A Guide to Physics Problems: Mechanics, Relativity, and by Sidney B. Cahn, Boris E. Nadgorny, C.N. Yang

By Sidney B. Cahn, Boris E. Nadgorny, C.N. Yang

In an effort to arm hopeful graduate scholars with the data essential to move the qualifying exam, the authors have assembled and solved average and unique difficulties from 4 significant American universities and Moscow Phys-Tech. quite a lot of fabric is roofed and comparisons are made among related difficulties of varied colleges to supply the coed with sufficient info to suppose cozy and assured on the examination.

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2b). a) In the Earth frame, how much time will pass before the rockets collide? b) How fast is rocket B approaching in A’s frame? How fast is rocket A approaching in B’s frame? c) How much time will elapse in A’s frame from the time rocket A passes point until collision? How much time will elapse in B’s frame from the time rocket B passes point until collision? 3 Photon Box (Stony Brook) An empty box of total mass M with perfectly reflecting walls is at rest in the lab frame. 3). RELATIVITY 35 a) State what the rest mass of the system (box + photons) will be when the photons are present.

B) Consider the motion in the interval before the loop. Assuming that the car always stays on the track, show that the velocity in the direction is related to the height as c) In the particular case that show that the time elapsed in going down the ramp from can be expressed as where and write as a definite integral. Evaluate the integral in the limiting case and discuss the meaning of your answer. 9 Pulling Strings (MIT) A mass is attached to the end of a string. 9), under which someone is pulling on the string to make it taut at all times.

29 17 Unwinding String (MIT, Maryland (a,b), Chicago (a,b)) A point mass is attached to a long, massless thin cord whose other end is attached to a fixed cylinder of radius R. Initially, the cord is snugly and completely wound up around a circular cross section of the cylinder, so that the mass touches the cylinder. 29a). The point P is the initial position of the mass, and Q denotes the instantaneous contact point between the cord and the cylinder. a) Find the Lagrangian and equation of motion in terms of the generalized coordinate as a function of time, satisfying the initial conditions.

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