Path Definition and 1000 Threads

Hi. This is my first message in this forum. I'm not English, so sorry my spelling. Homework Statement Calculate the optical path done by a meridional ray, supposing it covers a horizontal distance, d, in z-axis direction. \gamma_0 is the launch angle (with z-axis).Homework Equations Optical...

Homework Statement Part 1 We fired a cannon 0 degrees to the horizontal line and had to calculate Vo. We then measured Delta x and Delta Y. Part 2 We were then given a degree in which to fire the cannon at, which was 12 degrees. We then had to calculate the projectile's path through...

Homework Statement Beam of excited H2 molecules travels in z direction, kinetic energy 1 eV.Then they decay & dissociate into 2 H-atoms.When one of the H atom has its final velocity perpendicular to z axis, its kinetic energy is always 0.8eV. Then what is the energy released in dissociative...

Homework Statement A 2 kg car travels in a flat circle. At a certain instant the velocity of the car is 24 m/s West and the total acceleration of the car is 9 m/s 2 at 53 degrees North of West. What is its radius? Answer in units of km. Homework Equations F=ma w=(2pi)/T a= w^2...

Homework Statement Show that G(q_2,q_1;t)=\mathcal{N}\frac{e^{iS_{lc}}}{\sqrt{\det A}} where \mathcal{N} is a normalization factor independent of q1, q2, t, and w. Using the known case of w=0, write a formula for G such that there is no unknown normalization factor. Homework Equations I...

This problem involves a an electron describing a helical path, but I've never worked with helixes in my life, so I'm completely stuck. Homework Statement An electron enters a region where a uniform magnetic field B, of magnitute B = 3.00 * 10^(-3) T exists. The velocity v of the electron...

Homework Statement For any S in X, show that S is path-connected if and only if there exists p in S such that any point x in S can be joined to p by a path.Homework Equations A metric space is path connected if any 2 points can be joined by a path in that metric space.The Attempt at a Solution...

Hello folks! How can we find the best path to drive in a circuit in order to do the best lap time? :) I've been trying to solve this problem for 2 weeks, trying to find some functional to minimize, but I'm stuck! Little help? :) P.S. This is not homework :) I just want to know how to beat...

Homework Statement Using spherical coordinates, show that the length of a path joining two points on a sphere is L=\int_{\theta_{1}}^{\theta_{2}}\sqrt{1+\sin^{2}\theta\phi'^{2}}d\thetaHomework Equations x=r\cos\theta\sin\phi y=r\sin\theta\sin\phi z=r\cos\phi The Attempt at a Solution The...

Homework Statement Beam of silver atoms are passing through air at a temp 273K and a pressure of 1 Pa. The beam is attenuated by a factor of 2.72 in a distance of 10^-2 m. Find the mean free path of the silver atoms and estimate the effective collision radius.. Homework Equations...

I am writing a program that uses Snell's Law for refraction of light through two interfaces and I've encountered a problem representing the geometry symbolically. I could determine the values numerically but I don't want the overhead as it would have to be called up to 1E7 times. The...

I will be starting a undergraduate program in Mechanical Engineering shortly and just have a few questions about what I should work for in the future. I have a few different career paths that I would like to pursue but don't know if they would all be applicable. I am interesting in working for a...

Right, I'm currently unsure of what career path I want to take. I'm currently in undergrad math taking all the possible physics modules. Here's the thing - I find doing experiments boring. I find doing pure math problems very boring. I'd probably find research pretty boring too. However, I...

Hi All, How do I begin with this long and complicated story? I am a forth year college student majoring in physics. I began college as an architecture student, made some life-altering realizations during first year that it is not truly progress at all, just a rehashing of shapes/art school...

Homework Statement Let X be locally path connected. Show that every connected open set in X is path connected. The Attempt at a Solution Let U be a connected open subset of X. Since, X is path connected, for any x in X and any neighborhood N of X, there exists a path connected...

Was curious, they seem to be the same, but if not, what is the difference?

Homework Statement Here's an exercise which seems a bit bizzare. Show that if U is an open connected subspace of R^2, the U is path connected. (Hint: show that, given any x0 in u, the set of points that can be connected to x0 by a path in U is clopen in U.) Now, given the fact that I...

Homework Statement As the title suggests, Let {Aj} be a collection of path connected subspaces of some space X, and let the intersection of these subspaces be nonempty. Is U Aj path connected? The Attempt at a Solution Again, my answer would be no, in general. But, since their...

I just went through and exercise which asks if a product of two path connected spaces is path connected. There seems no reason to believe it is in general, for the only thing we know is that if two spaces X, Y are path connected, then they are connected, and their product X x Y is connected...

Homework Statement A cyclist intends to cycle up a 8.2^\circ hill whose vertical height is 180 m. The mass of the bike and the cyclist is 95kg. If each complete revolution of the pedals moves the bike 4.7 m along its path, calculate the average force that must be exerted on the pedals...

Hello everybody! I'm currently in the last year of my undergraduate studies in physics and I'm really happy because I'm finally having the chance to focus on what I like, Astronomy. Next year I'll be starting a Master Degree in the National Observatory here in Colombia but I'm also planning...

Let me just state my situation. I got a bachelor's degree recently, and I've been looking for work. However, the past several years I've been back and forth on wanting to study physics. If I did want to, I'm unsure how I would go about that. I guess I'm technically not an undergraduate...

Im currently a senior in high school and have fallen in love with the deepest mysteries of the universe. However, during my first three years of high school I slacked off, something i deeply regret. Now I am stuck with my poor GPA and I am wondering what steps i can take to pursue a career in...

Hello, everyone. Please excuse my English since its not my native language. I'm a college freshman about to major in Physics (shifting from M. E.) and while in M. E. I've had this problem of playing computer games in between classes with my peers. Many times I would think of refusing but since...

Is there a low energy way to alter the path of a photon in the direction you want. From what I've read on here photons pretty much follow the shortest path. Magnetic fields in energy levels that can be reasonably produced do nothing to alter their path. Large gravitational fields distort...

Homework Statement An ant positioned on the very edge of a Beatles record that is 18.00 cm in radius revolves through an angle of 110.0o as the disk turns. What is the ant's path length? What is the magnitude of the ant's displacement? Homework Equations Ac=v^2/r T=2pir/v...

How is it possible to see the light path of a green laser pointer?

Homework Statement Evaluate the path integral \int (x^2+y^2+z^2)dr from a =(0,0,0) to b= (3,4,5). Homework Equations The Attempt at a Solution I'm lost. Had the dr been a ds I could do it, but my calculus book only deals with situations where \int F.dr.Edit: I figured it out, it's been a...

I'm new to this site. This concern that I have has various parts. Here we go. I started out studying CE up to sophmore year at FAMU-FSU School of Engineering and ended up completing a B.A. in Math at another university in 1998 (financial issues). Joined the Navy in 1999 and about to leave...

==quote from Dah-Wei Chiou's latest paper== In the research of loop quantum gravity (LQG), the sum-over-histories formulation is an active research area that goes under the name “spin foam models” (SFMs) (see [9] and references therein for LQG and SFMs). In particular, over the past years, SFMs...

I need help understanding how a projectile that moves in a parabolic path can have a point where a-> is parallel to v-> or perpendictular to v-> Is this meaning that the lines tanget to the path are perpendicular or the actuall path? And i would think that both parallel and perpendicluar are...

Hey, there is something I don't really understand about the path integral (functional integral) formalism in QFT: Why do you need to introduce a coherent-state representation of the Dirac fields in order to evaluate their path integral? Where is the crucial point why it doesn't work like...

I'm not quite satisfied by the derivation I've found in Sakurai (Modern Quantum Mechanics) and was trying to 'derive' it myself. I'd like some help to seal the deal. I've described below what I've done. Please tell me where to go from there. I know the solution to the Schrodinger equation can...

Homework Statement A ball is hit from the ground with an angle of 36 degrees above the horizontal. The ball hits a target 30m ahead and 4m above the ground. Find the initial velocity of the ball. Homework Equations Vavg = Δd/Δt aavg = Δv/Δt Δd = voΔt + 1/2aΔt2 The Attempt at a...

Homework Statement A car is traveling with constant speed over a hill and down a hill. The radius of the curve is the same. At the top of the hill, the driver experience no normal force from the ground. The mass of the driver is 70.0kg a) calculate the value of the normalforce experienced by...

Homework Statement 1. Construct a path connected space X such that the fundamental group of (X,x_0) where x_0 is the base point; such that the fundamental group is the symmetric group on 3 letters? 2. Let Z be the space obtained from a hollow cube by deleting the interior of its faces...

Homework Statement A projectile is fired at spead v0 and angle \Theta. What is the radius of curvature of the parabolic motion a) at the top? b) At what angle should the projectile be fired so that the radius of curvature at the top equals half the maximum height? (the projectile is fired...

This is from How Stuff Works: The power company essentially uses the Earth as one of the wires in the power system. The Earth is a pretty good conductor and it is huge, so it makes a good return path for electrons. "Ground" in the power distribution grid is literally "the ground" that's all...

I attend Canadian university and in civil engineering program(I finished up my 2nd year). I am thinking of transferring into mechanical engineering. However, I do not know what kind of career path I can expect in Canada with mechanical engineering. There is not any big company in Canada and...

Hi, in high school I think we all learned that "the path of light is invertible (reversible?)". My interpretation would be that if a ray of light hits a flat mirror at 90^{o}, it will trace its path exactly back. Question: does this still hold in the general theory of relativity when space is...

<tl;dr> I'm 27 and miserable. I want to make a positive change, but the options that I have offer little positive and much negative. What do I do? Important Details: I am employed full-time and I have ~$13,000USD in savings, but I am deep in debt with absolutely terrible credit and my wages...

I wanted to find out whether i could draw a certain figure or not , so i used graph theory to get an answer.Just wanted to know if my analysis is correct.Please check the below link to see my analysis. http://cyberscrawler.blogspot.com/2010/09/this-figure-is-impossible-to-draw.html

1. Homework Statement what is the mass of a particle which travels in a circular path with a kinetic energy of 3.2 x 10 ^-19 J moving perpendicular to a 0.200t magnetic field if it has a charge of 1.6 x10 ^-19 C and the path radius is 10 cm 2. Homework Equations ke= 1/2 mv^2 mv^2/r =...

Greetings, I know that position state ket is a continuous state ket satisfying X|x> = x|x>. There is however one notation I don't understand. What does it mean when we label the position ket with a discrete index and then use these to expand operators as <x_i|H|x_j>? What does it generally...

Homework Statement A rabbit starts at the origin and runs at speed a along the right branch of the parabola y = x2. At the same moment, a dog starts at the point (c,0) and runs at speed b directly towards the rabbit. Write a differential equation for the path of the dog. Homework...

Hi all! For a year or two, I've been extremely interested in physics for the past two years. I've decided for sure that I want to be a Theoretical or Astrophysicist now. I'm currently in the first quarter of my Eighth Grade Year. All of middle school I've been an A/High B student in gifted...

So i know the whole picture starting from power from the generating plants that go all the way to our homes..and the ground serves as a return path to complete the circuit..What i don't get is...how does that current find its way back to the source through ground?..is the source somehow...

Hi. I am extremely new to this wonderful forum. I am hoping that I can receive the same awesome advice as the other members on this forum. Background about me- I am second year math(B.S.) student who is quite adept at mathematics and was advised to cross over and achieve a second degree...

Homework Statement A glass optical fibre of length L = 3.2 m is in a medium of glycerine with a refractive index n0 = 1.47 . The fibre has a core of refractive index, n1 = 1.58 and diameter, d = 100μm surrounded by a thin cladding of refractive index, n2 = 1.53. The end of the fibre is cut...

Hi I'm now reading about Vector fields, everything is clear and intuitive for me as curl divergence ..ect , except one simple thing that I'm straggling with for the last 4 days! I searched Internet and a lot of math & physics books but in vain : Why Conservative field is Path independent...