Cone Definition and 490 Threads

Hi, consider an "half-cone" represented in Euclidean space ##R^3## in cartesian coordinates ##(x,y,z)## by: $$(x,y,\sqrt {x^2+y^2})$$ It does exist an homeomorphism with ##R^2## through, for instance, the projection ##p## of the half-cone on the ##R^2## plane. You can use ##p^{-1}## to get a...

Gravel is being dumped from a conveyor belt at a rate of $30\displaystyle\frac{ ft}{min}$ 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...

It has a straight cone and a plane that cuts it as shown in the image. What angle should the plane form with the base of the cone ?, so that the plane cuts the cone in 2 parts of equal volume.

How can I calculate radiation transfer efficiency of a Winston cone, assuming a constant efficiency for every reflection at 99% and that the source is perfectly diffuse and covers completely the wider entrance of the cone? Also, are there more efficient non-imaging radiation concentrators with...

Im trying to calculate the principals moments of inertia (Ixx Iyy Izz) for the inertia tensor by triple integration using cylindrical coordinates in MATLAB. % Symbolic variables syms r z theta R h M; % R (Radius) h(height) M(Mass) % Ixx unox = int((z^2+(r*sin(theta))^2)*r,z,r,h); % First...

i designed a cone drill bit with right hand thread to give friction and grab inside to give pulling force. my question is can this type of cone drill bit drill hard rock formations like normal tricone drill bits with teeth or the cone drill bit will be weak to penetrate hard rock formations .

Homework Statement A cone of height h and base radius R is free to rotate around a fixed vertical axis. It has a thin groove cut in its surface. The cone is set rotating freely with angular speed ω0, and a small block of massm is released in the top of the frictionless groove and allowed to...

As per Wikipedia, there are three types of cone cells. Quoting Wikipedia: I searched a bit more, and found that there are three different types of iodopsin pigment in these cells. Quoting Wikipedia again: Can you say what reaction occurs for each of the pigments when they are exposed to...

Hi All I read somewhere that at close to C the light emitting from a regular light globe ie diffuse light in all directions, will form a cone. what is the thinking behind this and does anyone have a link where I can read about it ?

Homework Statement Homework Equations f=ma v^2/r The Attempt at a Solution I am confused about this question because i am not given an angle theta for the normal force on the ball. My x component has only the normal force, my y component has only the gravitational force. I set my y...

Homework Statement Homework Equations f=ma v^2/r The Attempt at a Solution ∑FX= FN ∑Fy= -mg We are not given an angle, i would have put FNcos(θ). I have my radius as 0.25 by relation of the triangles at that point of the height being .50m so ∑FX= FN = v^2/r = (1.2)^2/.25 = 6.25N

Homework Statement question attached- I am stuck on some of the reasoning as to why we set ##B(r=0)=0## please not as described in the attempt I am interested in the concepts and have not posted my solution to A, nor any solutions not relevant to the concepts I am trying to understand...

$\textsf{Find the volume of the given solid region bounded by the cone}$ $$\displaystyle z=\sqrt{x^2+y^2}$$ $\textsf{and bounded above by the sphere}$ $$\displaystyle x^2+y^2+z^2=128$$ $\textsf{ using triple integrals}$ \begin{align*}\displaystyle V&=\iiint\limits_{R}p(x,y,z) \, dV...

i have a problem about find volume of hemisphere I do not know the true extent of radius r (0 to ?) i think... cone ( 0 < r < R cosec(\theta) ) hemisphere (0 < r < R)

Volume of hemi-sphere = ∫ ∫ ∫ r2 sinθ dr dθ dφ i thing (r < r < (r + R)cosθ ) ( 0 < θ < 60 = π/6) and ( 0 < φ < 2π) integral = 2π ∫ ⅓r3 sin θ dθ = 2π ∫ ⅓ [((r+R)cosθ)3 - r3] sin θ dθ i don't know how to find volume of hemi-spere

Is mach cone the area of the shock wave or the wave front of the Mach wave? Usually the diagram for mach cone is this, However I still see some author states that the Mach cone is the shock wave. Shouldn't the shock wave be at the intersection(between the circles) and if the Mach cone is about...

Homework Statement Homework Equations First derivative=maxima/minima/vertical tangent/rising/falling Volume of a cone: ##~\displaystyle V=\frac{\pi}{3}r^2h## The Attempt at a Solution $$L=a^2+b^2~\rightarrow b^2=L-a^2$$ $$V=\frac{\pi}{3}a(L-a^2)$$...

Hi, This a Classical Mechanics problem I've been trying to solve for a few days now. I cannot use Lagrangian or Hamiltonian formulation, it must be solved using classical Newtonian formulation. One must determine the equations of movement of the particle in cartesian, spherical and cylindrical...

Water is being drained from a container which has the shape of an inverted right circular cone The container has a radius of $6 in$ at the top and a length of $8 in$ at the bottom. when the water in the container is $6 in$ deep, the surface level is falling at a rate of $0.9 in/sec$ find the...

$\tiny{15.4.17}$ Find the volume of the given solid region bounded below by the cone $z=\sqrt{x^2+y^2}$ and bounded above by the sphere $x^2+y^2+z^2=128$ using triple integrals $\displaystyle\int_{a}^{b}\int_{c}^{d} \int_{e}^{f} \,dx\,dy \,dz$ not real sure where to to start with this?

Homework Statement With two fingers, you hold an ice cream cone motionless upside down, as shown in the figure. The mass of the cone is m and the coefficient of static friction between your fingers and the cone is μ.μ When viewed from the side, the angle of the tip is 2Θ. What is the minimum...

For example, the curvature due to a mass; does that curvature continue passing from within to outside the mass's light cone? If so, is the mass subject to the external curvature? If not, does the curvature have a discontinuity at the light cone surface?

I am confused about the pressure depending only on the depth of the liquid, particularly for a cone. Up until P=mg/A=ρVg/A I understand it, but the problem I have is cancelling the area with the volume to give the height. How does this work when the volume of the liquid in the cone is not given...

Homework Statement A cone has half angle θ0 and lateral surface area S0 in the frame in which the cone is at rest. If someone moves at relative speed β=v/c along the cones symmetry axis, what surface area will they see for the cone? Homework Equations I believe the lateral surface area of a...

Hi. I wonder if following thought experiment (which is most probably impossible to be put into practice) could have any implications concerning interpretations of QM. Consider five parties A, B, C, D and E, lined up in that order and with no relevant relative motion. No pair of them have ever...

A cone with base radius $r$, vertical height $h$ and slant height $l$ has its curved surface slit and flattened out into a sector with radius $l$ and angle $\theta$. By comparing the arc length of this sector with the circumference of the base of the cone, show that $l\theta = 2\pi r$, and...

Homework Statement A sector with central angle θ is cut from a circle of radius R = 6 inches, and the edges of the sector are brought together to form a cone. Find the magnitude of θ such that the volume of the cone is a maximum. Homework Equations Volume of a Cone = ⅓ * π * r2 * h Area of a...

Hi PF! Some classmates and I were talking about the streamlines around a submerged cone being pulled at a velocity ##V##. The picture is attached. Can someone shed some light on the streamlines of this flow, assuming it is inviscid? I take a frame of reference that moves with the cone...

Homework Statement Why is it that when you integrate to find the moment of inertia of a cone standing on its vertex (like a spinning top) with height h mass M and radius R do you integrate the R limits as 0 to (R/h)z in the triple integral (cylindrical coordinates) below? Homework Equations I =...

Hello I am a little confused by the following problem: Mass in cone: A particle of mass m slides without friction on the inside of a cone. The axis of the cone is vertical, and gravity is directed downward. The apex half-angle of the cone is θ, as shown. The path of the particle happens to be a...

question 1 The vector field F(x, y, z) = 2xi + 2yey2+z j +(ey2+z + cos z) k is conservative. Find a corresponding potential function. * e raise to power (Y square +z) Question 2 Consider a solid sphere of radius R, a cylindrical shell of outer radius R, inner radius a, and height h, and a...

What is the correct formula for a double cone, is it 3/10 mr^2, or 3/5 mr^2..?

Homework Statement Show that the moment of inertia of a hollow cone of mass M, radius R, and height h about its base is ##\frac{1}{4}M(R^2+2h^2)## Homework Equations ##I=\int r^2dm## where r is the perpendicular distance from the axis Surface Area of a cone ##= \pi R (R^2+h^2)^{1/2}## The...

I have been trying to understand why two woodwind bore shapes behave so differently. My understanding is that one end of a woodwind is an antinode (driven by the reed of the instrument) and the other end is a node (where the tube is open to the atmosphere). a - - - - - - - - - - n In the...

Desperate times call for desperate measures. I hope someone can show me how to do this. I don't want to offend anyone, but the truth is i have no work to show. I have exam on monday and i know a task like this will be given, exactly the same just different numbers. I have no vision on studying...

Homework Statement Find the center of mass of an inverted cone of height 1.5 m, if the cone's density at the point (x, y) is ρ(y)=y2 kg/m. Homework Equations The formula given for this problem is rcm=1/M * ∫rdm, where M is total mass, r is position, and m is mass. The Attempt at a Solution...

Both the problem and my attempt at a solution are provided. However, I become stuck. The answer book (question 27, as pictured in the next post, the upload size limit made me create a second post and both images are about 4mb), suggests that I use dV/dH, which is the portion of the cone volume...

1. A uniform right circular solid cone of weight W is suspended by two vertical strings attached to the ends A and B of a diameter of its base. If the cone hangs in equilibrium with its vertex vertically below A, find the tension in the strings. 2. Centre of mass of cone from the vertex is 3/4...

Homework Statement Consider the truncated cone tank submerged in water: inside the truncated cone tank there is air. Evaluate the forces acting on the truncated cone tank. Homework EquationsThe Attempt at a Solution The forces are the following Boyuant force : $$F_b= \rho_w g V_{tank}$$...

In the elementary proof of the slant surface area of a cone ##A=\pi r s##, where ##s## is the slant height, it is assumed that the net of a cone is a circular sector. In other words, if we cut the slant surface of a cone from its apex to its base along a straight line, the resulting surface can...

Homework Statement Hi there! So I have a problem regarding a particle of mass m moving down an inverted cone under the force of gravity. The cone is linear with equation z(r) = r, in cylindrical coordinates (r, theta, z) A. Write down the Lagrangian, include the constraint that the particle...

Imagine a right circular cone with smooth surface. The cone is stated such that its axis is parallel to the standard gravitational field g. And you have a piece a thin homogeneous chain. Then you connect the tips of the chain to obtain a loop. You put this loop on the cone: It is clear...

Homework Statement Homogeneous body with the shape of a truncated rotating cone has a base shaped like a circle. The radius of the lower base is R2 = 8 cm and radius of the upper base is R1 = 4 cm. The height h = 8 cm (see figure). Calculate the total electric resistance between the base...

Homework Statement Find the volume of a right circular cone with height h and base radius r. Homework EquationsThe Attempt at a Solution I've chosen the case where y = x = r = h. Then, I solve the integral in the image above and I got the book's answer. But is it actually correct?

A right circular cone is inscribed inside a larger right circular cone with a volume of 150 cm3. The axes of the cones coincide and the vertex of the inner cones touches the center of the base of the outer cone. Find the ratio of the heights of the cones that maximizes the volume of the inner...

<<Mentor note: Thread split from https://www.physicsforums.com/threads/torque-opposite-in-direction-to-change-in-angular-momentum.866882/>> it can be proved that in this case pure rolling without slipping is impossible ive assumed the cone to be right circular proof by contradiction...

From the last few sentences of the below attached paragraph, when the inertia ellipsoid is prolate, the body cone rolls outside the space cone; when it is oblate, the body cone rolls inside the space cone. Whether the body cone rolls outside or inside the space cone should depend on whether the...

Homework Statement Hi! I'm trying to solve a simple problem of mechanics, but I'm getting the wrong results and I suppose I don't yet grasp the concept of instantaneous axis of rotation very well. So, a cone (see attached picture) is rolling without slipping on a plane. Vp is point P linear...

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...

On this wikipedia page https://en.wikipedia.org/wiki/Cone_(linear_algebra) , "a subset ##C## of a real vector space ##V## is a cone if and only if ##\lambda x## belongs to ##C## for any ##x## in ##C## and any positive scalar ##\lambda## of ##V##." The book in this link...