Cylinder Definition and 1000 Threads

If the question had been asking about the flux through the whole surface of the cylinder I would have said that the flux is 0, but since it is asking only about the lateral surfaces I am wondering how one could calculate such a flux not knowing how the cylinder is oriented in space. One could...

I am confused why we don't take into account the lids of the cylinder since the Gaussian cylinder is of finite height L as shown in the image

I need to know if I have solved the following problem well: A spin-less particle of mass m is confined to move on the surface of a cylinder of infinite height with a harmonic potential on the z-axis and Hamiltonian ##H=\frac{p_z^2}{2m}+\frac{L_z^2}{2mR^2}+\frac{1}{2}m\omega^2z^2## and I need to...

My question is about the contraint we need to use to solve this problem. The answer to the question use the following constraint: $$(r+R)\theta = r\phi$$ Where $\theta$ is angle from the radius of the fixed cylinder to, say, the vertical axis. And $\phi$ is the angle that the rolling cylinder...

3 cm is inside the cylinder. We can use a gaussian cylinder to enclose the inside of the cylinder up to 3 cm. Because the outer cylinder is infinite there is no flux out of the end caps with the inner cylinder. There is also no charge enclosed in the cylinder. So the electric field 3cm away from...

Hi PF! I have been on and off working on a fluids problem for 2 years. I am SO close but the answer isn't coming out clean. I'll highlight the equations I solve and the technique. If you can help me finish this, I'll not only be incredibly grateful but I'll either thank you in the paper...

A rocket has length L with a separate head on top. The rocket lands in a cilinder on Earth with height L with speed v. From the point of view of the rocket, the cylinder undergoes a Lorentz contraction. The rocket will therefore collide with the bottom of the cilinder and damage it. From the...

I'm building a gas supply system that will dump half the contents of a compressed gas cylinder of nitrogen in 10 minutes. I need to ensure the output delivery pressure doesn't fall below a certain limit because of cooling during the gas expansion. If the cooling effect is excessive, I will...

I have a stp file (PF does not support it so I cannot upload it here. If there is a way I can share it please let me know) of an orifice and I want to create a new file where the orifice is fit inside a cylinder. What software do you recommend me to use? Thank you! :)

I believe I got the first part of this questions solved. For part b, we are asked to find the change in internal energy. We know ΔE=Q+W. The cylinder,gas and piston head are the system. The cylinder and piston head are well insulated, so there will be no head transfer, therefore Q=0. So now...

Since the question says that "velocity along the cylinder axis" and "magnetic field perpendicular to the cylinder axis". So cross product of velocity and magnetic field becomes their magnitude. ##\vec v\times \vec B=||v|| \\ ||B||## So ##\vec F=qvB## ##mg=qv\frac{\mu_0 nI}{4\pi r}## At first...

From ##\oint_{\Gamma}\vec{H}\cdot d\vec{l}=\sum I## by Ampere's Law which gives ##H \Delta l=\Delta N\cdot i\Leftrightarrow H=n i## where ##n=## number of turns per unit length so ##i=\frac{H}{n}=\frac{10^3 A / m}{\frac{200}{0.2m}}=1 A##. Since ##\vec{H}=\frac{\vec{B}-\mu_0\vec{M}}{\mu_0}## we...

Hello, i have tried to calculate the acceleration (COM) of the cylinder (even though in the question they asked about the angular acceleration) and the answer is: 𝑎(𝑐𝑜𝑚)=𝐹(𝑟/𝑅−𝑐𝑜𝑠(𝑡ℎ𝑒𝑡𝑎))/(𝐼/𝑅2+𝑀) and my answer is with minus (I/R^2 - M) . in their solution they wrote in the torque equation-->...

$$V=πr^2h$$ $$V=πr^2(6-r)$$ $$\frac {dV}{dr}=12πr-3πr^2$$ For max/min value, $$\frac {dV}{dr}=0$$ $$12πr-3πr^2=0$$ $$3πr(4-r)=0$$ ##r=0## or ##r=4## $$⇒V_{max}= 32π$$ $$⇒V_{min}= 0$$, I do not think there is another way of doing...

What materials would be suitable for a cylinder and piston that is thermally insulating, reasonably durable for low speeds and very slow cycle rates, and not be a carbon or silicon based polymer? I've been looking at manual lever operated espresso machines lately. Particularly ones that are...

Hi All, I am looking to determine how these Vases where modeled using maths on this webpage https://www.3dforprint.com/3dmodel/sine-wave-vase-generator/2116. It looks like the surface is parametrically defined and wrapped around a cylinder. Interestingly he mentions "Sine waves combine to...

Hi all, I have a doubt when calculating the electric field of a uniformly polarized cylinder P along its longest axis. The cylinder has length L and radius a. Using Gauss's law: $$\int D\cdot ds = \rho_{f} =0 \, \, (eq .1)$$ The electric field inside of cylinder would be: $$E =-...

I am confused because according to my solution the disk is already rotating at constant angular velocity. I have written the translational equilibrium on the horizontal and vertical component: ##N_1## and ##f_2## will have a positive horizontal contribution, while ##N_2## and ##f_1## will have a...

I just have a question that could you guys make an equation that expresses the terminal velocity based on followed condition? - When diameter increase, velocity decrease - velocity should change depending on both cylinder and sphere's diameter - We know every variable - The sphere is in...

Hi! I think I solved the problem but I would like you to take a look at it please, is it right? is there a better way to solve it?

A drop of fuel is ignited in an engine cylinder, that produces heat, light and sound energies from the chemical energy stored in the drop of oil. What I am not clear about is how heat energy gets transformed into mechanical work? I think the heat energy produced from ignition flows from burnt...

So I'm working on a project that involves the design of an O'Neill Cylinder, and there was a consideration that I had never made before. Say you are in a cylinder that is generating enough force for 1G in its spin. This means that while you are spinning, the motion means that your body is being...

The cylinder will cease to be in equilibrium when the sum of the torques on the cylinder calculated with respect to the rightmost point of contact of the cylinder with the plane will be unbalanced. Now, the liquid is homogeneous and the cylinder has negiglible mass so the forces (normal force of...

A person wrote that ##L=\frac{1}{2} m (\dot{r}^2+r^2 \dot{\phi}^2 +\dot{z}^2)## But, how to find equation of that coordinate system?

The problem is a classical one, basically to find the equations of motion of cylinder of radius a inside a fixed cylinder of radius b, the cylinder that rolls rotate about its own axis in such way that it does not skid/slip. Now, the thing that is making myself confused is the constraint...

When I look at this question, I can see two possible values of electric flux depending on how I take the normal area vector for either ends ##A \text{ and } A^{'}##. What is wrong with my logic below where I am ending up with two possible answers? The book mentions that only ##2E\Delta{S}## is...

how to find volume and surface area of this without using the upper lid

Solution attempt : Option : I am sure that my work is wrong. But, I must add solution attempt in PF that's why I just added that. How can I solve the problem?

It is my fault. The cage/cabinet where all the cylinders are stored on the side of the building all have dial locks and I know it sounds really bad but my success rate with dial locks is close to zero. I was trying to swap out the 3/4 full argon cylinder for nitrogen but couldn't unlock it so I...

I need to find the magnetic field of a permanently magnetized cylidner: In calculating the magnetic field, i find that it should be $M_{0} \mu / 2$ and $H = M_{0} / 2$ inside. I just want to make sure that i understand the concepts in this type of problems. Since $M = H \chi (1)$, does this...

Could I please ask for help with the following: Given: The centre of gravity of a uniform solid right circular cone of vertical height h and base radius a is at a distance 3h/4 from the vertex of the cone. Such a cone is joined to a uniform solid right circular cylinder of the same material...

I can calculate the fields generated by the cylinder and the wire but I don't know how to calculate their vector sum to evaluate it at point A. Cylinder field inside: ρR^2/2rε Cylinder field outside: ρr/2ε Field generated by the wire: λ/2πr I should break the fields into components but I don't...

I imagine the shape will be like this: and I need to find the volume of the shaded part. I am planning to use: ##V=\int A(y) dy## I tried to take the cross-sectional area A(y) to be triangle: and the base of the cylinder to be: So it means that the base of the triangle will fulfill the...

This was the answer key provided: My questions are the following: if the force required for rotational equilibrium is more than the limiting static friction, then the body will rotate aka slip over the surface. When it slips, the frictional force will be kinetic and not static, right? If I...

Good afternoon, I am trying to calculate the massflow of steam required in a cylinder used for paper drying but I think there is a bug in my calculation and I would love to get your help to find where the issue is! Saturated steam is continuously supplied to a cylinder. The steam condenses in...

When a magnetic field is applied to a SC during cool down, the field goes through the hole of the hollow cylinder. When the cool down first takes place and then later a magnetic field is applied, the magnetic field does not go through the hole of the hollow cylinder but rather is expelled to the...

I did the question as attached, so I think A and D are correct but the given answer is E. Where am I wrong? Thanks.

Edit: Below is my work but i believe i have chosen the wrong values of the separation vector in the s direction. Any ideas as to what it should be?

Hi, We have a cylinder held by a rope . The rope holds it around its lower half. If the center of mass of the cylinder is not in the middle, but towards a side, a distance "a". How does this offset affect to the friction on the rope? or How big does "a" have to be so the cylinder starts...

I wondered if anyone could help, I work in the fire protection industry. We currently have a project using a pressurised cylinder. The cylinder hold 200 lites of water plus 40 litres of nitrogen gas as a propellant at 10.0 bar. I’m trying to work out once the 200 litre water volume has been...

a) I have calculated (1) λ = ρA = ρπr^2 = 2.49 * 10^-10 C/m and placed it into (2) yielding E = λ / (2πεx^2) = 106.73 N/C. This doesn't seem to be correct by the feedback, however. b) Here just to consider the proportion of the cylinder mass constrained by y.

Please I do not want the answer, I just want understanding as to why my logic is faulty. Included as an attachment is how I picture the problem. My logic: Take the volume of the cone, subtract it by the volume of the cylinder. Take the derivative. from here I can find the point that the cone...

I have a solid cylinder of diameter 40mm and length 14mm and I have used plane stress approximations in my calculations so far. I know for to assume a thin walled cylinder/tube the wall thickness needs to be less than 1/20 of tube or cylinder diameter. However, what I have found so far is that...

I have a problem understanding what is going on in the region called the ergosphere of a "fast" Kerr black hole. - Relativity teaches us that no frame of reference can have relative displacements greater than the speed of light, ok. - The ergosphere of a fast Kerr black hole can contain light...

Cylinders rolling down inclines are a common demo. But how do you model the movement of a sphere rolling within a rolling cylinder? I teaching a physics class and this question came up and my dynamics math is a little rusty. But I haven't found anything like this in any book or online. There's...

This comes from a list of exercises, and setting ##m_1 = 5.4kg##, ##m_2 = 9.3kg## and ##F=5N##, the answer should yield ##2.19m/s^2## (of course, supposing the answer is right). If I knew the radius ##R## of the cylinder, I could find its momentum and use it to find the linear acceleration...

Hello! The magnetic force is to the right. ##I_c## is the moment of inertia of the cylinder. For the net force on the centre of mass, I have the frictional and magnetic forces ##F=F_B-f##. I know that ##F_B## is ##IdB##. I also know that ##rf=I_c\alpha=I_c\frac ar##, so that...

the equation of a parabola that is obtained by taking a cross-section passing through the center of the paraboloid is ##y = ax^2## breaking the paraboloid into cylinders of height ##(dy)## the volume of each tiny cylinder is given by ##\pi x^2 dy## since ##y = ax^2## we have ##\pi (y/a) dy##...

Hi, I am trying to calculate the heat flow across the boundary of a solid cylinder. The cylinder is described by x^2 + y^2 ≤ 1, 1 ≤ z ≤ 4. The temperature at point (x,y,z) in a region containing the cylinder is T(x,y,z) = (x^2 + y^2)z. The thermal conductivity of the cylinder is 55. The...