exam1_sol - PHY 3221: Mechanics I Fall Term 2010 Exam 1,...

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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 right-hand 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.

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exam1_sol - PHY 3221: Mechanics I Fall Term 2010 Exam 1,...

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