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374aex1 - Exam#1 Phys374Spring 2006 Wednesday Mar 15 2006...

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Exam#1 —Phys374—Spring 2006 Prof. Ted Jacobson Wednesday, Mar. 15, 2006 Room 4115, (301)405-6020 www.physics.umd.edu/grt/taj/374a/ [email protected] 1. We previously used dimensional analysis to determine the dependence of drag force on a body moving through air. In so doing we took account of the density of the air but neglected its viscosity. For this problem consider the effect of viscosity: suppose a sphere of radius R is moving with speed v through a fluid with viscosity η . (a) Using dimensional analysis determine how the viscous drag force can depend on R , v , and η . ( Hint : Recall that the viscous force in the presence of a velocity gradient perpendicular to a surface is η ( dv/dx ) per unit surface area.) [8 pts. ] (b) Using “geometrical analysis”, would you expect any factors of π in the exact result for the force? If so, how many, and exactly where? [2 pts. ] 2. Consider the cubic equation ay 3 + y + 2 = 0, with a > 0. (a) Display the location of the real roots graphically, by sketching the graphs of y +2 and - ay 3 and seeing where they intersect. Show in
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