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Homework 1

# Homework 1 - ,September10 Hint: . Goldstein2.2,2.4,2.12...

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Physics 601 Homework 1---Due Friday, September 10 Hint: For some of these problems it will be helpful to use Mathematica or some other symbolic manipulation program. If you make use of such a program please include the output with your homework solutions. Goldstein 2.2, 2.4, 2.12 In addition: 1. Consider a particle that is constrained to move in 1 dimension and is confined to a 1‐dimensional box of length L . The particle bounces elastically back and forth between the walls of the box. Thus at the wall there is an impulsive force which flips the velocity ( ˙ x → − ˙ x ) conserving energy. This problem explores what happens if at time t=0 the particle has velocity v 0 and one of the walls is moved slowly (either inward or outward) so that size of the box is now a function of time L(t). Since the wall is moving it can add or remove energy from the system. The goal is to find an adiabatic invariant relating the energy to L .

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Homework 1 - ,September10 Hint: . Goldstein2.2,2.4,2.12...

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