# hw5 - Homework 5 PHZ 3113 Due Monday Chapter 4-5 1 Recall...

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Homework 5 PHZ 3113 Due Monday, February 15, 2010 Chapter 4-5 1. Recall in class we showed how to find the average kinetic energy of a gas particle when the gas is at constant temperature T . In particular, we found h 1 2 mv 2 i = 3 2 k B T . The integrals in this problem are quite similar. Consider a pendulum of length L and mass m moving in one-dimension in the grav- itational field of the Earth with g = 9 . 81 m/s 2 . The displacement of the pendulum from equilibrium can be described by an angle θ . The potential energy of the pen- dulum can be shown to be V ( θ ) = - mgL (cos θ - 1). a) Show that for small angles θ , we can approximate the potential energy by V ( θ ) = mgL 2 θ 2 and hence the system is a simple harmonic oscillator. b) Now imagine that the pendulum is bombarded with gas atoms at a temperature T . If the mass m of the pendulum is small, and we have a very sensitive apparatus, we might just be able to see that the gas atoms cause the pendulum to be slightly displaced from its equilibrium position θ = 0.

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