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RENSSELAER POLYTECHNIC INSTITUTE TROY, NY EXAM NO. 2 INTRODUCTION TO ENGINEERING ANALYSIS (ENGR-1100) – Fall 15 NAME: Section: ___________ RIN: _______________________________ Wednesday, October 21, 2015 8:00 – 9:50 Please state clearly all assumptions made in order for full credit to be given. Problem Points 1 25 2 25 3 25 4 25 Total 100 Score Problem #1 (25) Consider the following matrices −5 0 −2 8 8 3 5 5 −7 Determine the following expressions. If an expression is not valid, STATE THE REASON. = 0 −9 5 −7 = 6 −2 6 0 = −1 0 0 5 −7 6 = (a) + (b) −2 (c) det( ) and (d) (e) det( ) using the duplicate column method (4) (4) (5) (9) (3) Note: show all steps. (a) (b) (c) (d) (e) Problem #2 (25) A lamp weighs 120 N and is supported by two cables AB and AC and a pole OA. The force in the pole acts along the axis of the pole. (a) Identify the particle to be analyzed (1). (b) Draw complete and separate Free-body diagram for the particle (5). (c) Express all forces in Cartesian vector form (7) (d) Write Equations-of-Equilibrium for the particle (9). (e) Determine the magnitudes of tensions in AB and AC and the support force along pole OA (3). Value TAB = TAC = FOA = Free-body diagram: Unit Problem #3 (25) The pipe assembly is subject to forces and couple moments as shown. (a) Determine the magnitude of moment of F1 about the pipe segment CD (5). (b) Replace the force-couple system by equivalent resultant force and couple moment at O (17). (c) Can this system be reduced to a single result force? Explain. (3). Value (a) M1CD = (b) FR = CR = (c) Yes/No (check 1) Explain: unit Problem #4 (25) A ship’s loading ramp has mass of 120 kg and a center of gravity at G. The ramp is attached to the ship at A by a smooth pin. The cable CD provides just enough force that the reaction at B is zero. a. Draw a complete and separate FBD of the ramp.(5) b. Write the equations of equilibrium for the ramp. (10) c. Solve the equations to determine the unknown reactions at A and C. (10) 2m 1m 1.5 m (b) (c)