Homework12-Spring-2011-Help

Homework12-Spring-2011-Help - ME 104 Engineering Mechanics...

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ME 104: Engineering Mechanics II Spring Semester 2011 Department of Mechanical Engineering University of California at Berkeley Professor Oliver M. O’Reilly Homework No. 12 Additional Help and Intermediate Results Notes: These is the homework help file for Homework 12. It discusses the assignments and gives helpful pointers on how to set up and solve the problems. The 5 problems featured in this homework involve using the balance laws: F = m ¯ a , and Either M = ˙ H or M O = ˙ H O . (1) In all but one of the problems, ω = ˙ θ E z and H = I zz ˙ θ E z . Consequently, you can easily use H O = H + ¯ x × m ¯ v to work out (for all but the one problem) H O = I Ozz ˙ θ E z . Alternatively, given I zz you can use the parallel–axis theorem to work out I Ozz . For all of these problems, you should use The Four Steps . The algebra can be involved so I recommend that you insert numbers at the very end. 1. Problem 6/39 (Non SI-Problem) (20 Points) First, you need to pick an origin O . Next, put a corotational basis on the bar and use it to calculate ¯ x , ¯ v , H O of the bar. The easiest choice here is to have e x pointing along the bar so that ¯ x = L 0 e x , where L 0 = 0 . 25 feet In step II, you will need to compute the total moment M O acting on the bar. Don’t forget the vertical gravita- tional force mg E z and the moment M c . The unknowns are R O , M c = M cx e x + M cy e y and ¨ θ , so which set of equations from ( 1 ) do you need to easily determine these unknowns? You will need to determine ¨ θ
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