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MTE_I - FACULTY OF ENGINEERING Mechanics 2(MP 104(Dynamics...

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FACULTY OF ENGINEERING Mechanics 2 (MP 104) (Dynamics) Mid Term Exam I Time: 1 Hour SPECHIALIZED SCIENTIFIC PROGRAMS Spring Semester, 2010 All Departments Lectures: Prof. Dr. Abd El-Fattah Rizk, Prof Dr. Galal Elkobrosy, Prof. Dr. Atef Ata, Dr. Mohamed Alsayad. NAME: ---------------------------------------- Group: -------- Section: ------- Prog. No: ---------- Answer the following questions: 1- A particle moves along a parabolic path whose equation is 18 2 2 + - = x y , where x and y are in meters. If the horizontal acceleration of the particle is 0 = x & & and at 0 = t , 3 = o x , m/sec 4 - = o x & , determine at 1 = x : a) The velocity and the acceleration of the particle. b) The rate of change of the particle’s speed and the normal acceleration. c) The radius of curvature and the coordinates of the center of curvature. Solution: 0 = x & & , at 0 = t , 3 = o x , m/sec 4 - = o x & Integrating with respect to t we get m/sec 4 - = = C x & Integrating again with respect to t we get - = t x dt dx 0 3 4 t x t x 0 3 ] [ 4 ] [ - = t x 4 3 - = - t x 4 3 - = ----(1) Substitute into the equation of the path 18 ) 4 3 ( 2 2 + - - = t y t t y 48 32 2 + - = ---------------(2) Equations (1) and (20) are the parametric equations
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