Solution_to_Midterm_Exam_Winter_2008

# Solution_to_Midterm_Exam_Winter_2008 - MECHANICAL AEROSPACE...

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MECHANICAL & AEROSPACE ENGINEERING DEPARTMENT UNIVERSITY OF CALIFORNIA, LOS ANGELES MAE 102 Mechanics of Particles and Rigid Bodies Winter, 2008 INSTRUCTOR CHATTERJEE, A. K. MIDTERM EXAMINATION February 22, 2008 INSTRUCTIONS: SHOW ALL CALCULATIONS ON THESE PAGES. ATTACH ADDITIONAL PAGES AS NECESSARY. NAME ______S O L U T I O N________________________________________ Student ID ____________________________________

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h Problem 1 (5+4+6) 1. Using the equation of motion R ma = % % , derive the equation of work-energy and conservation of energy. What are the differences between these two equations? 2. Can you determine the normal forces from these equations? If not, explain the procedures that allow you to determine the normal forces. 3. A bead P of mass m is given an initial speed 0 v at A along the smooth, vertical guide. The radius of curvature at B is ρ , determine the magnitude and direction of force exerted by the guide on the bead at B. Express your answers in 0 , , and and m v g h ρ Solution 1. Equation of motion: R ma = % % . Taking the dot product of both sides with differential tangent vector dr r , and integrating from location A to location B on the particle path, we have the work- energy equation, . . = = - = = - = = ° r r r r r r 2 2 1 1 . . 2 2 . B B B B A A B A A A B B A A B A ma dr mvdv mv mv F dr U T T F dr U When a force is conservative, a potential energy function V exists such that .
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