midterm exam - Physics 507: MIDTERM EXAM PROBLEM 1. (5...

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Physics 507: MIDTERM EXAM PROBLEM 1. (5 pts.) A classical particle of mass m moves in the presence of the following force f eld in one dimension: F ( x )= kx ¡ 2 x 2 a 2 ¢ . At moment t =0 the particle is found at point x 0 = a , with zero velocity. Find its position as a function of time t . PROBLEM 2. (5 pts.) Consider a uniform, F at rectangular object of mass m , with linear dimen- sions a × b . The object freely rotates about the stationary axis coinciding with its diagonal. Find the magnitude of torque exhorted on the axis, if the angular velocity is ' . PROBLEM 3. (5 pts.) A classical particle of mass m , with total energy E , is scattered by a step-like repulsive potential: U ( r ½ U 0 , r<a 0 ,r > a Find the range of the impact parameter, for which the particle cannot penetrate into the inner region of the potential, (In this regime, the potential acts as a hard sphere). 1
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Solution to Problem 1: First, f nd the potential energy: U ( x )= Z F ( x ) dx = kx 2 ¡ x 2 a 2 ¢ 2 .
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This note was uploaded on 09/28/2008 for the course PHYS 507 taught by Professor Anon during the Spring '04 term at Cornell University (Engineering School).

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midterm exam - Physics 507: MIDTERM EXAM PROBLEM 1. (5...

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