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ProblemSet1 - R A Harris and K B Whaley Problem Set 1 Chem...

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R. A. Harris and K. B. Whaley Chem 120A Spring 2006 Problem Set 1 1. Two particles, one of mass m 1 , the other of mass m 2 , are on a line. They interact with potential energy, 2 1 2 1 2 1 ( ( ), ( )) ( ( ) ( )) , 2 V x t x t k x t x t = where k is called the interaction strength. a) What is the dimension of k? b) What is the force that particle one feels? What is the force that particle two feels? c) Show that the total momentum of the particles is conserved. Show that the total velocity is not conserved. Under what condition is the velocity conserved? Be sure to define all terms that you use. Now, suppose that in addition to their mutual attraction, the two particles are constrained to move under an external potential given by, 2 2 1 2 1 1 2 2 1 ( ( ), ( )) [ ( ( )) ( ( )) ] 2 U x t x t k x t k x t = + . d) What is the total potential energy that the particles feel? e) Repeat part “b” with this external potential. f) Prove that momentum is no longer conserved. 2. Consider the experimental setup depicted in Figure 1 below.
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