Cone Definition and 490 Threads

Homework Statement Hi there. I haven't used iterated integrals for a while, and I'm studying some mechanics, the inertia tensor, etc. so I need to use some calculus. And I'm having some trouble with it. I was trying to find the volume of a cone, and then I've found lots of trouble with such a...

I'm given a problem where I need to parameterize a cone, but only the segment between two planes, being z=2 and z=3. This is what I ended up with: r(u,v)=(ucos(v),u(sin(v),u) u:[2,3] v:[0,2\pi] Is this right?

Homework Statement Find the Dimensions of the right circular cone of minimum volume which can be circumscribed about a sphere of radius 8 inches.Homework Equations N/A The Attempt at a Solution So this is my try, i did the question to find the minimum volume of the cone, For Larger Size...

Homework Statement Consider the two-dimensional spacetime spanned by coordinates (v,x) with the line element ds^2=-xdv^2 +2dvdx Calculate the light cone at a point (vx) The Attempt at a Solution I don't even know how the light cone for flat spacetime is calculated. So if that one's...

Hey all. I had a question. What makes the different cone cells in your eye respond to different wavelengths of light? I know that light strikes Retinal and causes it to undergo photoisomerisation, which starts the chain that leads to you seeing something. Do the different cone cells contain...

Homework Statement A cone has the base radius of 8 cm and height of 10 cm. The height of the cone is changing at at a rate of 1cm/hour whilst radius of the base is changing with it keeping the volume constant. At what rate is the surface area of the entire cone changing at this exact...

Homework Statement The height h of the cone is 1/3 of l the circumference of the base . Homework Equations Calculate the angle alpha. Give your answer with 2 decimals. The Attempt at a Solution h=1/3 * 2*Pi*r and then we don't have the radius

Homework Statement Evaluate the volume inside the sphere a^2 = x^2+y^2+z^2 and the cone z=sqrt(x^2+y^2) using triple integrals.Homework Equations a^2 = x^2+y^2+z^2 z=sqrt(x^2+y^2) The solution is (2/3)*pi*a^3(1-1/sqrt(2)) The Attempt at a Solution I first got the radius of the circle of...

hello, I need help finding the moment of inertia of a cone using triple integral. can you also explain how can we get dV with details?

Hi! If we have a 2x2 matrix [x y;y z] belonging to a positive semidefinite cone. Why is it equivalent to say x>=0, z>=0, and xz>=y^2? Thanks!

Homework Statement A water tank is shaped like an inverted cone with height 6 m and base radius 1.5 m If the tank is full, how much work is required to pump the water to the level of the top of the tank and out of the tank? Homework Equations Integral of ( density * g...

Homework Statement This is an optimization problem but I'm having trouble modeling the question. There is a sphere encased in a cone. The sphere has a fixed radius R and the cone has a variable height h and radius r. There is also a variable angle theta at the base of the cone. Express the...

Homework Statement I'm working out of Griffith's "Intro to Electrodynamics" and the problem states: "A conical surface (an empty ice-cream cone) carries a surface charge \sigma. The height of the cone is h as is the radius of the top. Find the potential difference between points a (the...

Homework Statement Let Y be a topological space. Let CY denote the cone on Y. (a) Show that any 2 continuous functions f, g : X --> CY are homotopic. (b) Find (pi)1 (CY, p). Homework Equations I have no idea. The professor said one problem would be way out in left, to see who could make the...

Homework Statement A water tank the shape of an inverted circular cone with a base radius of 2m and height of 4m. if water is being pumped into the tank at a rate of 2m^3/min, find the rate at which the water level is rising when the water is 3m deep. dv/dt = 2m^3/min h = 3m r = h/2...

Homework Statement A cone with height h and radius R. The radius R is located at the top of the cone. We have to find moment of inertia of the cone. The disc has a radius r, height of dz, and is located z below the circular surface with radius R. Homework Equations dI = \frac{1}{2}\ dm\ r^2...

Homework Statement From Goldstein's Classical Mechanics (Chapter 5 - Exercice 17 - Third Edition) A uniform right circular cone of height h, half angle A, and density B rolls on its side without slipping on a uniform horizontal plane in such a manner that it returns to its original position...

Homework Statement I have been searching online for help with this equation but have found nothing at this stage. I am looking for an equation to satisfy the Volume of a Frustum of a cone. The liquid level is measured via a sensor located in the centre point, top circle(area) of the...

I need help understanding a problem for my homework assignment. I'm not sure how to set up the problem. If anyone could help I would greatly appreciate it. Homework Statement Water is being pumped into an inverted conical tank at a constant rate. However, water is also leaking out of the...

Show the intersection of complex sphere (|z1|^2+|z2|^2+|z3|^2=1) in C^3 and the complex cone (z1^2+z2^2+z3^3=1) in C^3 is a smooth submanifold of C^3. I am trying to do it using regular level set, but I am not sure which one of (1,0) or (1,1,0) should be set to be the regular value?

Hi, I know that you can determine that the Gaussian curvature of a cone tends to infinity at the vertex, but seeing as the curvature anywhere else on the cone is zero, how is this possible?

Homework Statement Using integration, Find the Volume of a right circular cone with height h and base radius r The Attempt at a Solution since the volume is V(x) = \int A(x) d(x) so I divided the cone into horizontal circles with radius r and r = \sqrt{s^{2} + y^{2}} where is the hypotenuse...

Finding the volume of a cone with a elliptic base! Homework Statement The area of an ellipse is (pi)ab, where a and b are the lengths of the semimajor and semiminor axes. Compute the volume of a cone of height h = 20 whose base is an ellipse with semimajor and semiminor axes a = 4 and b = 6...

Hi, I have a cone on the z axis with his summit on height h meeting a cylinder on the x axis. The expressions should be: cylinder: y2+z2=r2 cone: x2+y2 =(z-h)2tan(phi)2 If we consider any straight line on the cone, what is the length of this line inside the cylinder? Is it...

I was looking for a paper or textbook that would provide "working equations" for Tipler Cylinders. In other words, is there an equation(s) that would provide the light cone tilt angle as a function of the cylinder's diameter, height, density, and angular velocity?

Homework Statement Consider a vertical cone of height h whose horizontal cross-section is an ellipse and whose base is the ellipse with major and minor semi-axes α and β. Verify that the volume of the cone is παβh/3. [ Hint: The area of an ellipse with major and minor semi-axes α and β is...

[PLAIN]http://img688.imageshack.us/img688/3941/fingernorm.jpg Because the cone is being held up, I said mg=2fy, where f is the friction force, so mg=2uNcos(x) (where x=theta), and I got N=mg/(2ucos(x)). The cone also isn't moving from side to side, so I said Nx=fx, so fsin(x)=...

Homework Statement I am basically given a cone with uniform volume charge and told to find the area of highest electric potential. Homework Equations I want to use the equation: V= q/4piEr The Attempt at a Solution I am having trouble finding anything in my book. I am comparing...

1. Homework Statement [/b] A small block with mass m is placed inside an inverted cone that is rotating about a vertical axis such that the time for one revolution of the cone is T. The walls of the cone make an angle v with the vertical. The coefficient of static friction is between the...

Hi, If you have a cone (right angle) with radius r, slant length l, how is the central angle theta = 2*pi*r/l? Thanks, Ivan77

What data do you need to calculate the failure point of a truncated cone when it is under uniaxial stress acting downward on the cone? The cone will be under stresses of roughly 30 tonnes and probably constructed of plastic. Thanks,

What data do you need to calculate the failure point of a truncated cone when it is under uniaxial stress acting downward on the cone? The cone will be under stresses of roughly 30 tonnes and probably constructed of plastic. Thanks,

Hi, If the cone is cut with a plane such that an ellipse has been formed. Let's say the major axis is 'a' and the minor axis is 'b'. Is there a way to find a and b from the geometry instead of getting them from the quadratic equation.

Homework Statement Water is leaking out of an inverted conical tank at a rate of 6500 cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of 20 cm/min when the...

Homework Statement Use polar coordinates to find the volume of the given solid: Under the cone z = Sqrt[x^2 + y^2] Above the disk x^2 + y^2 <= 4 2. The attempt at a solution I tried using formatting but I couldn't get it right so I'll explain...I changed variables by making the upper and...

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 what is the flux entering a cone of radius r and height h located in a uniform electric field E parallel to its base? Homework Equations flux = E.ds The Attempt at a Solution

I was helping my 17 year old daughter (just starting calculus) with the optimization problem of maximizing the volume of a right circular cone that can inscribed in a sphere. She tried what she thought was a short cut by using a cone with vertex at the center the sphere (instead of the top) and...

Homework Statement Let A be the region that in space bounded by the balls: x^2 +y^2 + z^2 =1 , x^2 +y^2 +z^2 =4 , above the plane z=0 and inside the cone z^2 = x^2 +y^2 . A. Write the integral \int \int \int_{A} f(x,y,z) dxdydz in the form: \int \int_{E} (\int_{g^1(x,y)}^{g^2(x,y)}...

Homework Statement A toy manufacturer wants to create a toy ice cream cone by fitting a sphere of radius 4 cm inside a cone with a height of 8 cm and radius of the base of 3 cm. The base of the cone is concave, but the rest of the cone is solid plastic so that with the sphere attached...

Homework Statement A right circular cone has height 6 cm and base radius 2. It is over-filled with ice cream, in the usual way. Place the cone so its vertex is at the origin, and its axis lies along the positive y–axis, and take the cross-section containing the x–axis. The top of this...

Homework Statement A right circular cone has height 6 cm and base radius 2. It is over-filled with ice cream, in the usual way. Place the cone so its vertex is at the origin, and its axis lies along the positive y–axis, and take the cross-section containing the x–axis. The top of this...

Homework Statement the task is to pump out the river from a cone with R radius and H height. How much will be the work (energy) used to do this? its a problem because I can't use here standard work definition W=\int F(s)\mbox{d}s, and I don't know what to do and how to start. please help:)

Homework Statement I'm not from an English speaking country. I hope that you'll understend my question. Cone made of steel is rotating on the wooden desk. Radius of cone is 4 cm, height is 10 cm. Density of steel is 7,8*10^3 kg/m^3. Angular velocity of cone is 3.14 rad/s. Find the force of...

Homework Statement Question B) Homework Equations The Attempt at a Solution So I know the flux of S1 U S2 is the same as the flux for S1 + flux of S2, that is Double Int of S(surface) = Double Int of S1 U S2 = Double Int S1 + Double Int S2 The problem I'm having is...

Hi everybody, Guys I'm a total stranger to physics. I need some help to find the relationship between the major/minor axes of an ellipse and the radius of a sphere in a cone of light. For example, imagine a light source is located at 'h' height from a plane and a sphere(with a radius of...

Homework Statement Evaluate the volume under z^2 = x^2 + y^2 and the disc x^2 + y^2 < 4. Just wondering what I should write to constitute a proper solution. Would this do?: V=(int)(int) z dA R is {x²+y² < 4} [context: R in other problems was the region over which integrals were performed]...

Block inside a spinning cone -- Newton's 2nd Law problem Homework Statement See attempt at solution. I have attached everything there.Homework Equations F_net = m * a_n (net force) W = mg (weight) a_n = 4*pi^2 * R * f^2 ... formula for "normal" component of acceleration where R = radius, f =...

Homework Statement I'm wondering whether or not it is possible to get the area of the base of an elliptical, non-right cone if the following two parameters are known: - length from center of ellipse up to vertex - angle that the sides make Here is a simple visual...

Homework Statement A particle is confined to move on the surface of a circular cone with its axis on the vertical z axis, vertex at the origin (pointing down), and half-angle a. (a) Write the Lagrangian L in terms of the spherical polar coordinates r and ø. (b) Find the two equations of...