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Unformatted text preview: PHY 3221: Mechanics I Fall Term 2010 Exam 1, September 29 2010 This is a closed book exam lasting 50 minutes. There are three problems worth a total of 20 pts. Begin each problem on a fresh sheet of paper. Use only one side of the paper. Avoid microscopic handwriting. Put your name, the problem number and the page number in the upper righthand corner of each sheet. To receive partial credit you must explain what you are doing. Carefully labelled figures are important! Randomly scrawled equations are not helpful. Draw a box around important results (or at least results which you think might be im portant). Good luck! 1 Problem 1. Conservative forces. [4 pts] Consider the following force: F x = y , F y = x , F z = z . Is this a conservative force? If so, find the potential energy U ( x,y,z ) associated with it. Solution To check if the force is conservative, calculate vector vector F : ( vector vector F ) x = F y z F z y = 0 0 = 0 . ( vector vector F ) y = F z x F x z = 0 0 = 0 . ( vector vector F ) z = F x y F y x = 1 1 = 0 . Therefore vector vector F = 0 and the force is conservative. It can be represented as vector F = U ( x,y,z ) F x = y = U x = U ( x,y,z ) = yx + C 1 ( y,z ) F y = x = U y = x C 1 y = C 1 y = 0 = C 1 ( y,z ) = C 2 ( z ) = U ( x,y,z ) = yx + C 2 ( z ) F z = z = U z = C 2 z = C 2 z = z = C 2 ( z ) = 1 2 z 2 + const The end result is U ( x,y,z ) = xy...
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This note was uploaded on 12/15/2011 for the course PHY 3221 taught by Professor Chan during the Spring '08 term at University of Florida.
 Spring '08
 CHAN
 mechanics

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