Homework13-Spring-2011-Help

# Homework13-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. 13 Assignments, Additional Hints, and Intermediate Results Due by 2:30 pm on Monday May 2, 2011 Announcements: A. The two part review session for the final will be held in class on Monday May 2, 2011 and Wednesday May 4, 2011. B. I will also be available in class on Friday May 6 to answer any questions you might have and to review old final exams and their solutions. C. On Wednesday April 27, we will be distributing evaluation sheets for the review sessions where you can write down which topics you would like to see reviewed/emphasized. D. The syllabus for the final exam is limited to rigid bodies. It includes Homeworks 9–13 and Chapter 8,9, & 10 of the Primer. I strongly encourage you to look at the old final exams in the blue reader. Notes: 1. The first 5 problems of this homework set involve using the balance laws: F = m ¯ a , and Either M = ˙ H or M O = ˙ H 0 . (1) In all 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 H O = I Ozz ˙ θ E z . Alternatively, given I zz you can use the parallel–axis theorem to work out I Ozz . If there is no fixed point O for the rigid body, then you should use M = ˙ H . 1 2. Problem 5 (6/149) uses energy conservation. You should practice using the work-energy theorem for a rigid body here: ˙ T = F · ¯ v + M · ω = K summationdisplay i =1 F i · v i + M p · ω . (2) Here, the kinetic energy of a rigid body is T = 1 2 m ¯ v · ¯ v + 1 2 H · ω . (3) 3. In many of the problems, you will need to calculate the angular momentum of a rigid body or particle relative to a point, say A, which is not the center of mass of the body. To do this, use the important identity: H A = H + (¯ x - x A ) × m ¯ v . (4) For a particle, H = 0 , and this identity simplifies to the usual definition of angular momentum for a particle.

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