Cone Definition and 490 Threads

Maxwell's demon is the little guy who opens an atomic door to a container to let atoms fly in, but shuts it before an atom flies out, thus increasing the internal pressure. Suppose the walls of a container had several small cone-shaped holes built into it. The inside hole might be pretty...

Homework Statement The z com of the entire ice cream cone, the base being an inverted right circular cone, the top a hemisphere. Equal density throughout. Must solve using integrals and density relationship. Homework Equations The z com of the top hemisphere (ice cream) is equal to 3/8 R...

The cone centre is the z-axis and has base ρ=1 and height z=1, I'm looking at the lecture notes and it says the limit φ=0 to 2pi, z=0 to 1, ρ=0 to (1-z). Could someone tell me where the (1-z) comes from please? Why is it not 0 to 1?

Zee's QFT in a Nutshell makes a short comment in the first chapter about the possibility of particles tunnelling outside their light cone - is there some probability that a particle could do this? I know the neutrino thing has been debunked as a faulty cable, but did not see this offered as an...

Homework Statement Find the inertia tensor for a uniform, thin hollow cone, such as an ice cream cone, of mass M, height h, and base radius R, spinning about its pointed end. Homework Equations I_{zz} = \sum x^{2}+y^{2} \rho = \sqrt{x^{2}+y^{2}} The Attempt at a Solution I first...

Hey there! I'm relatively new to this website and I have a quick question. If I have some function t(x), that is time for a given x, with a M (mass) constraint, namely... M^2 = 1 --> Null M^2 > 0 --> Time-like M^2 < 0 --> Space-like If I wanted to see what these space-time...

Homework Statement A cone is resting on a tabletop as shown in the figure with its face horizontal. A uniform electric field of magnitude 4550 N/C points vertically upward. How much electric flux passes through the sloping side surface area of the cone? Homework Equations flux = ∫...

Hi everyone, I need some help ASAP please! I have forgotten how to calculate the length of a spiral in a cone. I am really only interested in part of the cone from where the diameter is 8m to the base where it will be 10m in diameter. in this part of the cone there will be 5 rotations each...

Homework Statement There's a problem that I don't even know really where to start. It seems extremely complex to me. Basically there's a reverted cone of mass M with a mass of mass m that can slides over it without friction. But there's a constraint of motion for the particule, it must stay...

As smatter in the subject therefore I have the following confused questions about the light-cone. As we all know that when a flash of light is released from source, light-rays spread out isotropically in space, tracing out a cone on a space-time diagram. As "light-cone" is expanded at the...

Homework Statement I understand everything except for the part where the -1 pops out of nowhere on step 4. why? how?

Hello everyone, I recently tried to find the surface area of a hollow cone (there is no base, like an ice cream cone) using spherical coordinates. With cylindrical coordinates I was able to do this easily using the following integral: \int \int \frac{R}{h}z \sqrt{\frac{R^{2}}{h^{2}} + 1}...

Here again Homework Statement Find the volume of a right elliptical cone with an elliptic base with semi-axes a and b and heigh h Homework Equations So: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 The Attempt at a Solution That's what I have, but answer should be...

Find the mass of the solid bounded by the cylinder (x-1)2 + y2=1 and the cone z=(x2+y2) 1/2 if the density is (x2+y2) 1/2 I know that I have to substitute for cylindrical co-ordinates x=rcos(theta), y=rsin(theta), and z=z, and then use the change of variables formula to get the mass by...

Homework Statement A frustum of a right circular cone with height h, lower base radius R, and top radius r. Find it's volume. Homework Equations We are currently learning the Method of Washers and the Method of Cylindrical Shells so I believe we are supposed to use this somehow. The...

Hello there :) I'm having tons of trouble figuring out how to finish this problem. A cone is to be constructed having a given slant height of l>0 . Find the radius and height which give maximal volume. I am unsure of which variables to keep in order for it to be maximized, and how to...

How can I design an experiment to find the drag coefficient of a cone without knowing the force of drag that is acting on the cone? Is this even possible?

I had this doubt studing GR, but let's consider SR for semplicity, where g_{\mu\nu}=\eta_{\mu\nu}the geodesics are 0=ds^2=dt^2-dr^2 we obtain the constraint we obtain the constraint r=(+/-)t So it is a well known light cone, but in SR we have that a (test?)particle can always move in a...

a smooth hollow circular cone of semi-angle y is fixed with its axis vertical and its vertex A downwards. A particle P,of mass m,moving with constant speed V describes a horizontal circle on the inner surface of the cone in a plane which is at a distance b above A. show V^2=gb...done b)...

Part of a chapter review problem. Say you have a sphere centered at the origin and of radius 'a'. And you have a (ice-cream) cone which has it's point at the origin and phi equal to ∏/3. How do I find the equation of their intersection? Which is the projection onto the xy plane...

Homework Statement g(x,y,z) = z2; Ʃ is the part of the cone z = \sqrt{x2+y2} between the planes z = 1 and z = 3. Homework Equations Conversion to polar coordinates ∫∫Ʃg(x,y,z)dS = ∫∫Rg(x,y,f(x,y)) \sqrt{fx2 + fy2+1} The Attempt at a Solution If we're talking in terms of r and θ...

Homework Statement Find the volume bounded between the sphere of radius a centered at (0,0,0) and the cone z=sqrt(x2 +y2). The Attempt at a Solution So, subbing our definition for z into the the equation for a sphere of radius a centered at (0,0,0): 2x2 + 2y2 = a2. Converting to...

Hi everyone Homework Statement I have a cone, upside down and a mass m in it, also a homogenous gravitiy field. I found the Euler-Lagrange equation already, which led to 2 equations of motion. Now I want to find a stationary path ( acceleration=0)Homework Equations - The Attempt at a Solution...

Homework Statement A solid cone is obtained by connecting every point of a plane region S with a vertex not in the plane of S. Let A denote the area of S, and let h denote the altitude of the cone. Prove that: (a) The cross-sectional area cut by a plane parallel to the base and at a distance t...

Man I hate to make two post in one day but I am really stuck! Homework Statement A particle slides on the inside surface if a frictionless cone. The cone is fixed with its tip on the ground and its axis vertical. The half angle of the tip is α. Let r be the distance from the particle to the...

inverted right-circular cone, with radius at the top 15 meters and depth 12 meters. rate of 2 cublic meters per minute. How fast is the depth increasing at the instant when the depth is 8 meters. When i try to solve it I get an equation with 2 varibles.

My problem is the following:There is a point charge inside a thin uncharged and insulated metal cone. Calculate the charge distribution on the cone and the force between the point charge and the cone. I presume "thin cone" means only the infinitely narrow surface of a cone.The relevant equation...

A water glass (10 cm diameter at the top, 6 cm diameter at the bottom, 20 cm in height) is being filled at a rate of 50 cm^3/min. Find the rate of change of the height of the water after 5 seconds. V=1/3(3.14) r^2h I'm a little unsure how to approach this problem for two reasons. A) The glass...

Homework Statement Set up intergral expression for center of mass of a cone using cylindrical coordinates with a given height H and radius R Homework Equations rdrddθdz is part of the inter grand. M/V=D volume of cone is 1/3π(r^2)H The Attempt at a Solution dm=Kdv dv=drdθdx K...

Im trying to figure out the center of mass of a cone for this research I'm doing. How do I find the center of mass of a cone?

This is something I remember as a standard problem given to college math and physics students ... I've been hunting for a model answer online but no luck: everyone is happy to do the cylinder on it's side or a truncated cone or the intersection of two objects with a lot of symmetry in common but...

Homework Statement Find the moment of inertia of a right circular cone of radius r and height h and mass m Homework Equations I = ∫r2 dm V = 1/3*π*r2*h The Attempt at a Solution Assume density is p dm = p dv divide both sides by dr dm/dr = p dv/dr dm/dr = p (d/dr * 1/3*π...

Homework Statement Calculate the X_com of the cone of mass M in terms of quantities given in the picture. The density of the cone is uniform. See the attachments for the picture. Homework Equations The Attempt at a Solution When I did it I got X_com = (3L)/2 and I am...

I have the cone x^2 + y^2 <= z^2 with |z| <= 2 The vector function F = (4x, 3z, 5y) With the divergence theorem I managed to reduce the equation to ∫∫∫ 4 dxdydz Now the problem is finding out the limits. I know z goes from 0 to 2, but what about x and y?

If I have a 45° right-angle cone and I place it on a table on the conical surface (not the base), there should be a line-contact along the cone (the table is tangent to the conical surface). The table can be seen as a cylinder with an infinite radius, so, my question is, what is the minimum...

Homework Statement Find the surface area of the cone with the following equations: x= u sin(a)cos(v) , y= u sin(a)sin(v), z=u cos(a) where 0<=u <=b , 0<=v<=2(pi), a is constant! The Attempt at a Solution Trying to solve this I first calculate the absolute value of the cross product of r'(u)...

Homework Statement I have to determine the resistance of a cone shaped resistor with the following dimmensions: Height at the first end: 1mm Lengdt: 250mm Height at the last end: 0.5 mm Rho: 14.5^10-6 Ohm*m Homework Equations \Omega = \frac{\rho \times L}{A} The Attempt at a...

Homework Statement A cone is circumscribed around a sphere. The radius of the sphere is 5 units. Write the volume of the cone in terms of x. There is a diagram.. I will try to describe it: It is a cross section of the object (sphere in cone). From the center of the circle to the bottom left...

Hi, I was reading my astrophysics textbook and came across solid angles. I'm not sure I fully understand, for example there was a problem in the book that went as follows. The attached "math.jpg" shows a light source (yellow) in the centre of an arc. The problem is 2D, but the arc is...

Homework Statement A cylinder of height 45mm and radius 12mm is placed inside a circular cone. What are the dimensions of the cone with the smallest volume to enclose this cylinder Homework Equations v=1/3(pi)r^2h v=(pi)r^2h SA=2(pi)rh The Attempt at a Solution I substuted values...

I have a set of given vectors, I want to find a rotation matrix to convert them to vectors belong to surface of a cone with vertex is origin(vectors with the same slant angle but different tilt angles). Is there anybody know what is the solution? Thanks

Hello, So I'm doing some independent study and I'm at a loss for this problem. Homework Statement Let's say we have an ellipse of the form (x2)/a + (y2)/b = 1 which we obtain by slicing a plane through a right circular cone with an opening angle of \theta (a fixed constant). We know...

Homework Statement A solid truncated cone is made of a material of resistivity 5.10 Ohm*m. The cone has a height h = 1.16 m, and radii a = 0.34 m and b = 0.84 m. Assuming that the direction of current is parallel to the axis of the cylinder, what is the total resistance for this cone? (Use...

Homework Statement A right circular cone has vertex down and is 10 feet tall with base radius 5 feet. The cone is filled with a fluid having varying density. The density varies linearly with distance to the top. Here "varies linearly" means the quantities are related by an equation of at most...

Hello :) I have been giving a mathematical problem. But I find difficulties solving this. Therefore, I will be very grateful if anybody might wanted to help? The problem is "Let K be a compact convex set in R^n and C a closed convex cone in R^n. Show that ccone (K + C) = C." - Julie.

Hi, so this morning I made an attempt at this... With javascript (website programming language) I was able to successfully yield the ratio of the volume of a cone compared with the volume of a cylinder (1/3). This is the source code: And basically this is the idea. It's a summation of the...

Homework Statement Show that the volume of an upright cylinder that can be inscribe in an upright cone is 4/9 times the volume of cone Homework Equations volume of cone volume of cylinder differentiation ?? similarity of triangle The Attempt at a Solution I draw the picture of...

What will be the limiting conditions?

1. A light, hollow cone is filled with sand set spinning about a vertical axis through its apex on a frictionless bearing. Sand is allowed to drain slowly through a hole in the apex. Calculate the fractional change in angular velocity when the sand level has fallen to half its original value...

So if you take a sphere with coordinates (r, \theta,\phi) and keep \theta constant you get a cone. The geodesic equations reduce to (by virtue of the euler - lagrange equations): \frac{\mathrm{d} ^{2}r}{\mathrm{d} s^{2}} - r\omega ^{2}\frac{\mathrm{d} \phi }{\mathrm{d} s} = 0 where \omega =...