 \pi d)(\pi r)\nonumber\\ &d=\frac {2r}{\pi}\nonumber \end{align}## Where ##d## is the distance of center of mass of the ring from its base...

Could I please ask for help with the following question: A uniform lamina of weight W is in the shape of a triangle ABC with AB = AC = 2a and the angle BAC equal to 2ᾳ. The side AB is fixed along a diameter of a uniform solid hemisphere of radius a. The plane of the lamina being perpendicular...

https://www.scientificamerican.com/article/flu-season-never-came-to-the-southern-hemisphere/?fbclid=IwAR3zGYGiCx8jdZDJ36n-ySRwsgTUNonhVhWwBfUkEUdfdQPGtxEg-acetlw

for this derivation, I decided to think of the solid hemisphere to be made up of smaller hemispherical shells each of mass ##dm## at their respective center of mass at a distance r/2 from the center of the base of the solid hemisphere. also, I have taken the center of the base of the solid...

Here is what the solution says: As usual, quote the general potential formula: $$V(r,\theta)=\sum_{l=0}^{\infty}(A_lr^l+\frac{B_l}{r^{l+1}})P_l(cos\theta)$$ The potential outside the sphere is: $$V(r,{\theta})=\sum_{l=0}^{\infty}\frac{B_l}{r^{l+1}}P_l(cos\theta)$$, which makes sense to me...

My attempt is for part a a. The electric field is into the base of the hemisphere and the area vector is coming out of the base Θ=180 Area of base of the hemisphere is = π * r^2; Hence the electric flux ∅ = ∫ E.dA; ∅ = E*π*(0.0568^2)*cos(180) = -2.5*π*0.00322= - 0.0253N.m2/C; b. For the part...

I emphasise again that this is a problem I created myself to better my understanding of moments of inertia and angular momentum. My latest approach: The method of successive approximations - Separate the hemisphere into a part with positive horizontal velocity and a part with negative...

Hello, So I've been toying with the following problem and I'd really appreciate some feedback and advice. The problem statement (as unambiguous as I can make it): A solid hemisphere is placed on a horizontal ledge so that its center is directly above the edge, fixed there by a delicate thread...

<Moderator's note: Moved from a technical forum and thus no template.> > The tank (hemisphere) is full of water. Using the fact that the weight of water is 62.4 lb/ft3, find the work required to pump the water out of the outlet. The radius of the hemisphere is 10. ##V =\pi x^2 h## using the...

Homework Statement There is an object at the top of a frictionless hemispherical hill with radius R. t time t=0, it is given a small impulse so that it starts sliding down the hill. Find the height from the ground where the ball becomes airborne. Express your answer in terms of R. Homework...

Hey, I was in my backyard and I noticed a star that was flickering orange, green and white, at about 30 degrees above the horizon, at 8:27 AEST in the afternoon on 20/11. Is it a star or a satellite, and more specifically, which one?

Homework Statement A perfectly reflecting solid hemisphere of radius R is placed in the path of a parallel beam of light of large aperture, if the beam carries an intensity I, what is the force exerted by the beam on the hemisphere? Homework Equations radiation pressure=I(1+ro)(cos^2(x))/c I...

Homework Statement Hey everyone, I'm studying for my physics and came across a question for the COM of a hemisphere.I made my attempt to calculate the COM. Homework Equations The Attempt at a Solution I tried to calculate the y coordinate of COM this way,please go through it- But,I am...

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 ##v_i##. What must be its minimum initial speed if the ball is never to hit the rock after it is kicked? Homework Equations...

Volume of hemi-sphere = ∫ ∫ ∫ r2 sinθ dr dθ dφ i thing (r < r < (r + R)cosθ ) ( 0 < θ < 60 = π/6) and ( 0 < φ < 2π) integral = 2π ∫ ⅓r3 sin θ dθ = 2π ∫ ⅓ [((r+R)cosθ)3 - r3] sin θ dθ i don't know how to find volume of hemi-spere

Homework Statement A hemispherical surface of radius b = 61 m is fixed in a uniform electric field of magnitude E0 = 3 V/m as shown in the figure. The x-axis points out of the screen. Enter the general expression for an infinitesimal area element dA in spherical coordinates (r, θ, φ) using...

Homework Statement As shown in the figure, the distance between the object and hemisphere lens is R0. The hemisphere lens radius is R0. Find the distance between the image and the flat side of the lens if observing from the curved side of the lens. Refractive index of glass and air are n and...

Homework Statement A solid sphere is cut in half and a homogeneous hemisphere of radius r and mass M is set upon a table(with its flat side up). The surface of the table is perfectly rough. The hemisphere rocks back and forth with small amplitude excursions from equilibrium. What is the length...

Homework Statement You have a hemisphere, like half a ping pong ball for example, sitting in a cup under a few centimeters of water. The hemisphere is sealed to the bottom so that no water can get underneath it. What is the buoyant force the hemisphere experiences? Homework Equations P = P0 +...

Cases of Zika virus infections (some of which are associated with newborn brain damage) have declined to an unexpected degree in North, South and Central Americas. For example: local transmission in the US went from 224 last year to 1 this year. Article above discusses why?

Homework Statement This isn't actually a coursework problem, but I can't solve it and I'd definitely be interested in the answer! The acceleration due to gravity at the surface of a uniform, spherical asteroid is ##g_0##. Half of the asteroid is destroyed in a collision, leaving only a...

To find the surface area of a hemisphere of radius ##R##, we can do so by summing up rings of height ##Rd\theta## (arc length) and radius ##r=Rcos(\theta)##. So the surface area is then ##S=\int_0^{\frac{\pi}{2}}2\pi (Rcos(\theta))Rd\theta=2\pi R^2\int_0^{\frac{\pi}{2}}cos(\theta)d\theta=2\pi...

Homework Statement A hemispherical bowl of mass m and radius R is placed on a rough horizontal surface. Initially the centre C of the bowl is vertically above the point of contact with the ground(see figure). Now the bowl is released from rest. Find the normal force acting on the hemisphere...

I have a 8mm diameter glass tube willed with water that have a bulge outward above the top. I know that the preasure inside the bulge is higher than the outside (not postive as to why, probably due to it being in a liquid compare to the atmophere) the question is: 1. how do I calculate the...

Homework Statement What is the electric field at the center of a hemisphere bounded by r=a, 0<θ<pi/2 / and 0<∅< 2pi with a uniform surface charge density? Homework Equations (1/4piε0) ∫ p(r') ((r-r')/[r-r']^3) dr' The Attempt at a Solution Forgive my formatting ds= (r^2)sinθdθd∅ (In direction...

Homework Statement Homework Equations ' The Attempt at a Solution Please excuse the poor writing. I believe it should be legible enough, but if you have any questions, i'll clarify or rewrite it. Please excuse the poor writing. I believe it should be legible enough, but if you have any...

Hey guys, I got this problem: We had the derivation of the ekman transport today in class. And what I wondered about is this: Usually the equation for the ekman transport looks similar to this (depends on the author) u = V_0 e^{az} cos(\frac{\pi}{4}+az) v = V_0 e^{az} sin(\frac{\pi}{4}+az)...

Homework Statement In the first and second photo , it's stated earlier that the C is the boundary of surface on xy plane , but in the question in the 3rd picture , it's not stated that the C is on which surface , so , how to do this question ? For ∫F.dr , i am not sure how to get r , coz i am...

I am trying to figure out how to get the Hamiltonian for a mass on a fixed smooth hemisphere. Using Thorton from example 7.10 page 252 My main question is about the Potential energy= mgrcosineθ is the generalized momenta Pdotθ supposed to be equal to zero because θ is cyclic? Or is Pdotθ=...

Homework Statement A bead of mass m kept at the top of a smooth hemispherical wedge of mass M and radius R is gently pushed towards right.As a result,the wedge slides due left.Find the magnitude of velocity of bead relative to the wedge. Homework Equations $$MV=m(v\cos(\theta)-V)$$ and...

Homework Statement edit: I had put this in the calculus section because it was a problem from Stewart but I guess it's closer to a physics problem considering the use of Gauss's Law. My apologies for any confusion this my [/B] I've been trying to do this problem without making use of the...

Homework Statement Homework EquationsThe Attempt at a Solution Using the fact that the sphere is in equilibrium in the 'y' direction , the force exerted by the floor N = 2mg . Now , if I consider the lower hemisphere then , vertical force exerted by top hemisphere + weight of lower...

Hello, My aim is to build a small reflecting sundial as designed by Sir Isaac Newton. I found from a website that it consists of a ceiling and a small mirror. What I want to know is how it works, the concepts behind it and how to build one. It's for an undergraduate project that I've got...

Why Earth rotates from West to East in southern hemisphere and East to West in northern hemisphere?? Is this true,if yes then explain please.

Hi. Given the area, what is the shape of an infinitely thin surface that can carry maximal load on water, i.e. has the best buoyancy just before water gets in? Is it the hemisphere?

Homework Statement A ball is rolling along a frictionless hemisphere with radius R. The question asks about when will the ball rolls off the hemisphere. I understand that this happens when the normal force vanishes. But I am also wondering what if the normal force provided by the hemisphere...

Homework Statement Hoping to outdo his physics professor, Doofus wants to dramatically demonstrate parabolic motion by throwing a cheese wheel of massm and radius r off of the top of the UW observatory, which is at a height 3R above the roof of the physics building, as shown in the diagram...

Please see the attached file if I have calculated the gravitational field g at the centre of a hemisphere correctly.

Homework Statement use spherical coordinates to find the volume of the solid inside the hemisphere z= √(25-x^2-y^2) and bounded laterally by the cylinder x^2+y^2=4 Homework Equations x=rcosθ =ρsinφcosθ , y=rsinθ =ρsinφsinθ z=ρcosφ r= ρsinφ The Attempt at a Solution I divided the solid into 2...

Homework Statement A solid hemisphere of radius b has its flat surface glued to a horizontal table. A second solid hemisphere of different radius a rests on top of the first one so that the curved surfaces are in contact. The surfaces of the hemispheres are rough (meaning that no slipping occurs...