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  1. J

    Muon decay and Special Relativity

    Homework Statement Cosmic muons are produced when protons in cosmic rays hit the atmosphere about 10km above us. How fast do muons have to travel in order to reach the Earth before decaying if they live 2.2μs before decaying? Consider the analysis for the rest frame of a) the Earth and b) the...
  2. J

    Fourier Series of an Odd Piecewise function

    Homework Statement Fourier Series of the following function f(x). f(x) is -1 for -.5<x<0 f(x) is 1 for 0<x<.5 Homework Equations b_{n} = \frac{1}{L}\int^{L}_{-L}f(x)sin(nπx/L)dx Where L is half the period. The Attempt at a Solution Graphing the solution, I know that it is odd, which is...
  3. J

    Relativistic motion in a particle accelerator: Rate of Energy Loss

    Mother of mercy, that's it! Solving for Kinetic Energy to get gamma, then solving for v using the equation I got, then plugging it all into the last equation got me my answer. It also helped me out on the two questions after the one I posted, where my velocities were all just a hair below the...
  4. J

    Relativistic motion in a particle accelerator: Rate of Energy Loss

    Homework Statement (a) Consider a 10-Mev proton in a cyclotron of radius .5m. Use the formula (F1) to calculate the rate of energy loss in eV/s due to radiation. (b) Suppose that we tried to produce electrons with the same kinetic energy in a circular machine of the same radius. In this case...
  5. J

    Fourier Coefficients of an Even Function

    ((Just a side note, sorry about posting this thread in the wrong board. I couldn't decide which one to post it in between the Introductory and the Advanced Physics boards and figured it might be upper-level introductory. Thank you for correcting my error. Also, I'll make the equations a bit...
  6. J

    Fourier Coefficients of an Even Function

    Given F(x) = \sum^{∞}_{n=1} A_{n}cos(\frac{2πnx}{λ}) Considering we're solving for A_{n}, I figure it couldn't be used in the integral (given in the original post). So: An = \frac{2}{λ}\int^{λ}_{0} F(x)cos(\frac{2πnx}{λ}) dx = \frac{2}{λ}\int^{λ}_{0} cos(\frac{2πnx}{λ})*cos(\frac{2πnx}{λ}) dx...
  7. J

    Fourier Coefficients of an Even Function

    Alright. Given that the function F(x) is an even function, the equations will only deal with cosines. Using the equation I was given in this book and the equations Matt gave me, my end result is: My integrals were: An = \frac{2}{λ}\int^{λ}_{0}cos2(\frac{2πnx}{λ})dx and An =...
  8. J

    Fourier Coefficients of an Even Function

    Modern Physics for Scientists and Engineers, 2nd Edition. Authors are John Taylor, Chris D. Zafiratos, and Michael A. Dubson. Chapter 6, problem #32. I figure more information than necessary is better than too little information.
  9. J

    Fourier Coefficients of an Even Function

    Homework Statement For a given periodic function F(x), the coefficients An of its Fourier expansion can be found using the formulas (Form1) and (Form2). Consider a periodic square pulse and verify that the Fourier coefficients are as claimed: An =(\frac{2}{πn})sin(\frac{πan}{λ}) for n≥1 and...
  10. J

    Michaelson Interferometer and changing length of glass rod

    Homework Statement The index of refraction of a glass rod is 1.48 at T=20°C and varies linearly with temperature, with a coefficient of 2.5 E -5 °C-1. The coefficient of linear expansion of the glass is 5 E -6 °C-1. At 20.0°C the length of the rod is 3.00 cm. A Michelson interferometer has...
  11. J

    Maximum Intensity Between Dark Fringes, Diffraction

    Ah yes. Radians. That was the issue. That always seems the case. Radians is a reoccuring enemy of mine. Thanks.
  12. J

    Maximum Intensity Between Dark Fringes, Diffraction

    Homework Statement Laser light of wavelength 632.8 nm falls normally on a slit that is 0.0210 mm wide. The transmitted light is viewed on a distant screen where the intensity at the center of the central bright fringe is 8.50 W/m2. a) Find the maximum number of totally dark fringes on the...
  13. J

    Angular Acceleration due to Light Waves

    I found the correct answer (1.46x10-13) after a bit of trouble (I was calculating Intensity wrong, haha...). I'm going to post a quick run through of my work so that anyone who invariably stumbles upon this problem might see it worked out neatly. Intensity = Emax2/2μoc = .001754 Prad total is...
  14. J

    Angular Acceleration due to Light Waves

    Alright, so the force on the black square would be (Area)(Intensity)/c and the force on the reflecting square would be twice that. As I mentioned earlier, the apparent (if that is the right word) force would be I/c on the right block. Torque (τ) is Fd and α is τ/Inertia. Plugging in all I...
  15. J

    Angular Acceleration due to Light Waves

    Homework Statement Two square reflectors, each 1.00 cm on a side and of mass 4.00 g, are located at opposite ends of a thin, extremely light, 1.00-m rod that can rotate without friction and in a vacuum about an axle perpendicular to it through its center (the figure ). These reflectors are...
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