ENGR 201 Summer 2018 Midterm Exam #1 1. A cargo ship at rest is moored to the dock by the ropes AC, and BD and BE, as shown in Figure 1. Under certain conditions of wind and other passing ships, the magnitude of the force carried by rope AC is 4 MN. Considering that: (i) the ropes lie in the x-y plane; (ii) the combined force carried by ropes BD and BE is 5 MN in the i-direction; and (iii) the weight of the ropes can be neglected: a. Determine the force vector acting on the rope AC (FAC) at anchor A. b. Determine the force vectors acting on the ropes BD and BE (FBD, FBE) all at B. c. Determine the resultant force vector at anchor B. d. Calculate the magnitude of the force in rope BD (FBD) in lbf. C A 75 m 180 m D 140 m B y 48 m E j i x 92 m 8 m Figure 1 NOTE: Each section of each problem is worth 10 points. The Catholic University of America Abot 1 Engineering Mechanics I Summer 2018 2. A man weighing 72 kg is rising a ladder as shown in Figure 2. a. Determine the moment vector at point A (at the bottom of the ladder), generated by the man reaching the tip of the roof at point B. b. Determine the moment vector at point A (at the bottom of the ladder), generated by the man reaching the top of the roof at point C. c. Determine the moment vector at point A (at the bottom of the ladder), generated by the gust wind force (1.1 kN) exerted on the roof at point D. C y 1.3 m 750 N D j i 4.3 m x B z, k A 1.2 m 5.2 m Figure 2 NOTE: Each section of each problem is worth 10 points. The Catholic University of America Abot 2 Engineering Mechanics I Summer 2018 3. A solid circle is subjected to a couple (pair of equal and opposite) forces as shown in Figure 3. a. Determine the moment vector created by the couple of force vectors at point O. b. Determine the moment vector created by the couple of force vectors at point C. c. Determine the force magnitude that needs to be applied at A and B to maintain the prior moment vector if the diameter of the circle is 4 m instead. C y j A i x O 750 N B 750 N z, k 5m Figure 3 NOTE: Each section of each problem is worth 10 points. The Catholic University of America Abot 3 Engineering Mechanics I Summer 2018