Cone Definition and 490 Threads

is the water pressure at the bottom of a cylinder tank full of water more than the water pressure at the bottom of an upsidedown cone tank full of water?? If so, what eqauation could be used to find the pressure at the bottom of the cone?

Homework Statement Find the triple integral for the volume between a hemisphere centred at ##z=1## and cone with angle ##\alpha##.The Attempt at a Solution What I tried to do first was to get the radius of the hemisphere in terms of the angle ##\alpha##. In this case the radius is ##\tan...

Use an appropriate volume integral to find an expression for the volume enclosed between a sphere of radius 1 centered on the origin and a circular cone of half-angle alpha with its vertex at the origin. Show that in the limits where alpha = 0 and alpha = pi that your expression gives the...

Just humour me, if you had an infinitely thin cone, would the surface area inside the cone be the same surface area on the outside of the cone? It must be right? Is there a formula for the surface areas of the inside and outside of a cone WITH thickness?

Homework Statement Hi! I need to find the opening angle of the loss cone at a given altitude, when the magnetic latitude is 65 deg. Homework Equations See below The Attempt at a Solution First, I used the following equation to calculate the magnetic field at a given altitude...

in Minkowksi, the set of all possible null rays from a point defines a cone (light cone). Now imagine I change the signature of Minkowski from (-,+,+,+) to (-,-,+,+) i.e. a space with two timelike directions and a metric ##ds^2=-dx_1^2-dx_2^2+dx_3^2+dx_4^2##. What kind of surface would the set...

Homework Statement A cone of height H and base radius A is charged with charge Q uniformly distributed in all its volume. Find electrostatic field intensity at the top of the cone. DATA: H, A, Q Homework Equations E=ρ/(4πε0) ∫Ω dΩ/R2) and R is a vector (rr^+zz^) r^ and z^ are versors The...

Hello I searched a lot but I am not sure if I understood correctly the change in the shape of light cone while speeding up. I am aware that the x and ct axis are getting closer to each other like scissors while you speed up as the graph below shows, both symmetricaly approaching the ct=x or v=c...

Homework Statement Wikipedia tells me that I can obtain the surface area of a sphere by realizing that the volume of a sphere is equivalent to the infinite sum of the surface areas of hollow, nested spheres, sort of like little Russian dolls. That makes sense, and then differentiating both...

Homework Statement S is the sphere of equation x2 + y2 + z2 = 10z and C the cone of equation z= sqrt(3*( x2 + y2)) . The axes are measured centimeters. R of sphere = 5 D = 10 Total height is 10 cm Illustrate the solid E bounded by the C cone and the sphere S and calculate its volume using the...

Homework Statement A conical tank (with vertex down) is 10 feet across the top and 12 feet deep. If water is flowing into the tank at a rate of 10 cubic feet per minute, find the rate of change of the depth of the water when the water is 8 feet deep. Homework EquationsThe Attempt at a Solution...

So here's my problem. For the past few years i have built a very large christmas tree in my front yard. 1200 lights or so... looks awesome it is 6m high, a 2m ring at the bottom and is a constant cone shape to the top point. To install the lights i start from the bottom and progress to the top...

Homework Statement Homework EquationsThe Attempt at a Solution The only thing I can think of in this problem is energy conservation . ##\frac{1}{2}mv^2_0 = mgh+\frac{1}{2}mv^2## Not sure how to proceed . I would be grateful if somebody could help me with the problem .

Homework Statement A loop of flexible chain, of total weight W, rests on a smooth, frictionless right circular cone of base radius r and height h. The chain rests in a horizontal circle on the cone, whose axis is vertical. Find the tension in the chain. Homework Equations Virtual work, but...

Hi, Given a 3D object in R3 space can we represent it using three basic primitive shapes like Sphere, Cone and Cylinder? Would this claim be valid?

Homework Statement So here is the problem, There is a .03kg block that is in an inverted cone, the cone has a slant length of 15 cm and a radius of 4 cm, and the coefficient of friction is .35. The block rotates around the inside of the cone, seamlessly, until it hits the bottom of the cone...

Homework Statement Find the geodesics on the cone whose equation in cylindrical-polar coordinates is z = λρ [Let the required curve have the form φ=φ(ρ)] check your result for the case λ→0 Homework Equations \frac{\partial F}{\partial y} - \frac{d}{dx} (\frac{\partial F}{\partial y'}) = 0...

A very basic question: does such a cone, where the broad end is not cut flat but follows the surface of the sphere whose radius is the length of the cone's side, and is centred at the cone's point, have a name?

I am trying to numerically calculate the electric potential inside a truncated cone using the finite element method (FEM). The cone is embedded in cylindrical coordinates (r,phi,z). I am assuming phi-independence on the potential, therefore the problem is essentially 2D; I am working only with...

Homework Statement Determine a simplified, factorised expression, in terms of the radius (r), for the surface area of a cone where diameter (D) = perpendicular height (h) Homework Equations A = πr (r + √(h^2 + r^2)) The Attempt at a Solution h=D=2r A = πr (r + √(2r^2 + r^2)) A/π = r (r +...

out to what distance in our light cone can we exclude the existence of an alien civilization broadcasting EM signals at about our current levels?

In my study I deal with tubulars frequently, and it is well known how to calculate stresses due to external pressure on a (hollow) uniformly-thick cylinder (i.e. a pipe). Suppose now that I have a cone, tapering downward like a V, with a hollow cylindrical interior (like the inside of a pipe)...

For a physics problem, I need to calculate the solid angle subtended by an oblique cone (cone where the apex does not lie on the line perpendicular to the cone's base from the center of the base). Consider the following problem: I have a 2D disk which emits light in an ever growing hemisphere...

The required Formulas are: Area of circle = Pi (r)^2 Volume of Cone = 1/3 Pi (r)^2 h Here is my try: I know the smaller cone and bigger ones are congurent, so 50/25 = 15/h h=7.5, but the answer is incorrect. Please help

I am trying to work out a formula for the approximate calculation of the lung capacity of a racehorse. http://performancegenetics.com/wp-content/uploads/2015/05/Horse.jpg I take three physical dimensions on the horse. 1) The measurement of the girth (which is the perimeter of an ellipse)...

Find the volume laying inside x^2 + y^2 + z^2 =2z and inside z^2 = x^2 + y^2. This is a problem my professor made, so I have no way of checking my answer. What I did first was completed the square for the sphere and got x^2 + y^2 + (z-1)^2 = 1, which is a sphere of radius one shifted above the...

How to calculate the potential at the apex of uniformly charged right circular cone (charge only at the curved surface), having height "h" and radius "R" and lateral height "l" and change density sigma?

Homework Statement Derive the equations of motion and show that the equation of motion for \phi implies that r^2\dot{\phi}=K where K is a constant Homework Equations Using cylindrical coordinates and z=\alpha r The kinetic and potential energies are...

Homework Statement Homework Equations Flux = ∫E.ds The Attempt at a Solution I need to get the projection of cone on a plane perpendicular to the electric field . The area thus obtained when multiplied by electric field would give the flux . I am not able to imagine the projected area...

I have a small problem with this question. In this problem, the cone exerts a normal force. This force, should be perpendicular to the inside surface of the cone. In equating the vertical forces, I need the vertical component of this normal force. I would draw this force perpendicular to the...

Homework Statement Find the centre of mass of solid cone. Homework Equations $$y_{cm}=\frac{1}{M}\int_0^Hydm$$ The Attempt at a Solution First I took thin disks. I got the answer when I assumed its thickness to be dy but then dysecθ would be more accurate if half angle of cone is θ since...

Homework Statement A point source emits visible light isotropically. Its luminous flux is 0.11 lumen. Find the flux whithin the cone that has half angle of 30 degree from the light source. Homework Equations luminous flux = luminous intensity * solid anlge The Attempt at a Solution I tried...

Homework Statement Hello was wondering what nose cone I should put on my rocket. We need to reach around 800ft, any higher/lower and points are deducted. I don't know whether to go with a rounded cone, parabola I've seen or a pointed cone... Homework EquationsThe Attempt at a Solution I know I...

Homework Statement A particle slide on the frictionless surface of the interior of a 45 degree cone ##x^2 + y^2 = z^2 ## a) Find the 2D Lagrangian in terms of the vertical coordinate ##z## and an angular coordinate ## \theta ##. b) Find the Hamiltonian ##H##. c) Show that ##p_\theta## and...

Hello. So, I'm designing an equatorial platform mount for my telescope at the moment. I'm also going to use it for another telescope that I'm in the process of building. I know that for both of the bearings, I can use small sections of two circles cut from a cone with an angle between the axis...

Homework Statement A hollow cone is put upside-down with its symmetry axis vertical. The surface of it makes an angle of theta with the vertical direction as shown in the figure . A small puck of mass m slides without friction on the inner side of this cone and remains within a horizontal plane...

Homework Statement Find the moment of inertia of a solid cone about its longitudinal axis (z-axis) The cone: x^2+y^2<=z^2, 0<=z<=h I_z = \int\int\int_T(x^2+y^2)dxdydzHomework Equations Representing the cone in cylindrical coords: x=zcos\theta y=zsin\theta z=z The Attempt at a Solution...

Homework Statement A rope of mass m forming a circle is placed over a smooth round cone with half angle θ. Find the tension in the rope . Homework EquationsThe Attempt at a Solution Since the half angle is θ , the normal force N acts at an angle θ with the horizontal . The weight acts...

Homework Statement Let a cone with height h and base area A have the density \rho (x) = \rho_{0} \frac{3x^{2} + 2xh}{h^{2}}, 0 \leq x \leq h the relation between cone radius r and distance from cone apex x is given by: r = (\frac{B}{\pi h^{2}})^{\frac{1}{2}}x Find the total mass M of the...

Hi guys, I'm trying to understand light cone coordinates for which I uploaded this picture. The light cone coordinates are given by x^{+}= \frac{1}{\sqrt{2}} (x^{0}+x^{1}) x^{-}= \frac{1}{\sqrt{2}} (x^{0}-x^{1}) Now how should I think of this? I guess the space curves do only life in the space...

Hello , I am new here , and at start id like to say that i`m lousy at formulas and math :) . I've been searching and googled my problem and i couldn't find any solution to it . So here it is. Ball and a cone are rubber coated .Ball is rolling inside enclosed cone, when ball reaches speed it...

Homework Statement A rope of mass ##m## forming a circle is placed over a smooth round cone with half angle ##\theta##. Find the tension in the rope. Homework Equations ##\sum{F}=0## The Attempt at a Solution I know how to solve the problem, but I have another way that I think should work but...

Homework Statement Sand falls from a conveyor belt at the rate of 10m^3/min onto the top of a conical pile. The height of the pile is always 3/8ths of the base diameter. How fast is the radius changing when the pile is 4 m high? 3. The Attempt at a Solution V = pir^2 (4/3) -- volume of a...

Homework Statement find the volume using spherical coordinates of the region bounded above by z=9 and below by z=sqrt(x^2+y^2) in the first octant. Homework EquationsThe Attempt at a Solution I found this volume using cartesian and cylindrical coordinates, so I know the answer I am looking...

A water tank has the shape of an inverted circular cone with base radius 2 m and height 4 m. If water is being pumped into the tank at a rate of 2 m^3/ min, find the rate at which the water level is rising when the water is 3 m deep. The answer to this question is $$\frac{8}{9\pi}$$But I got a...

Let \text{ } H \text{ }be \text{ }a \text{ } Hilbert \text{ } space, \text{ }K \text{ }be \text{ }a \text{ }closed\text{ }convex\text{ }subset \text{ } of \text{ }H \text{ }and \text{ }x_{0}\in K. \text{ }Then \\N_{K}(x_{0}) =\{y\in K:\langle y,x-x_{0}\rangle \leq 0,\forall x\in K\} .\text{...

Can someone please look at the diagram below and tell me how u1 is obtained. If it is through the use of m3 please explain how the gradient m3 is obtained.

I'm still confused on some of these volume problems, so please bear with me :) Homework Statement Find the volume of a reentry spacecraft nose cone that has a cross-section radius of (1/4)x2 taken x feet from the nose and perpendicular to the axis of sym. We are given that the length of...

Homework Statement We consinder a doble cone with a radius R and an angle α (pike) and the mass m. It is located on two rails with an opening angle β. The rails enclose the angle γ with the ground. A is the lowest point of the rails. First, the center of mass of the double cone is locatd...

Homework Statement I am given the weight (force) of the rope as W. It sits on a cone about halfway down, with the cone's top angle ø. Radius at a given placement is r, and h is our height at a given placement. I need to find the tension, T, in the rope. Homework Equations W=mg Integral (F *...