Cylinder Definition and 1000 Threads

Homework Statement Find the area of that part of the cylinder x^2 + y^2 = 2ay that lies inside the sphere x^2 + y^2 + z^2 = 4a^2. Homework Equations [/B] If a surface S can be parametrized in terms of two variables u and v, then dS = Norm[dR(u,v)/du x dR(u,v)/dv]. The surface area is given...

Homework Statement Homework Equations Stoke's Theorem: The Attempt at a Solution ∇×A = (3x,-y,-2(z+y)) I have parametric equation for wall and bottom: Wall: x(θ,z) = acosθ ; y(θ,z) = asinθ ; z(θ,z) = z [0≤θ≤2π],[0≤z≤h] Bottom: x(θ,r) = rcosθ ; y(θ,r) = rsinθ ; z(θ,r) = 0 [0≤θ≤2π],[0≤r≤a]...

Homework Statement A cylinder on a inclined plane is rolling without slipping. Inclined plane is connected to wall with a spring and cylinder is connected to wall with a spring too. All frictions will be neglected, and all the given data has shown on the image below. As seen above, k2 spring...

Homework Statement A copper tube has a 2 cm inside diameter and a wall thickness of 1.5 mm. Over the tube is an aluminum sleeve of 1.5 mm thickness having 100 pin fins per centimeter length. The pin fins are 1.5 mm in diameter and are 4 cm long. The fluid inside the tube is at 100 ºC, and the...

Dear experts, I´m trying to model in ANSYS Mechanical (v14.5) the linear buckling behavior of a cylinder made of BEAM4 elements under combined loading (axial compression and bending moment) applied at the ends. How should I set up the boundary conditions of a cylinder to keep rigid the ends...

Homework Statement There is an infinite conducting cylinder positioned at the axis with radius R. An infinite line charge (+λ) is placed distance d from the axis and d>R. I was supposed to 1. Find the potential and then 2. find the surface charge on the cylinder. Homework Equations V = -∫...

I have a problem for a written assignment in my calc 2 class involving the volume of a cylindrical glass. A cylindrical drinking glass 10 in tall and 4 in in diameter is filled with water, and then tilted so that the water pours out until half the base is exposed. Write an integral to find the...

Homework Statement A solid metal cylinder of radius ##R## and length ##L##, carrying a charge ##Q##, is surrounded by a thick coaxial metal shell of inner radius ##a## and outer radius ##b##. The shell carries no net charge. a) Find the surface charge desnities ##\sigma## at ##R##, at ##a##...

I am struggling with a question in my coursework, and would appreciate some guidance. The question is: The component shown in Fig 1 is made from a material with the following properties and is subjected to a compressive force of 5kN. Material Properties : Young’s Modulus of Elasticity – 200...

Homework Statement This is just a qualitative question that is along side my main lecture with Griffiths EM book. Basically we have a very long cylinder with charge density sigma and radius a along the z axis. This is mostly beside the point and is just to setup the question. The question...

Good day all, someone gave me this problem to try to figure out (for fun) and I'm having a bit of a hard time: A closed cylinder of radius R and length L is filled with liquid. The volume of the liquid is equal to 1/3 the total volume of the cylinder. If the cylinder is layed flat (horizontal...

Homework Statement [/B] A solid cylinder of mass m and radius r lies flat on frictionless horizontal table, with a massless string running halfway around it, as shown in Fig. 8.50. A mass also of mass m is attached to one end of the string, and you pull on the other end with a force T. The...

Homework Statement Homework EquationsThe Attempt at a Solution Since the cylinder is in equilibrium ,net force and torque on it should be zero. I am not sure whether we are required to calculate force due to the two fluids as it seems to be a simple conceptual problem . I think I am...

Homework Statement A thin glass plate is pressed at the end of a glass cylinder. The glass cylinder with the glass plate at the bottom is dipped in water so that the plate is 25 cm under the water surface (The glass cylinder i open, meaning only the bottom part is closed, due to the glass...

The potential on the side and the bottom of the cylinder is zero, while the top has a potential V_0. We want to find the potential outside the cylinder. Can I use the same boundary conditions as for case of inside cylinder potential? What is different?

http://postimg.org/image/onxjqc26l/ I have found the shear stress of the inner cylinder to be 405 Pa like in the solution but I am having trouble visualizing the total moment of this stress about the center line. I was wondering if someone could explain where that d(theta) in the moment...

Hi, I am wondering how i could parameterise the following rectangular cross section of the hollow cylinder in cylindrical co-ordinates. If this surface is better parameterised via a different co-ordinate system then by all means use that system. After I have completed the parameterisation i...

Hello PF, I am having a bit of difficulty understanding this question. Homework Statement "A thin wire with linear charge density λ is surrounded by a conducting cylindrical shell." (There is a hollow cylinder with a wire though it) "If the electric field must be zero inside a conductor, is...

Hello everyone, I have an rather large piston-cylinder containing gas that is compressed when the piston extends. Using three sensors I am measuring the pressure, temperature and volume of the gas while I force the piston out using a winch. The system is closed and no gas is released or added...

Homework Statement Consider water contained in a cylinder at 25C with a frictionless piston with some weights on it. Initially the pressure inside the piston is 100kPa and then the water is heated such that the water does 290kJ/kg of work on the piston. Find the final temperature of the...

Homework Statement An infinitely long cylinder of radius a in free space is charged with a volume charge density ρ(r) = ρ0*(a-r)/a (0 ≤ r ≤ a), where ρ0 is a constant and r the radial distance from the cylindrical axis. Find the charge per unit length of the cylinder. Homework Equations...

Homework Statement Infinitely long cylinder of radius R with uniform charge ρ. Calculate the electric potential at all points in space. Homework Equations V(a)-V(b)=-∫ba\vec{E}(\vec{r}')°dr'\hat{r} The Attempt at a Solution Generally potential is calculated with a reference...

I attached an image of two expansion cases I am analyzing. Both cases involve an insulated cylinder that is divided by a separating element (diaphragm for case A and piston for B). The portion on the right is evacuated. The left contains a calorically perfect gas with an initial pressure and...

Homework Statement A rod with charge linear density λ is located at the long axis of a cylinder with charge linear density 2λ. With this information use Gauss's law to find (a) the charge linear density on the interior and exterior surfaces of the cylinder (b) the electric field outside of the...

Hello all, I have some confusion about rotating. The bad thing is that I don't know where the point is which my confusion starts. As I want to check also my fundamental knowledge about the topic I will ask my questions step by step to see where my problem begins. I hope you don't mind. My...

Homework Statement A closed, insulated cylinder is divided into two equal parts by a piston. One compartment contains Nitrogen at T=300K, P1=5bar, the other Carbon Dioxide at T=300K, P2=20bar. The cylinder contents then reach mechanical and thermal equilibrium. 1. Assuming that the gases...

This is from a physics course, but felt more appropriate to post here. I just want some sanity checking on my procedure, since I'm not this far in my calculus course yet but am having to work through it anyway for physics. I have no idea how to approach part c, not even an inkling of where...

This actually isn't a homework problem -- I'm just trying to understand an example in my textbook. The example shows how to calculate the volume of a cylinder (maybe it's actually a shell, I'm not sure) using an integral, but it occurred to me that I should be able to simply "unwrap" the...

Must double integrate using type I or type II planar region D to find volume bounded by Cylinder y^2+z^2=4 And Planes X=2y X=0 Z=0

Homework Statement Charge is uniformly distributed with charge density ρ inside a very long cylinder of radius R. Find the potential difference between the surface and the axis of the cylinder. Express your answer in terms of the variables ρ, R, and appropriate constants. Homework Equations...

Maybe I'm plugging my website but I just finished writing a versatile cylinder calculator. If you know two variables (Volume Area Radius Height), it calculates the other two. http://www.1728.org/diam.htm It was a little tricky deriving the formulas but I'm glad I did. (Yes, I know if you...

Homework Statement We have a horizontal cylinder with an ideal piston, both are made from a heat nonconductive material. There is 10 liters of steam at 3 bars and 200 degrees Celsius in the cylinder. The cylinder is surrounded with atmosfere with pressure of 1 bar and temperature at 20 degrees...

For a uniform, hollow cylinder, why is this derivation wrong? M = mass of whole solid cylinder m = mass of missing cylindrical piece R = radius of whole cylinder r = radius of missing cylindrical piece moment of inertia = moment of inertia of whole cylinder - moment of inertia of...

Hi, all. I'll be experimenting with water mist injection (amongst other things) on a small single cylinder engine. Because the electrical generation capability of the engine's alternator is limited, I have to find some other way of pressurizing the water for injection (not enough juice for an...

Homework Statement Find the Volume of the solid that the cylinder ##r = acos\theta## cuts out of the sphere of radius a centered at the origin.Homework Equations The Attempt at a Solution I have defined the polar region as follows, $$D = \{ (r,\theta) | -\pi/2 ≤ \theta ≤ \pi/2 , 0 ≤ r...

I am wondering if my reasoning is correct for determining the energy due to the buoyancy of a deformed water surface. Essentially, one has a floating cylinder that depresses the surface of a liquid in an infinite tank as seen in the figure. I want to compare the energy of a flat surface with...

Hi :) I'm doing my A-Levels and have a maths investigation project for which I decided to model the working of a shishi-odoshi. (http://en.wikipedia.org/wiki/Shishi-odoshi) The shape of the water in the shishi-odoshi is a cylindrical segment and I want to use integration to find the...

I have a 50KG cylinder with 1-2LB of SF6 at 15PSI. I want to transfer it into another cylinder by temperature differential. Keeping it simple. I try to model it with two cylinders that has a valve on each cylinder. Connecting the cylinder with a 1/4" hose. Both valves are closed. The...

An empty cylindrical vessel with a small circular hole of radius r at the bottom is dipped vertically in a liquid of density d keeping the bottom downward. At what maximum depth can it be dipped before the liquid enters into it? The surface tension of the liquid is S. The answer given in the...

I'm having some difficulty setting up a problem. I'm trying to model the temperature of a thermistor connected to a constant current source. The thermistor's resistance varies with temperature, so with a fixed current, I would expect to see the thermistor's temperature to oscillate with time...

Homework Statement Find volume of the ellipsoid ##x^2 +2(y^2+z^2) \le 10## intersected by the cylinder ##y^2 + z^2 \le 1 ## The Attempt at a Solutionseems like changing to cylindrical coordinates would be best so I have \left\{ \begin{array}{cc} r^2cos\theta + 2r^2sin^2\theta +2z^2 \le 10...

hi.I would like to know something about the IC engine.I just read an article.It said that 30% efficiency is gone through conduction of heat by the cylinder wall.If it is reason for one of the efficiency loss why can't we build an cylinder coated with a material that is non conduction.So only...

Homework Statement The density of a cylinder is calculated from the following data: ##m= (2.8±0.8)g## ##d = (2.2±0.1)cm## ##h = (4.0±1.0) cm## What is the error on the density, before rounding, in ##\frac{g}{cm^3}##? Homework Equations ##V = \pi r^2 h = \frac{1}{4} \pi d^2...

what is the advantage of moving piston-fixed cylinder arrangement over visa-versa ??

Homework Statement A solid cylinder of radius R is spun and then placed on an incline having coefficient of friction μ=tanθ (θ is the angle of the incline). The solid cylinder continues to spin without falling for time: (A)Rωo/3gsinθ (B)Rωo/2gsinθ (C)Rωo/gsinθ (D)2Rωo/gsinθ The Attempt at a...

Homework Statement Find the area of the cylinder x^2 + y^2 -y = 0 inside the sphere x^2 + y^2 +z^2 =1 Homework Equations dA = sec \gamma dydz where sec \gamma = \frac{|\nabla \phi|}{|\partial \phi/ \partial x|} The Attempt at a Solution The method shown in this section is to...

Homework Statement A cylinder of mass M and radius R, with moment of inertia: I_c = \frac{1}{2}MR^2 rolls down without slipping through an inclined plane with an angle of θ, while pulling a block of mass Mb with an attached frame (of insignificant mass) which is connected to the axis of...

Homework Statement A uniform cylinder 20 cm long, suspended by a steel wire attached to its mid-point so that its long axis is horizontal, is found to oscillate with a period of 2 seconds when the wire is twisted and released. When a small disc, of mass 10 g, is attached to each end the...

Homework Statement A long insulating cylinder of radius R1 has a cylindrical hole parallel to the axis of the cylinder. The radius of the hole is R2, and the distance from the centre of the cylinder to the centre of the hole is a. There is a uniform fixed charge per unit volume ρ throughout...

Hi, I'm looking for the Moment Coefficient (Cm) for a 3D Rotating Cylinder, this means, I there is a free stream of fluid and there is inmerse a cylinder rotating about its own axis , and also rotating about an axis parallel to the free stream. I found in the book of Peter Childs, called...