A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex.
A cone is formed by a set of line segments, half-lines, or lines connecting a common point, the apex, to all of the points on a base that is in a plane that does not contain the apex. Depending on the author, the base may be restricted to be a circle, any one-dimensional quadratic form in the plane, any closed one-dimensional figure, or any of the above plus all the enclosed points. If the enclosed points are included in the base, the cone is a solid object; otherwise it is a two-dimensional object in three-dimensional space. In the case of a solid object, the boundary formed by these lines or partial lines is called the lateral surface; if the lateral surface is unbounded, it is a conical surface.
In the case of line segments, the cone does not extend beyond the base, while in the case of half-lines, it extends infinitely far. In the case of lines, the cone extends infinitely far in both directions from the apex, in which case it is sometimes called a double cone. Either half of a double cone on one side of the apex is called a nappe.
The axis of a cone is the straight line (if any), passing through the apex, about which the base (and the whole cone) has a circular symmetry.
In common usage in elementary geometry, cones are assumed to be right circular, where circular means that the base is a circle and right means that the axis passes through the centre of the base at right angles to its plane. If the cone is right circular the intersection of a plane with the lateral surface is a conic section. In general, however, the base may be any shape and the apex may lie anywhere (though it is usually assumed that the base is bounded and therefore has finite area, and that the apex lies outside the plane of the base). Contrasted with right cones are oblique cones, in which the axis passes through the centre of the base non-perpendicularly.A cone with a polygonal base is called a pyramid.
Depending on the context, "cone" may also mean specifically a convex cone or a projective cone.
Cones can also be generalized to higher dimensions.
My research is on radar images and the images are collected in several conical surfaces. These conical surfaces have the same origin, the same maximum length (max flare or max range), but different elevations angles. The images are collected on the surface of the cones only.
I want to determine...
Suppose I have a cylindrical shell of radius r, height h. I can easily express the surface as
$$(r cos(\theta)) i + (r sin(\theta)) j + t k$$
$$0<\theta<2π , 0<t<h$$
For a conical surface of base rad ρ and height h,
$$z=kr -> z=k, r=ρ$$
$$k=\frac{h}{ρ}$$
Then the surface is
$$ \frac...
In analysing the conical pendulum, it can be shown that the period is given by T=2pi.sqrt(L.cos(phi)/g) and that therefore, g = 4.pi^2.L.(cos(phi)/T^2).
L = pendulum length, phi is measured at the top of the pendulum (at the point of suspension).
Graphing cos(phi) vs T^2 should produce...
I am new in Vgate software.
I've tried a lot of things, but nothing works. I need to create a conical source that is 4 cm in radius and 16 cm in length. Example in photo attached
Consider a conical pendulum like that shown in the figure. A ball of mass, m, attached to a string of length, L, is rotating in a circle of radius, r, with angular velocity, ω. The faster we spin the ball (i.e., the greater the ω), the greater the angle, θ, will be, and thus, the smaller the...
I have written a solver for my thesis which determines various parameters of a conical horn antenna for astronomy application. It is done with Mode Matching Technique (MMT) and some Rumsey's integrals for the aperture free space transitions. I have made some goal functions with the solver which...
I require a small conical spring to open from its compressed pancake height of its wire diameter to a free length of 11mm > 0.2 seconds (20 milliseconds)
The large end outer diameter = 7.80mm.
The small end inner diameter must be greater than or equal to 2.75mm.
The conical's spring's will be...
The diagram for the problem is shown alongside. In the vertical (##\hat z##) direction we have ##T \cos \theta = mg##.
In the plane of the pendulum, if we take the pendulum bob at the left extreme end as shown in the diagram, we have ##T \sin \theta = \frac{mv^2}{r}## (the ##\hat x## axis of...
My approach was that I consider the pressure of cross section A first
Pa= P + dgh
Now by writting Bernoulli's Equation between the cross-section A and the opening :
$$ Pa + 2dgh + 2dV^2/2 = Pb + 2dV'^2/2$$
Where Pb is the pressure of the opening which is equal to the atmospheric pressure...
I read about semiconductor laser and its beam shape is conical with 50' of dispersion angle.
But for me, it is hard to accept that it is conical because every single drawing I see is rectangular and the plan that laser going out is also a plain, not a hole.
And this is the picture I saw...
Here is a picture of the problem.
I have chosen the origin to lie in the middle of the circle around which the mass moves. I have also chosen the z axis to pass through the origin and through the vertex of the right circular cone. The x-axis and y-axis are so that one when curls his or her...
So I'm doing a lab in class, and when I graphed the Period vs Length of the string, I got it in the form $T=A\sqrt{L}$, but I don't really know what the value $A$ represents nor what its unit is... Can someone help me?
Is Sphere a more generalized form of Cone i.e. formed by 2 dimensional rotation to 360° of a cone?
Or is Cone a more generalized form of Sphere since sphere can be formed by rotating about Z axis a zero eccentric planar intersection of a cone?
@fresh_42 @FactChecker @WWGD
Homework Statement
(From Griffiths problem 2.26) :
A conical surface (an empty ice-cream cone) carries a uniform surface charge σ. The height of the cone is h, and the radius of the top is R. Find the potential difference between points a (the vertex) and b (the center of the top).Homework...
Homework Statement
A pendulum of length l at the north pole is moving in a circle to the east at an angle \theta to the vertical. It has some period T_E as measured in the rotating Earth frame. The experiment is then repeated except now the pendulum is moving to the west with period T_W...
Hi, a buddy of mine is working on a projecting trying to find the best way to transmit electromagnetic wave frequencies, and he wants to use a horn antenna for his project.
I was looking into horn antennas, and I'm just curious, the wiki page leaves two separate equations for gain, one with a...
Hello all,
I am 100% untrained in even reading about spring making let alone making them. There's a project I want to complete though and I need to make some props involving them. I say these conical springs would be roughly the diameter of a basketball to start with (9.55") and cone to a...
Homework Statement
[/B]
find the period with only using L (for the long of the rope), R (for the radius), M (for the mass), and G (for the gravity)
Homework Equations
V=ωR
Fcentripetal = ##\frac {MV^2} {R}##
Fgravity = MG
phytagoras
basic trigonometry
The Attempt at a Solution
[/B]
i have...
Homework Statement
Homework Equations
v = ωr
The Attempt at a SolutionHonestly speaking I have very little idea about the problem . I am not understanding the setup clearly . What role does the rails play while the cones move on them .Are the cones fixed to the rails ? Does the tuning of...
Hey guys!
The question is related to problem 2.26 from Electrodynamics by Griffiths (3ed).
1. Homework Statement
A conical surface (an empty ice-cream cone) carries a uniform surface charge σ. The height of the cone is h, as the radius of the top. Find the potential difference between points a...
Homework Statement
A conical tank filled with kerosene is buried 4 feet underground. The density of kerosene is 51.2 lbs/ft3. The kerosene is pumped out until the level drops 5 feet. How much work is needed to pump the kerosene to the surface if the variable is given as:
A. The distance...
Homework Statement
Mass ##M## hangs from a string of length ##l## which is attached to a rod rotating at constant angular frequency ##\omega##. The mass moves with a steady speed in a circular path of constant radius. Find ##\alpha##, the angle the string makes with the vertical.
Homework...
Homework Statement
A conical Pendulum, a uniform, thin rod of mass m and length l, rotates about a vertical axis with angular velocity omega. Find the angle between the vertical and the rod.
Homework EquationsThe Attempt at a Solution
I know the usual approach to solve this question, write the...
Homework Statement
A model airplane has a small gas powered motor in it to allow it to fly. It is tethered its controller by a long
cord. The plane will fly in a circle at the end of this cord around the controller who uses the tether to control
the altitude of flight of the plane. Currently...
http://www.pjoes.com/pdf/19.4/749-756.pdf
i would like to learn about the calculations formulas involve in this mechanism.
Any notes or formulas with explanation on the calculations of pressure loss, volumentric velocity, velocity, ect. will be very much helpful.
In the pdf of the given link...
Hello. In class today, we studied conical pendulum but I was confused at the part about its components. In all the diagrams ( http://dev.physicslab.org/img/90c0fb7a-ffb4-4573-b389-b50a559732c8.gif ) if shows The x-component as being sine, but I always thought x-comp was cos?? (...
Homework Statement
Two vertical tanks have their vertices connected by a short horizontal pipe. One tank initially full of water has an altitude of 1.8 meters and a diameter of base 2.2 meters. The other tank initially empty has an altitude 2.7 meters and a diameter of a base 2.4 meters. If the...
The sistem above is the one I'm interested in. There is two equally charged spheres spinning on a plane. The line has L=\sqrt{2} m and the spheres weight 0.6Kg. The angular speed is \omega = 2rad/s.
The radius for the circular trajectory is R=1m and so the centripetal force is...
Homework Statement
I'm doing an EPI on horizontal circular motion and for one test the independent variable is mass and I need to control the velocity by using the 2πr/T formula. So I know how to use the forumula to find an unknown but how do I use it for two unknowns (r and T). Is there a...
Hey everyone, I'm new to this site and I figured this would be the best place to ask this question.
We've been using maple to solve two specific problems on the time it would take two tanks to drain. One being cylindrical, and the other conical. They have the same height, the same volume...
Homework Statement
I am trying to understand a solved problem which is about finding electrostatic potential at point b of the following conical surface with a given surface charge:
I have attached the worked solutions to this post. In the solutions, I don't understand how they have got the...
In the book "Introduction to Mechanics" by K&K, in the section on conical pendulums, the net force in the ##\hat{k}## direction is set to zero, since the ##z##-coordinate of the particle doesn't change. However, later on the effect of changing ##\omega## on ##\alpha## (the angle the rod makes...
Homework Statement
A small ball of mass m suspended from a ceiling at a point O by a thread of length l moves along a horizontal circle with constant angular velocity ##\omega##. Find the magnitude of increment of the vector of the ball's angular momentum relative to point O picked up during...
I need to make a net for a frustum. The following web page explains how to do it... http://www.analyzemath.com/Geometry/conical_frustum.html
I have tried but am unable to do this complicated, advanced (o.k basic) math.
In the following figure I have the values R,r and h.
R = 40
r = 35
h =...
Homework Statement
A conical pendulum with an unelastic tether has a mass of 4.25 kg attached to it. The tether is 2.78 m. The mass travels around the center every 3.22 seconds.
What angle does the rope make in relation to its original position?
m=4.25 kg
T=3.22 s
L=2.78 m
Homework Equations...
Homework Statement
Finding the time period of a conical pendulum by D'Alembert's principle. The string is of a constant length and all dissipations are to be ignored.
Homework Equations
The time period of a conical pendulum is 2\pi \sqrt{\frac{r}{g\tan\theta}}. I need to arrive at this result...
Homework Statement
Assuming we know the length of the string L, radius of the swept out circle r, angle formed by string and centre of circle, \theta, and angle the swept out circle is to the horizontal, \alpha, what is the speed, v, of the mass if it is constant?
picture...
I am designing a constant pitch, helical conical compression spring (round wire cross section) that will be compressed into a final desired shape. So my issue at hand is figuring out the pre-compressed geometry that will give me my desired final geometry once compressed.
The compression will...
Homework Statement
Water drains out of an inverted conical tank at a rate proportional to the depth (y) of water in the tank. Write a diff EQ as a function of time.
This tank's water level has dropped from 16 feet deep to 9 feet deep in one hour. How long will it take before the tank is...
Homework Statement
I would like to find a general equation for calculating the centre of gravity (COG) of a hollow conical frustum.
Homework Equations
Consider a solid conical frustum as shown below:
The COG of this shape may be derived as follows:
COG =...
Homework Statement
Hey, thanks for taking a look at this.
"The figure below shows a conical pendulum, in which the bob (the small object at the lower end of the cord) moves in a horizontal circle at constant speed. (The cord sweeps out a cone as the bob rotates.) The bob has a mass m...
Homework Statement
Derive a differential equation (do not solve) for the temperature distribution in a straight conical fin. Assume one dimensional heat flow. This equation is assumed to be 1-D steady state conduction.
Homework Equations
For this problem, we can use the generalized...
"Two co-axial conducting cones (opening angles ##\theta_{1} = \frac{\pi}{10}## and ##\theta{2} = \frac{\pi}{6}##) of infinite extent are separated by an infinitesimal gap at ##r = 0##. If the inner cone is held at zero potential and the outer cone is held at potential ##V_{o}## find the...
For this problem, it reminds me of related rates problems, except I'm not given a constraint such as dr/dt = something at r = something.
I tried using partial derivatives to solve it, but I'm not seeing a way to get rid of the r terms, or its derivative
A mass of 80g is moving in a horizontal circle supported by a string 1.2m long suspended from a fixed point in the centre of the circle. The mass completes each revolution in 0.85s. Calculate the tension in the string.
Relevant equations: I'm not entirely sure, but these were the ones I...