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1. ### 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. ### 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. ### 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...
4. ### 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...
5. ### 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...
6. ### 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...
7. ### 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...