Cone Definition and 514 Threads

Hi all, Homework Statement Given a right circular cone with origin at the centre of the base, the positive z-axis pointing towards the apex, and the height is h and radius of base is r. What is the cartesian equation of the cone? Homework Equations The Attempt at a Solution...

Homework Statement Find the moment of inertia of the right circular cone or radius r and height h with respect to its axis, and in terms of its mass. *As of this point, I am supposed to use solids of revolution, and so I need to rotate a line about an axis, and find the moment of inertia with...

Hi! I have a question and would greatly appreciate your help. I've been wondering about how a light that is a emitted in the shape of a cone from a source (such as, a flashlight) can reach certain points outside the cone of light (although, much less intensly). The simple answer you are...

When discussing EPR experiments on this forum I made the claim that Bell's theorem does not prove classical determinism false because there is always the possibility that the correlations between distant measurements can be a result of the common past shared by particle source and the two...

:confused: PROBLEM: A cone with a 30degree angle and a hieght of 1 must fit a sphere of icecream in it with a maximum volume. what is that volume, and what percentage of the sphere is in that cone!? PLEASE HELP!? this is all i have R= (h-a)(sin15) a=distance between center of sphere...

Homework Statement Consider a cone of height H and base radius R with its apex (tip) at the origin, and its base at circular end at z = H. Derive the equation for the surface of the cone in cylindrical coordinates. You may assume z is proportional to r. Homework Equations I assume the...

Source: Physics and Scientists for Engineers, Ch. 24 #7 A cone of radius R and height h sits on a horizontal table. A uniform electric field parallel to the table penetrates the surface of the cone. What is the flux entering the cone? Diagram: (N.B. the dots in the cone are just to give it...

Homework Statement Water is draining from a conical tank with height 12 feet and diameter 8 feet into a cylindrical tank that has a base with area 400 \pi square feet. The depth, h, in feet, of the water in the conical tank is changing at the rate of (h-12) feet per minute. A) Write an...

Homework Statement Dynamics Problem: Spinning cone with mass!? The sides of a cone make an angle "THETA" with the vertical. A small mass "m" is placed on the inside of the cone and the cone, with its point down, is revolved at a frequency "f" about its symmetry axis. If the coefficient of...

I am wondering if someone can help clarify the following? Suppose that I’m asked to find the volume of a cone. So, the volume would be ∫∫∫dxdydz or using polar coordinates ∫∫∫rdzdrdθ. Therefore the volume would be if I have a cone with base radius R and height H, I can express the radius r at...

Homework Statement find electric flux that enters left hand side of a cone (with base radius R and height h). electric field penetrates the cone horizontally (cone is on a horizontal table). Homework Equations flux = surface integral of EdA where E represents component of electric...

im actually bugged of finding a solution for d topic mentioned can any 1 pleasezzz help me

1. I have a cone frustum with known height (h) and known base diamter (d) and cap diameter (D). From this, I can calculate the volume. Question: if the frustum is half full of liquid, how can I calculate the height of the liquid? 2. V = pi/12 x h x (D2 + d2 + D x d) 3. I guess I...

Hi! Please follow the link; its a guy juggling balls in an inverted cone. What he does is he uses the cone as a surface, and he rolls the balls around him in circles. ITs really entertaining so this shouldn't be too much of a chore. I thought I'd post it here because it demonstrates simple...

Find the location of the CM of a hollow ice cream cone, with base radius R and height h, and uniform mass denisty. How does your answer change if the cone is solid, instead of hollow? Okay, so I'm pretty sure that I need to work with slices, and that you need the mass which I believe is...

Hello there, this is my first posting on this board. I am a third year physics major and I've taken a lot of courses but I've always just scraped by with a large amount of help from small groups. I'm thinking about reconsidering my major because I feel like I no longer can understand the...

I'm stuck on this question: "A man is sipping soda through a straw from a conical cup, 15 cm deep and 8 cm in diameter at the top. When the soda is 10 cm deep, he is drinking at the rate of 20 cm^3/s. How fast is the level of the soda dropping at that time?" So you are given height = 15...

Here's a cute problem I came across recently. Suppose you have a rubber band with spring constant k, mass m and unstretched radius r. Now suppose you have a frictionless cone and the angle of the peak is 2 \theta (that is, if you project the shape of the cone onto a plane it looks like a...

I stumbled across this while looking for something else. This might be of interest to AE's. http://en.wikipedia.org/wiki/Nose_cone_design

Ok i need to calculate the work done by gravity , while filling a truncated cone of bottom radius R and upper radius r (R>r) and height H , with sand of density 'd' , if we start filling the cone from bottom.. What i did was , I considered a disc of radius 'x' as a part of the cone and with...

I have been presented with this problem. I somewhat know what I need, I just don't know how to get it :blushing: The problem: A truncated cone, top diameter of 1m bottom diameter of 1.5m and a height of 10m. With a given density(I do not have it with me at this moment, I do not remember...

sphere in a cone (ball in a martini glass) A problem a friend mentioned to me years ago. You have a cone with height H and angle A. What is the radius R of a sphere that when placed in the cone, displaces the most volume? One suggestion was to reduce this to a two dimensional case.

Surface area integral sorry, this is not about flux integration... but surface area! sorry about the title! Find the surface area of the part of the sphere x^2+y^2+z^2=36 that lies above the cone z=\sqrt{x^2+y^2} z=\sqrt{36-x^2-y^2} A(S)=\int\int_D \sqrt{1+\left( \frac{\partial...

I need to find the inertia tensor for a uniform thin hollow cone,spinning about its ponted end. When the cone is solid then everything goes very smoothly by using cylindrical polar coordinates. But how should I find if it is a hollow cone. To be able to write the density of the cone I have...

Hi, I have this problem: Compute volume of solid bounded by these planes: z = 1 z^2 = x^2 + y^2 When I draw it, it's cone standing on its top in the origin and cut with the z = 1 plane. So after converting to cylindrical coordinates: x = r\cos \phi y = r\sin \phi z = z...

Before these threads get pushed too far aside (or worse dumped into the bit bucket to make room for more threads), I propose to assemble them together, perhaps in a place like Classic Discussion Threads. They are quite entertaining reading and had me laughing :smile: reading some of our PF...

Imagine that I have a pipe that is on a constant slope at any percent. On the low end of the pipe, there is a container filled with water. The water has naturally found a leveling point up into the pipe. Provided the level of water in the container is above the top of the pipe, a portion of...

What is the shock wave cone half-angle for a supersonic airplane flying at Mach 2.30? Would you use Mach=1/sin(theta) and then divide by 2 to get the half angle? So 2.30=1/sin(theta)=12.9 degrees

Hi , I don't know how to get the edge of the cone in cylindrical coordinates. For example, we have a cone starting at the origin, of heigth 2 and the top is a circle of radius 1 (center at the origin). the edge of the cone is z=2r. but I don't know how they find it. Please can someone...

I am trying to understand this example of finding the center of mass of a uniform solid cone. please refer to the attached figure. We know for obvious reasons that the center of mass will be on the z-axis. I will be referring to the integral that my book used to find the center of mass which is...

I'm an "on-my-own-free-time" arm-chair student of physics. Lol. So if this question is way off the mark my apologies. Feel free to let me know where I’m off base. Anyway... For me, a great visual example of the twin paradox was found at this site...

Thanks to everyones help i was able to understand the center of mass of a cone. Now i have to find the angular momentum along the z-axis as i understand the angular momentum will change as the radius gets larger because the larger radius must spin faster . H = height of cone so the...

I need to find the center of mass of a cone with point facing downwards, of height H and radius R. Since the density is constant throughout and because of axial symmetry the center must be somewhere on the z-axis. I know from convention that this is H/4 but i need to derive this. Rcm...

A circular cone is inscribed in a sphere with a radius of 30cm. The semi vertical angle is theta. Derive a trigonometric equation for the volume of the cone. This has be stumped. I tried looking up proofs for the expression of the volume of a cone for inspiration but all involve calculus.

For a homework assignment i was asked to proof that the positive cone {x^2 + y^2 = z^2, z>= 0} cannot be a submanifold of any dimension of R^3. It apparently goes wrong at the origin. I guess it's because you can't really speak of a tangent space at that point. So I tried to prove by...

volume of a cone is 10 cubic cm... Q: a cone shaped paper drinking cup holds 10 cubic cm of water. We would like to find the height and radius that will require the least amount of paper. Volume of a cone is: (b x h)/3, or with radius is: ((pi r squared x h))/3. I think you solve this...

This is a problem I had in a test and almost everyone got different answers for it, we discussed and well, I spotted mistakes in their solutions so I think mine is right but I wanted to check here and also ask if there is an easier/faster way to do it. There is a container that is similar to...

I have two questions. How do you find the equation of a cone given data points? I've found lots of info on the equation of a cone, but can't find anything on one that is rotated and not centered at the origin. What is the equation for a rotated translated cone? Second, given the equation of a...

Can someone help me with this problem?: We will define a cone in n-dimensions as a figure with a cross - section along its height X_n that has a constant shape, but each of its dimensions is shrunk linearly to 0. a)let D be a cone in R^n with height h (ie. X_n \epsilon...

Hi, I need to find the volume of the solid that lies above the cone with equation (in spherical coordinates) \phi = \frac{\Pi}{3} and inside the torus with equation \rho = 4\sin\phi . I thought that the bounds are: 0\leq\rho\leq4\sin\phi, \frac{\Pi}{3}\leq\phi\leq\frac{\Pi}{2}, and...

We have a right circular cone of base radius a and height a with a uniform surface charge sigma. I want to determine the potential difference between the apex of the cone and the center of the base (this cone doesn't have any charge on the base). My plan of attack for the problem was to...

Hey, im trying to write a program that computes Volume of Intersection of a Cone with a Sphere. Can anyone point me to the math i need to know. Any links, material is good. Thanx

Hi all I have just had what may be an interesting thought. Take a square piece of graph paper, label the horizontal axis "Time" and the vertical axis "Length". We will be using natural units so one grid line in the horizontal axis is one natural unit of time, and one grid line in the...

Hi there, I was hoping that someone here could maybe give me a hand with a couple of issues I'm having to do with moments of inertia. For a right circular solid cone of mass m, height h and base radius a, we have to show that its moment of inertia about a line through its vertex and...

Hello, I have a problem I can't solve. Need assistance! :bugeye: You cut out a piece of a circle (like you cut a piece of a cake), then make a cone by joining the edges of what remains of the circle. What angle must the "cakepiece" have to maximize the volume of the resulting cone? I...

Hi, could someone explain to me the concept and calculation of Solid Angle? I don't think we've actually covered it in our Vector Calculus lectures and I have a question to do on it! Tried searching on the web, but not much information and I really don't understand it. Also, my question is...

FTL travel in a light cone? I read in several places there there is one condition in GR, that will allow you to travel faster than light, and allow time travel to the past. Can someone explain this further, without getting too mathamatical (Ok, maybe a little math). Thanks in advance :smile:

AA loud speaker cone is connected to a AC signal genetator.When the frequency of the signal genetor is alterned the amplitude of the cone changes.why? My working: As the frequency increases the amplitude decreases because there is less change in the magnetic flux and vice versia...I am a bit...

Can there be such a thing as a cone of Ignorance? Can somebody be so ignorant as to drag other people down to their level just by being in close proximity to them? And if this can be so, does that mean that a cone of depression can also exist? Are there any other cones that you can think of?

The area (not including the base) of a right cone is pi*radius*sqrt(height^2+radius^2). What is the area of an inclined cone? (Where the segment joining the tip and the center of the base circle is not perpendicular to the base plane). So what is the area of this, considering we know the...