Class 3 Notes - PROBLEM 2.46 Ropes AB and AC are thrown to...

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Unformatted text preview: PROBLEM 2.46 Ropes AB and AC are thrown to a boater whose canoe had capsized. Knowing that a = 25° and that the magnitude of the force FR exerted by the river on the boater is 70 1b, determine the tension (a) in rope AB, (b) in rope AC. SOLUTION Free-Body Diagram: IA”; 40 l 19 :15" lo" 10° 11¢ 2F; = O: — TABcos25° —- TAC cos40° +(701b)cos10° = 0 (l) 2F), = 0: TABsin25° — TACsin40° + (70 1b)sin10° = 0 (2) Solving Equations (1) and (2) simultaneously: (a) TAB = 38.6 lb 4 (b) TAC = 44.3 lb 4 PROBLEM 2.57 A load of weight 400 N is suspended from a spring and two cords that are attached to blocks of weights 3 W and Was shown. Knowing that the constant of the spring is 800 N/m, determine (a) the value of W, (b) the a unstretched length of the spring. SOLUTION Free-Body Diagram At A: First note from geometry; The sides of the triangle with hypotenuse AD are in the ratio 12:35:37. The sides of the triangle with hypotenuse AC are in the ratio 3:45 The sides of the triangle with hypotenuse AB are also in the ratio 12:35:37. Then: _+- 2p; = 0: flow) +£(W)+13FS = 5 W n 01' Fs = 4.4833W and +12% = 0: gm) + %(W)+§§Fs —400N = 0 Then: %(3W) + ;—:(W) + %(4.4833W) — 400~N ~= 0 01' W = 62.841 N and fl=%HMJ 01' (a) l W = 62.8 N 4 PROBLEM 2.57 CONTINUED (b) Have spring force Fs = k(LAB ‘ L0) Where FAB = kAB(LAB ‘ L0) and LAB = (0.360 m)2 + (1.050 m)2 = 1.110m So: 281.74N = 800N/m(1.110 — lO)m or L0 = 758mm 4 PROBLEM 2.70 h A load Q is applied to the pulley C, which can roll on the cable ACB. The pulley is held in the position shown by a second cable CAD, which passes over the pulley A and supports a load P. Knowing that P = 800 N, determine (a) the tension in cable ACB, (b) the magnitude of load Q. SOLUTION Free-Body Diagram: Pulley C (a) _+. ZFI = 0: TACB(cos3O° — cos50°) — (800 N)cos50° = 0 Hence T AC3 = 2303.5 N TACB = 2.30 kN 4 (b) +1 ZFy = o; TACB(sin3O° + sin50°) + (800 N)sin50° — Q = 0 (2303.5 N)(sin30° + si1150°) + (800 N)sin50° — Q = 0 or Q = 3529.2 N Q = 3.53 kN 4 ...
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