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CIV-101F Sample Problem Sets Section J Fall 2006 SAMPLE PROBLEM SETS MODULE -2 Question M2-1 For the force A= 2i – 6j – 9k that is exerted at point (3, 7, -2), find: a) The moment of A about the origin b) The moment of A about point B (0,4,-5) c) The moment of A about point C (3,7, 2) Question M2-2 Consider the following points in space: A(-1, 5, -3) B(0, 6, 2) C(7, -3, 3) a) Find the angle formed by vectors AB and AC. b) Find the magnitude of the component of AB in the direction of AC Question M2-3 The 7m tree trunk is held stable by 2 cables BC and BA. Knowing that TBA= 555N, TBC=660N. Determine the moment produced by the resultant of the 2 forces about O. CIV-101F Sample Problem Sets Section J Fall 2006 Question M2-4 The shown boom carries a 4kN load as shown. Find the magnitude of the tension force in cables BD and BE. Question M2-5 Three children standing on a 5x5m mat at the shown positions have the following weights: A: 375N B: 260N C: 400N Where on the raft should a fourth child weighing 425N stand if the resultant of their weights is to pass through the center of the raft? Hint: Try taking moments about the x and z axis. Question M2-6 The 6m pole is supported at A by a pin support and by the two cables shown. A 455N acts at C as shown. For a=3m find the forces in cables BE and BD and the 3 reaction components at A. CIV-101F Sample Problem Sets Section J Fall 2006 Question M2-7 The turnbuckle is tightened until the tension in the cable AB is 1.2KN. Assuming the arm weighs Arm 0.4KN and the pole weighs 1.5kN, find the reaction components at the fixed connection at O. You can assume the center of gravity of the arm is in the middle [@ (0.8, 0, 2)]. Of course you would normally find that as in problem 1. Pole Question M2-8 The pipe assembly supports the vertical loads shown. Determine the components of the reaction at the ball-and-socket joint A and the tension in the supporting cables BC and BD CIV-101F Sample Problem Sets Section J Fall 2006 Question M2-9 The uniform rod AB which has a mass of 45 kg is supported at A by a ball-and-socket, at B by a smooth vertical wall in the y-z plane, and by cable CD. Point C is 240 mm above the x-z plane. Determine the force in the cable. Question M2-10 The beam BC is subjected to the shown loading and is held by a hinge at C and a single rope tied at A and B. Find the reaction components at C and the tension in the rope [Note: you have to show a FBD]. CIV-101F Sample Problem Sets Section J Fall 2006 Question M2-11 The boom AB of weight 50kN is supported by a ball-and-socket joint at A and by the two cables at B. The boom is subjected to two F forces of magnitude 75kN and 140kN that act in the x-y plane [the 75KN force is parallel to 8m the Y axis]. a. Calculate the tension in each cable and the reaction components at A [Note: you have to 6m show a FBD] b. if the weight of the boom is 3000kg, which E values in “a” would change? By How much? Question M2-12 The pipe AD is subjected to a 800N.m couple that twists the pipe around the y and z axis as well as a 500N force acting as shown. The pipe is supported by a ball and socket at D, a cable at B and a bearing at A that provides only 2 reaction components in the x and y directions. Determine the force in cable CB and the 2 reaction components at A. CIV-101F Sample Problem Sets Section J Fall 2006 Question M2-13 The concrete slab is being hoisted with constant velocity using the cable arrangement shown. If the slab has a mass of 1800 kg and a center of gravity at G determine the tension in the 1m supporting cables AC, BC and DE. 1.5m 2m 1.5m 1m Question M2-14 200mm A building column is subjected to a 1500N force acting at the end of a 1500N supporting bracket. Replace this force with an equivalent force and couple moment acting: a) At point O b) At point A 3200mm 120mm 90mm