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 2 1000 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) 75 + 40 + β 180 β 180 75 40 65 1000 lb T1 sin 75 sin 65 T 1 938 lb (b) 1000 lb sin 75 sin 40 665 lb 11
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 (50 + 25 ) 105 Then and 2 2 2 (75 N) + (50 N) 2(75 N)(50 N)cos105 2 2 10,066.1 N 100.330 N sinγ sin105 75 N 100.330 N sinγ 0.72206 γ 46.225 Hence: γ 25 46.225 25 21.225 100.3 N 21.2 20
POBLEM 2.34 Determine the resultant of the three forces of Problem 2.24. 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 48.0 +90.0 106 lb +56.0 +90.0 200 lb 160.0 120.0 152.0 60.0 i+ j ( 152 lb) i+ (60.0 lb) j 60.0 lb 152.0 lb 0.39474 α 21.541 60.0 lb sin 21.541 163.4 lb 21.5 36
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 172.7 lb AC T 231 lb BC 48
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 180 85 β 47.5 (a) P 2(800 N)cos 47.5 1081 N Since P 0, the solution is correct. P 1081 N (b) α 180 50 47.5 82.5 α 82.5 59