# Search results

1. ### I Help getting started with this differential equation

I need to solve ∂2Φ/∂s2 + (1/s)*∂Φ/ds - C = 0 Where s is a radial coordinate and C is a constant. I know this is fairly simple but I haven't had to solve a problem like this in a long time. Can someone advise me on how to begin working towards a general solution? Is the method of...
2. ### I Finish and plot this separation of variables problem

I have a PDE which I have solved numerically using a guass-seidel method, but I want to compare it to the analytical solution. I have used separation of variables to get the general solution, but I need help applying it. The PDE is (1/s)⋅(∂/∂s)[(s/ρ)(∂ψ/∂s)] + (1/s2)⋅(∂/∂Φ)[(1/ρ)(∂ψ/∂Φ)] - 2Ω...
3. ### I Best method to solve this discretized PDE

I am attempting to solve the following PDE for Ψ representing a stream function on a 2D annulus grid: (1/s)⋅(∂/∂s)[(s/ρ)(∂ψ/∂s)] + (1/s2)⋅(∂/∂Φ)[(1/ρ)(∂ψ/∂Φ)] - 2Ω + ρ(c0 + c1ψ) = 0 I have made a vertex centered discretization: (1/sj)⋅(1/Δs2)⋅[(sj+1/2/ρj+1/2,l){ψj+1,l - ψj,l} -...
4. ### I Help discretizing this PDE (stream function)

I have a PDE that I want to solve for a stream function ψ(j,l) by discretizing it on a 2D annulus grid in cylindrical coordinates, then solving with guas-seidel methods (or maybe a different method, not the point): (1/s)⋅(∂/∂s)[(s/ρ)(∂ψ/∂s)] + (1/s2)⋅(∂/∂Φ)[(1/ρ)(∂ψ/∂Φ)] Where s and Φ are...
5. ### Photovoltaics and time near a black hole (as a key story element)

I'm a physics student and science fiction writer, and I've never been to this section of PF before! But I have an idea I think is cool for a novel or short story and I'd like some input on the physics involved. As I'm not overly worried about this idea being stolen I'm going to provide a short...
6. ### Equation of motion for oscillations about a stable orbit

Homework Statement A) By examining the effective potential energy find the radius at which a planet with angular momentum L can orbit the sun in a circular orbit with fixed r (I have done this already) B) Show that the orbit is stable in the sense that a small radial nudge will cause only...
7. ### Bound surface charge on a linear dielectric half-cylinder

Homework Statement Problem statement in attached photo. This is an ungraded assigned problem which I am using to study for an exam, so I don't need the whole solution just help with a couple of points I am confused about. One: Part d) is really important to how I will answer part b). If we can...
8. ### How can I plot equipotentials from this series?...

Homework Statement The problem is given in the attached picture, but I already have a solution to part a) which I am confident in (I have checked it carefully, compared to other students and confirmed it with my graduate-TA). Part b) asks us to plot the equipotentials but I cannot figure out...
9. ### Temperature as a function of time in black body radiation

Homework Statement 2. Consider a metal sphere of radius R and heat capacity C, initially at a temperature To which is much hotter than the background temperature. a) Derive an analytical result for the temperature of such a sphere as a function of time. Clearly state any simplifying...
10. ### Bizarre Atmospheric Physics Problem

Homework Statement For an atmospheric physics class, we are given this problem that I and a classmate have been struggling with for days. Reaching out here for some help. Full Problem statement in the image attached. We have a balloon at 293 K and 101,300 Pa. How much fuel is needed to raise...
11. ### Partition Function for N Quantum Oscillators

Homework Statement For 300 level Statistical Mechanics, we are asked to find the partition function for a Quantum Harmonic Oscillator with energy levels E(n) = hw(n+1/2). No big deal. We are then asked to find the partition function N such oscillators. Here I am confused. Homework Equations...

Homework Statement I was never great in diffEQ, but now I have to solve this problem for physics homework and I'm pretty lost. d^4x/dx^4 - d^2x/dx^2 + a =0 Where a is a parameter. Homework Equations The Attempt at a Solution I have tried solutions like e^kt which work accept for the...
13. ### Where does one shop for SEM components?

I am working (as an undergraduate) assisting in the repair of a JEOL Scanning Electron Microscope. Without going into too much detail, some components of the SEM control system may be damaged and need complete replacement. I am working with an instrument engineer who has mentioned that he has...
14. ### Difficult Vector Field Integral

<Moderator's note: Image substituted by text.> 1. Homework Statement Given the following vector field, $$\dfrac{2(x-1)\,dy - 2(y+1)\,dx}{(x-1)^2+(y+1)^2}$$ how do I integrate : The integral over the curve x^4 + y^4 = 1 x^4 + y^4 = 11 x^4 + y^4 = 21 x^4 + y^4 = 31 Homework Equations...
15. ### Integration for the Volume of an Ellipsoid

Homework Statement Let E be the ellipsoid x^2 + 2xy +5y^ +4z^2 = 1 Find the Volume of E Homework Equations None, just various integration methods. The Attempt at a Solution I know we're not supposed to say 'I don't know where to start' but with this one I really don't. If the best approach...
16. ### Partial derivative problem... why is my answer wrong?

Homework Statement The entire problem is in the attached picture. I have been checking and double checking for about an hour, found solutions online which agree with my solution, but I cannot find any answer beside -3.697 m/s which is marked wrong by the computer program. Homework Equations Is...
17. ### I How does one make an Amplitude vs. Frequency plot?

I am working on homework for a physics lab course and I am asked to write a python function which will produce an amplitude v.s frequency plot. In a previous problem I wrote a function which simulates data from a sine wave in the form of a time series; the new function should be able to take...
18. ### I Alternate form of wave equation

Apologies if this question is better posed in the mathematics section, it is for a quantum mechanics class so I decided to post it here: We are asked to verify that the following equation is a solution to the Schrodinger wave equation for a free particle: Psi(x,t) = Ae^i(kx-wt) - Ae^-i(kx+wt)...
19. ### B Algebra Identity I can't figure out

I seem to remember this Algebra identity being covered in one of my classes years ago, but it has cropped back up in studying the relativistic doppler effect for light. Can anyone please show me the intermediate steps to show that: (1+x)/(sqrt(1-x^2) = sqrt((1+x)/(1-x)) or similarly...
20. ### Probability that two measurements have the same true value

Homework Statement I am in a lab course studying Brownian motion. I have gathered data for for movement in two dimensions. I currently have a fairly large data set for ∆x and ∆y and have taken the mean and standard deviation of each. The lab asks what is the probability that these two sets of...
21. ### Maximum mass value possible to fuel a spaceship

Homework Statement We are given that a spaceship converts mass directly to light (emitted backwards) in order to accelerate. If an energy mc^2 has been converted to light ( from the Earth's reference frame) then what is the final speed of the ship (w.r.t. Earth) if the ship's rest mass is M and...
22. ### Stress on fabric under tension

Suppose we have a dome of fabric supported by radial rigid beams. The pressure (air or water pressure) outside the dome is significantly higher than inside the dome (perhaps the inside is even at vacuum). Because the material is fabric (non rigid) the compressive force from the higher pressure...
23. ### Courses Linear Algebra or Computer Science?

I am going to have two slots available this year for electives and I want to use one of them for Astronomy. For the other, I am struggling to decide between Linear Algebra or Computer Science (CIS 210 at my university) which focuses on Python programming. If I can only choose one, which is more...
24. ### Resources for statics, engineering concepts related to stability under tensile & compressive stress

I am attempting to learn more about the field of statics, engineering concepts related to stability under tensile and compressive stress, and related topics. I realize this a broad area of physics but educating myself piece by piece on wikipedia is tedious and disjointed, and Khan academy...
25. ### Volumetric flow rate conversions

I'm trying to learn more about how air compressors work (not how they mechanically function - how they're input/out pressures and flow rates work) and I'm having a lot of trouble getting a specific questioned answered even after a lot of google searching. Suppose I have a compressor that the...
26. ### Engineering How to seek input on a non-patented invention

I am an undergraduate physics student and I've been working on a personal research project for almost a year which has turned into a design for an invention. I am waiting on a physics professor and a friend who's a mechanical engineer, both very busy people, to review my design and tell me if...
27. ### Resources for air flow/air compression physics

I am attempting to identify how long it would take to bring different volumes to a specific pressure using air compressors. I understand that the flow rate given for an air compressor will change as the outlet pressure increases, but I am having some trouble finding the equations to describe...
28. ### Air-tight, High Specific-Strength Textiles

I am an undergrad student working on a personal research project involving aeronautics. For the purposes of my project I have found that I need a fabric with a specific strength (tensile strength over density) of greater than 130 kNm/kg which is can be made air-tight. Kevlar, Zylon and Spectra...
29. ### Theoretical model for damped harmonic oscillation.

Homework Statement Hello all, I have a question regarding the damping constant for a model of a vertically oscillating mass on a spring. I have read through one or two similar questions on this site but I think I can manage to be a little more specific about what I'm asking. I am in a physics...