Ex 4
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Statics – Exercise No. 4 3.104 A rectangular block is acted upon by the three forces shown, which are directed along its edges. Replace these forces by an equivalent wrench and determine (a) the magnitude and direction of the resultant force R, (b) the pitch of the wrench, (c) the point where the axis of the wrench intersects the yz plane. Answer: (a) R = 56.6 N; θx = 45°; θy = 90°, θz = 45° (b) p = -25 mm (c) y = 125 mm; z = 137.5 mm
3.122 Replace the three forces showing by (a) a force-couple system at A, (b) a wrench. (Specify the pitch and axis of the wrench.) Answer: p = 48.0 mm; x = 123.2 mm, y = 0 4.2 A gardener uses a 50-N wheelbarrow to transport a 220-N bag of fertilizer. What force must she exert on each handle? Answer: F = 36.8 N 4.3 The gardener of prob. 4.2 wishes to transport a second 220-N bag of fertilizer at the same time as the first one. Determine the maximum allowable horizontal distance from the axel A of the wheelbarrow to the center of gravity of the second bag if she can hold only 65 N with each arm. Answer: x = 257 mm 4.10 Three loads are applied as shown to a light beam supported by cables attached at B and D. Knowing that the maximum allowable tension in each cable is 12 KN and neglecting the weight of the beam, determine the range of values of Q which the loading is safe when P = 0. Answer: -8.5 kN ≤ Q ≤ 10.25 kN
4.16 The lever AB is hinged at C and attached to a control cable at A. If the lever is subjected at B to a 500-N horizontal force, determine (a) the tension in the cable, (b) the reaction at C.
Answer: (a) FAD = 400 N (b) C = 458 N ∠ 49.1° 4.18 Determine the reactions at A and B when (a) α = 0, (b) α = 90°, (c) α = 30°. Answer: (a) A = B = 187.5 N (b) A = 488 N ∠50.2°; B = 313 N (c) A = 249 N ∠71.2°; B = 160.8 N ∠120°
4.27 A 70 kg overhead garage door consist of a uniform rectangular panel AC, 2100 mm high, supported by the cable AE attached at the middle of the upper edge of the door and by tow sets of frictionless rollers at A and B. Each set consist of two rollers located on either side of the door. The rollers A are free to move in horizontal channels, while the rollers B are guided by vertical channels. If the door is held in the position for which BD = 1050 mm, determine (a) the tension in cable AB, (b) the reaction at each of the four rollers. Answer: (a) T = 549 N (b) A = 343 N B = 275 N 4.34 A uniform rod AB of length l and weight W is suspended from to cords AC and BC of equal length. Determine the angle θ corresponding to the equilibrium position when a couple M is applied to the rod. −1 2 M cot α Answer: θ = sin Wl
4.38 A force P of magnitude 400 N is applied to end E of cable CDE which passes under pulley D and is attached to the mechanism at C. neglecting the weight of the mechanism and the radius of the pulley, determine the value of θ corresponding to equilibrium. The constant of the spring k = 4 kN/m, and the spring is unstretched when θ = 90°. (Hint: solve by trial and error.) Answer: θ = 19.4°
3.122 Replace the three forces showing by (a) a force-couple system at A, (b) a wrench. (Specify the pitch and axis of the wrench.) Answer: p = 48.0 mm; x = 123.2 mm, y = 0 4.2 A gardener uses a 50-N wheelbarrow to transport a 220-N bag of fertilizer. What force must she exert on each handle? Answer: F = 36.8 N 4.3 The gardener of prob. 4.2 wishes to transport a second 220-N bag of fertilizer at the same time as the first one. Determine the maximum allowable horizontal distance from the axel A of the wheelbarrow to the center of gravity of the second bag if she can hold only 65 N with each arm. Answer: x = 257 mm 4.10 Three loads are applied as shown to a light beam supported by cables attached at B and D. Knowing that the maximum allowable tension in each cable is 12 KN and neglecting the weight of the beam, determine the range of values of Q which the loading is safe when P = 0. Answer: -8.5 kN ≤ Q ≤ 10.25 kN
4.16 The lever AB is hinged at C and attached to a control cable at A. If the lever is subjected at B to a 500-N horizontal force, determine (a) the tension in the cable, (b) the reaction at C.
Answer: (a) FAD = 400 N (b) C = 458 N ∠ 49.1° 4.18 Determine the reactions at A and B when (a) α = 0, (b) α = 90°, (c) α = 30°. Answer: (a) A = B = 187.5 N (b) A = 488 N ∠50.2°; B = 313 N (c) A = 249 N ∠71.2°; B = 160.8 N ∠120°
4.27 A 70 kg overhead garage door consist of a uniform rectangular panel AC, 2100 mm high, supported by the cable AE attached at the middle of the upper edge of the door and by tow sets of frictionless rollers at A and B. Each set consist of two rollers located on either side of the door. The rollers A are free to move in horizontal channels, while the rollers B are guided by vertical channels. If the door is held in the position for which BD = 1050 mm, determine (a) the tension in cable AB, (b) the reaction at each of the four rollers. Answer: (a) T = 549 N (b) A = 343 N B = 275 N 4.34 A uniform rod AB of length l and weight W is suspended from to cords AC and BC of equal length. Determine the angle θ corresponding to the equilibrium position when a couple M is applied to the rod. −1 2 M cot α Answer: θ = sin Wl
4.38 A force P of magnitude 400 N is applied to end E of cable CDE which passes under pulley D and is attached to the mechanism at C. neglecting the weight of the mechanism and the radius of the pulley, determine the value of θ corresponding to equilibrium. The constant of the spring k = 4 kN/m, and the spring is unstretched when θ = 90°. (Hint: solve by trial and error.) Answer: θ = 19.4°
