PROBLEM 2.9. sin 75 sin 65. R = 665 lb. sin 75 sin 40
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1 POBLEM 2.9 A telephone cable is clamped at A to the pole AB. Knowing that the tension in the right-hand portion of the cable is T lb, determine b trigonometr (a) the required tension T 1 in the left-hand portion if the resultant of the forces eerted b the cable at A is to be vertical, (b) the corresponding magnitude of. Using the triangle rule and the law of sines: (a) β 180 β lb T1 sin 75 sin 65 T lb (b) 1000 lb sin 75 sin lb 11
2 POBLEM 2.18 For the hook support of Prob. 2.10, knowing that P 75 N and α 50, determine b trigonometr the magnitude and direction of the resultant of the two forces applied to the support. POBLEM 2.10 Two forces are applied as shown to a hook support. Knowing that the magnitude of P is 35 N, determine b trigonometr (a) the required angle α if the resultant of the two forces applied to the support is to be horizontal, (b) the corresponding magnitude of. Using the force triangle and the laws of cosines and sines: We have β 180 ( ) 105 Then and (75 N) + (50 N) 2(75 N)(50 N)cos ,066.1 N N sinγ sin N N sinγ γ Hence: γ N
3 POBLEM 2.34 Determine the resultant of the three forces of Problem POBLEM 2.24 Determine the and components of each of the forces shown. Components of the forces were determined in Problem 2.24: Force Comp. (lb) Comp. (lb) 102 lb lb lb i+ j ( 152 lb) i+ (60.0 lb) j 60.0 lb lb α lb sin lb
4 POBLEM 2.46 Knowing that α 55 and that boom AC eerts on pin C a force directed along line AC, determine (a) the magnitude of that force, (b) the tension in cable BC. Free-Bod Diagram Force Triangle Law of sines: (a) (b) FAC TBC sin 35 sin 50 sin 95 F AC sin 35 sin 95 T BC sin 50 sin 95 F lb AC T 231 lb BC 48
5 POBLEM 2.57 Two cables tied together at C are loaded as shown. Knowing that the maimum allowable tension in each cable is 800 N, determine (a) the magnitude of the largest force P that can be applied at C, (b) the corresponding value of α. Free-Bod Diagram: C Force Triangle Force triangle is isosceles with 2β β 47.5 (a) P 2(800 N)cos N Since P 0, the solution is correct. P 1081 N (b) α α
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