301 (F98) Exam #4

301 (F98) Exam #4 - Physics 301(Fall 1998 Fourth Exam Name...

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Physics 301 (Fall 1998) Fourth Exam (November 20, 1998) Name 1. [25 points] A particle of mass m is constrained to move on a smooth long sheet extending uniformly in the z-direction with xy-cross sections forming an exponential curve, y = b e -ax , where a and b are positive constants. A uniform gravitational force is acting in the negative y-direction. A. Find the Lagrangian for the particle. Show your work. B. Use Lagrange’s method to find the equations of motion. Show your work. (Hint: You should have one equation for x and one equation for z.) y = b e -ax x y
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2. [35 points] A bead of mass m moves without friction on a parabolic wire, z=ar 2 (where r is the cylindrical coordinate), under the influence of a uniform gravitational force in the negative z-direction. The wire rotates about the z-axis with constant angular velocity ϖ . We have already worked this problem as homework. We found that the Lagrangian for the bead is: A. Find the generalized momentum, p r . Show your work. B. Is the Hamiltonian for the bead equal to the energy of the bead?
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This document was uploaded on 10/29/2011 for the course PHSX 301 at MSU Bozeman.

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301 (F98) Exam #4 - Physics 301(Fall 1998 Fourth Exam Name...

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