Question

A force p is applied to a small wheel which rolls on the cable acb aa shown in the fig knowing that the tension in the cable is 600 . Determine the magnitude and direction of p

Answer 1

Answer:

PROBLEM 2.1 Two forces are applied to an eye bolt fastened to a beam. Determine graphically the magnitude and direction of their resultant using (a) the parallelogram law, (b) the triangle rule. SOLUTION (a) (b) R = 8.4 kN We measure: α = 19° R = 8.4 kN 1 19° PROBLEM 2.2 The cable stays AB and AD help support pole AC. Knowing that the tension is 500 N in AB and 160 N in AD, determine graphically the magnitude and direction of the resultant of the forces exerted by the stays at A using (a) the parallelogram law, (b) the triangle rule. SOLUTION We measure: α = 51.3°, β = 59° (a) (b) We measure: R = 575 N, α = 67° R = 575 N 2 67° PROBLEM 2.3 Two forces P and Q are applied as shown at point A of a hook support. Knowing that P = 15 lb and Q = 25 lb, determine graphically the magnitude and direction of their resultant using (a) the parallelogram law, (b) the triangle rule. SOLUTION (a) (b) R = 37 lb, α = 76° We measure: R = 37 lb 3 76° PROBLEM 2.4 Two forces P and Q are applied as shown at point A of a hook support. Knowing that P = 45 lb and Q = 15 lb, determine graphically the magnitude and direction of their resultant using (a) the parallelogram law, (b) the triangle rule. SOLUTION (a) (b) We measure: R = 61.5 lb, α = 86.5° R = 61.5 lb 4 86.5° PROBLEM 2.5 Two control rods are attached at A to lever AB. Using trigonometry and knowing that the force in the left-hand rod is F1 = 120 N, determine (a) the required force F2 in the right-hand rod if the resultant R of the forces exerted by the rods on the lever is to be vertical, (b) the corresponding magnitude of R. SOLUTION Graphically, by the triangle law F2 ≅ 108 N We measure: R ≅ 77 N By trigonometry: Law of Sines F2 R 120 = = sin α sin 38° sin β α = 90° − 28° = 62°, β = 180° − 62° − 38° = 80° Then: F2 R 120 N = = sin 62° sin 38° sin 80° or (a) F2 = 107.6 N (b) 5 R = 75.0 N PROBLEM 2.6 Two control rods are attached at A to lever AB. Using trigonometry and knowing that the force in the right-hand rod is F2 = 80 N, determine (a) the required force F1 in the left-hand rod if the resultant R of the forces exerted by the rods on the lever is to be vertical, (b) the corresponding magnitude of R. SOLUTION Using the Law of Sines F1 R 80 = = sin α sin 38° sin β α = 90° − 10° = 80°, β = 180° − 80° − 38° = 62° Then: F1 R 80 N = = sin 80° sin 38° sin 62° or (a) F1 = 89.2 N (b) R = 55.8 N 6 PROBLEM 2.7 The 50-lb force is to be resolved into components along lines a-a′ and b-b′. (a) Using trigonometry, determine the angle α knowing that the component along a-a′ is 35 lb. (b) What is the corresponding value of the component along b-b′ ? SOLUTION Using the triangle rule and the Law of Sines sin β sin 40° = 35 lb 50 lb (a) sin β = 0.44995 β = 26.74° α + β + 40° = 180° Then: α = 113.3° (b) Using the Law of Sines: Fbb′ 50 lb = sin α sin 40° Fbb′ = 71.5 lb 7 PROBLEM 2.8 The 50-lb force is to be resolved into components along lines a-a′ and b-b′. (a) Using trigonometry, determine the angle α knowing that the component along b-b′ is 30 lb. (b) What is the corresponding value of the component along a-a′ ? SOLUTION Using the triangle rule and the Law of Sines (a) sin α sin 40° = 30 lb 50 lb sin α = 0.3857 α = 22.7° (b) α + β + 40° = 180° β = 117.31° Faa′ 50 lb = sin β sin 40°  sin β  Faa′ = 50 lb    sin 40°  Faa′ = 69.1 lb 8 PROBLEM 2.9 To steady a sign as it is being lowered, two cables are attached to the sign at A. Using trigonometry and knowing that α = 25°, determine (a) the required magnitude of the force P if the resultant R of the two forces applied at A is to be vertical, (b) the corresponding magnitude of R. SOLUTION Using the triangle rule and the Law of Sines Have: α = 180° − ( 35° + 25° ) = 120° Then: P R 360 N = = sin 35° sin120° sin 25° or (a) P = 489 N (b) R = 738 N 9 PROBLEM 2.10 To steady a sign as it is being lowered, two cables are attached to the sign at A. Using trigonometry and knowing that the magnitude of P is 300 N, determine (a) the required angle α if the resultant R of the two forces applied at A is to be vertical, (b) the corresponding magnitude of R. SOLUTION Using the triangle rule and the Law of Sines (a) Have: 360 N 300 N = sin