Cone Definition and 514 Threads

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 *...

Homework Statement I have gotten the following task: "A smal object is placed in a right circular cone turned "upside-down" with an apex angle equal to 90-2α degrees. The coefficient of friction is big enough to keep the object at rest when it's placed on the inne-side of the cone. After...

Hello, 1) I am looking for numerical data behind plots like this one. 2) Also, any information on the experiments the data comes from would be helpful. Are cone cells directly measured, or does it involve a human matching colors to a pure color light source? 3) Will I be able to write a...

Guys, I have a problem I'm trying to solve for work (we're trying to inspect a hole, and I'm trying to determine its angle using a gage pin and a ball bearing). An image of the problem is attached. The known dimensions which we can measure are shown in black, and I am trying to solve for...

Help me to understand my physics homework Suppose if a ball is rolling down in an inclined plane, what happens to the normal force acting on it? How to understand the Normal force in this situation Please explain Thanks

So, this has really stirred my interest. To be clear, I'm not citing these as sources, simply linking for discussion; An article on the subject, And the abstract. Talking about this elsewhere I seem to find no shortage of objections. But to me it seems fundamentally pretty sound. One...

I'm not sure what "differential" geometry is, so hopefully this is the right section. I need to find the point on a cone that is farthest in a given direction. This can be done easily if the shape were a sphere which is represented as a point and a radius: farthest_point = sphere_origin +...

Homework Statement Homework Equations ∫∫∫dV The Attempt at a Solution Ok so I started by setting my bounds equal to √(200-x^2-y^2) ≥ z ≥ √(x^2+y^2), √(100-x^2) ≥ y ≥ -√(100-x^2), 10 ≥ x ≥ -10 which I got from solving z^2 = (200-x^2-y^2) = x^2+y^2 => x^2+y^2 = 100 but it...

how can we write and interpret Lorentz generators in light cone coordinates?

Homework Statement A uniform right circular cone of height h, half angle α, and density ρ rolls on its side without slipping on a uniform horizontal plane in such a manner that it returns to its original position in a time \tau. Find expressions for the kinetic energy and the components of...

Homework Statement Find the volume enclosed by the cone x^{2}+y^{2}=z^{2} and the plane 2z-y-2=0. Homework Equations \int\int\int dV The Attempt at a Solution In the image Cono=Cone and Plano=Plane

Homework Statement Calculate the moments of inertia I_1, I_2, and I_3 for a homogeneous cone of mass M whose height is h and whose base has a radius R. Choose the x_3 axis along the axis of symmetry of the cone. Choose the origin at the apex of the cone, and calculate the elements of the...

Hi. I am trying to develop a cone clutch for torque transmission. I have looked a lot over the internet but I cannot find how to calculate the maximum torque transmission capability of a cone clutch. Everywhere they use the equations with inputs of axial force. I want to find the maximum torque...

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 origin (pointing down), and half-angle α(alpha) a) write down the lagrangian in terms of spherical coordinates r and ø (phi) Homework Equations...

I'm having a little bit of trouble understanding the equation of a cone.. It is given by (x^2)/(a^2) + (y^2)/(b^2) = (z^2)/(c^2) I understand that if a ≠ b you have an elliptical cone, but I'm not sure how to set the equation up to define the cone as having a height. Can anyone clarify...

Homework Statement (See attachment) Assume that the surface has friction and a small ring of radius ##r## rolls on the surface without slipping. Assume conditions have been set up so that (1) point of contact between the ring and the cone moves in a circle at height ##h## above the tip...

Homework Statement A cone of circular cross section having base radius R, mass M and height L is suspended from its base as shown in figure. The material of cone has Young's modulus Y. If the elastic potential energy stored in the cone can be expressed as: $$E=\frac{m^ag^bL^c}{d\pi^eY^fR^g}$$...

In the example in the attachment, Laplaces Equation is used to find the potential of a cone. My qustion is, How do they know the potential only varies with angle theta (theta is the angle between the positive Z-axis and the surface of the cone.)

Homework Statement A cone made of insulating material has a total charge Q spread uniformly over its sloping surface. Calculate the energy required to take a test charge q from infinity to apex A of cone. The slant length is L. Homework Equations The Attempt at a Solution...

Consider an oblique circular cone of altitude h, base radius R, with apex directly above a point on the base circumference. What is the mean length (& variance) for the set of all rays from the apex to points on or within the base circumference?

choose the diameter of a sphere so that when it is inserted into a cope of form conic (depth H and RADIUS R) fill of water, spilling as much as possible of liquid when the sphere rests is on the walls of cope. ( volume of a segment spherical of radius "r" y height "h' es: V = pih2{r- ( h ))...

Homework Statement The metric for this surface is ds^2 = dr^2 + r^2\omega^2d\phi^2, where \omega = sin(\theta_0). Solve the Euler-Lagrange equation for phi to show that \dot{\phi} = \frac{k}{\omega^2r^2}. Then sub back into the metric to get \dot{r} Homework Equations L = 1/2 g_{ab}...

A triangle hypotenuse given rectangle is rotated around one of their legs to generate a right circular cone? find the cone of greater volume. resp V= (2Sqrt(3)pi L^3)/27 It says hypotenuse given but it has no value According to the answer you can name it L

From A circular sheet of RADIUS "R" a sector tie is cuts so that the coil Gets a funnel. Calculate the angle of the circular sector to cut back so of funnel has the maximum capacity. Answer tha angle is 2sqrt(6)pi/3

3) Calculate the dimensions of the straight circular cone, smaller volume that can be circumscribed around a cylinder of RADIUS "R" and height "H". Answer is h = 3H and r= 3R/2

Homework Statement A masspoint finds itself under the influence of gravity and constrained to move on a (inverted) circular cone. Using D'Alembert's Principle find the equations of motion on cylindric coordinates. Homework Equations D'Alembert's Principle: (\vec{F_a}...

Here is the question: I have posted a link there to this thread so the OP can view my work.

A solution is draining through a conical filter into an identical conical container (both are $h=12$ and $r=4$ at top of cone) The solution drips from the upper filter into the lower container at a rate of $\displaystyle\frac{\pi\ cm^3}{\text{ sec}}$ and $\displaystyle...

I could really do with some help. I'm trying to show that the face of a face of a convex polyhedral cone is again a face of that polyhedral cone. I have spent a couple hours thinking about this and CAN'T show it. The following apparently gives a proof of this, but it's surely invalid...

Homework Statement Problem (also attached as TheProblem.jpg): Find the center of mass of the surface of the sphere x^2 + y^2 + z^2 = a^2 contained within the cone z tanγ = sqrt(x^2 + y^2), 0 < γ < π/2 a constant, if the density is proportional to the distance from the z axis. Hint: R_cm =...

Homework Statement A large container has the shape of a frustum of a cone with top radius 9 metres , bottom radius 2 metres , and height 7 metres. The container is being filled with water at the constant rate of 4.2 cubic meters per minute. At what rate is the level of water rising at the...

1. Gravel is being dumped from a conveyor belt at a rate of 30 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 10 ft high? Homework Equations...

Hello. My friend said a truncated cone that is the upside down (the hole is open downwards) may be held in the air by a stream of water... How? It is really true? Ok, consider a constant mass flow of water. How can I create a formula, which tell how high I have to place the cone? - (I want to...

Homework Statement I've worked through both parts of this question twice in what I assume is the correct manner, but I'm receiving an unexpected result from part B. The question is as follows: Sand is dumped such that the shape of the sandpile remains a cone with height equal to twice...

The figures in http://www.astro.virginia.edu/class/whittle/astr553/Topic16/t16_light_cones.html are very useful in understanding the various world lines in concordant diagrams. Is there any easy way to see how a velocity cone (at the observer's worldline) from a later time than the Big Bang...

(a) Find the rate of change of the volume with respect to the height if the radius is constant vol of right circular cone is $$V=\frac{1}{3} \pi r^2 h$$ from this $$h=\frac{3V}{\pi r^2}$$ $$\frac{dh}{dt}=\frac{3}{\pi r}\frac{dV}{dt}$$ $$\frac{\pi r}{3}\frac{dh}{dt}=\frac{dV}{dt}$$ not...

Here is the question: I have posted a link there to this topic so the OP can see my work.

Homework Statement Grit, which is spread on roads in winter, is stored in mounds which are the shape of a cone. As grit is added to the top of a mound at 2 cubic meters per minute, the angle between the slant side of the cone and the vertical remains 45º. How fast is the height of the mound...

Homework Statement Find the minimum value of the volume of a cone that is transcribing a four-sided prism with a=42cm and h=8cmHomework Equations V=\frac{r^{2}H\pi}{3} \frac{H}{r}=\frac{h}{r-\frac{a}{2}} The Attempt at a Solution From the equation above it follows that H=\frac{2hr}{2r-a}...

if correct? wasn't sure if $$\pi$$ should be in answer since answer is in$$\frac{\text{in}^3}{min}$$

Q: Consider the solid that lies above the cone z=√(3x^2+3y^2) and below the sphere X^2+y^2+Z^2=36. It looks somewhat like an ice cream cone. Use spherical coordinates to write inequalities that describe this solid. What I tried to do: I started by graphing this on a 3D graph at...

Homework Statement A piece of conically-shaped material is placed in a circuit along the x-axis. The resistivity of this material varies as rho=(6*10^6)*x^4 (where x is measured in meters and rho is measured in ohm*meters), and its radius varies linearly as a function of x, ranging from...

Homework Statement Sketched below is a solid, truncated cone, with a side profile of y=Cx. Based on the geometry, the area (in m2) of the left (truncated, x = 1m) and the right face of the cone is 4∏ and 36∏, respectively. The temperature of the left face is T1=50°C and T2=30°C. Assuming...

Homework Statement http://gyazo.com/fa8026ffdf2ccb97d0b09b9e74460455 Homework Equations Fnet=mg The Attempt at a Solution I said that the letter B was the normal force which I derived from just drawing an FBD of the ball on the left side of the code For acceleration I used...

Hi everyone! Homework Statement We're given a three dimensional cone with perimeters d0 at the top and d1 at the bottom and a substance that diffuses through the cone with diffusion constant D from top to bottom. The concentration of the substance is held constant at the top plane of the...

Thanks again to those who participated in last week's POTW! Here's this week's problem! ----- Problem: A right circular cylinder is inscribed in a cone with height $h$ and base radius $r$. Find the largest possible volume of such a cylinder. -----

I understand why the leading edge of a projectile creates a Mach cone in front of which the air is undisturbed. But apparently the trailing edge of the projectile also creates its own Mach cone behind which the air is undisturbed. I don't understand why this is the case.

Homework Statement A round cone A of mass ##m## and half-angle ##\alpha## rolls uniformly and without slipping along a round conical surface B so that its apex O remains stationary. The centre of gravity of the cone A is at the same level as point O and at a distance ##\ell## from it. The...

Hi guyss~ I need some help for one of my assignment about heat loss from a cone shape fin as we can see through the picture I've attached with this thread. Looking forward to all of your answers