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Problem 1 [20 Pts] The position vector rAB = 150i - 85j + AB,z k has magnitude equal to 188 m. a) Determine the z-component rAB,Z (positive). b) If the coordinates of point A are (25, 50, -20)m, define the coordinates of point B. c) Find the angle in degrees of the vector with the y-axis. d) Express a unit vector parallel to rAB in terms of components. Problem 2 [20 Pts] y The cables AB and AC are attached B (5, 6, -2) m at the support on the floor at A. The C (-2, 5, 1) m magnitudes of the tension forces in the two cables are TAB = 300 N and TAC = 450 N, respectively. a) Express the forces TAB and Tac in terms of their components. X b) Define the total force exerted by the two cables at point A. Problem 3 [20 Pts] www A An object with a mass m = 250 kg is suspended from the ceiling at point A with a weight-less rope, while an athlete is pulling with a second rope, attached at point B, applying a force F. The whole system is in equilibrium. Given the geometry shown in the figure, draw the appropriate free body diagram and then calculate the magnitude of the force F applied by the athlete. TAC TAB A (3, 1, 4) m 25° F 30° B m
Problem 4 [20 Pts] An object of mass m = 981 kg is suspended from a rope that is attached at point B (5, 4, 3) and passes from a frictionless pulley at C (7, 1, 8). A (-2, 3, 5) m 4.5 m Determine the moment MOA about the line OA due to the force in the rope. 0 (0, 0, 0) C (7, 1, 8) m m Problem 5 [20 Pts] If the following two systems are equivalent, calculate the unknown couple Mo and the forces FA and Fc. 100 KN Fo M₂ 50 KN T D C D 3.0 m 3.0 m FA 20 KN A T L 20 KNm 5.0 m 5.0 m 160 KN System 1 System 2 Problem 6 [20 Pts] The following system is in equilibrium. Draw the free-body diagram of the frame and apply the equilibrium equations to determine the reactions at the supports A and B. 30⁰ 20 KN 30 KNm 1.0 m + 2.0 m B mum 2.0m 2.0m 3.0 m MENG-250 Engineering Mechanics: Statics - Mid-term examination - Spring 2022 A mfunde B 10 KN ID A B (5,4,3) m B Page 2