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hw3_sol

# hw3_sol - ENGINEERING MECHANICS STATICS 2nd Ed W F RILEY...

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Unformatted text preview: ENGINEERING MECHANICS - STATICS, 2nd. Ed. W. F. RILEY AND L. D. STURGES 2-58 For the force shown in Fig. P2—58 {a} Determine the x, y, and z scalar components of the force. (b) Express the force in Cartesian vector form. SOLUTION {a} 9;? F cos ¢ 475 cos 60° 237.5 F sin ¢ 445 sin 60° = 411.4 a 411 N FXY cos = 237.5 cos (-127°} —142.93 N a —142.9 N ny sin 6 = 237.5 sin {—127°) —189.68 N a -139.7 N = «142.9 E — 139.7 3 + 411 E N 2-59* For the force shown in Fig. P2-59 (a) Determine the x, y, and z scalar components of the force. (bl Express the force in Cartesian vector form. SOLUTION [a] d = x2 + y2 + z 2 + (10 )2 + (8)2 = 14.142 X F cos 9 = - 254.6 1b 3 255 1b F cos 9Y - 424.3 1b = F cos 62 = 339.4 lb A {b} F = 255 i + 424 ENGINEERING MECHANICS - STATICS, 2nd. Ed; W. F. RILEY AND L. D. STURGES 2—63* Two forces are applied to an eyebolt as shown in Fig. P2—63. (a) Determine the x, y, and z scalar components of force F1. (b) Express force F1 in Cartesian vector form. (c) Determine the angle a between forces F1 and F2. Fig. P2-63 SOLUTION (—6)2 + (3)2 + (7)2 = 9.695 ft ’ -556.99 lb 2 -557 lb 278.49 lb a 278 lb 649.82 lb 2 650 lb + 278 3 + 650 R lb (—6)2 + (6)2 + (3)2 = 9.00 ft 6 _ 2 9.695 3 ENGINEERING MECHANICS - STATICS, 2nd. Ed. W. F. RILEY AND L. D. STURGES 2—32* Determine the magnitude R of the resultant and the , and 9 Y z . between the line of action of the resultant and the angles 6x, 9 positive x-, y-, and z- coordinate axes for the three forces shown in Fig. P2—82. SOLUTION e 47.29° A): II d- 9:! = 63.430 CD II ﬂ. BO {3 63.430 33 II 6 + 8 x FA cos AX FB cos 80 cos 47.29° + 100 cos 63.430 + ?5 cos 90° = 08.99 N + FC cos 6 Bx Cx 53 II F cos 6 + F8 cos 9 6 y A A? + FC cos BY CY -80 cos 42.710 + 100 cos 26.5?0 + ?5 cos 63.430 = 64.20 N :13 ll - 8 2 FA cos A2 + F3 cos 6 80 cos 90° + 100 cos 90° + T5 cos 26.570 = 67.08 N R = /R: + R: + R: /{98.99)2 + {64.20)2 + (67.08}2 135.?2 + PC cos 9 B2 C2 1| N i 135.? N O 43.17° s 43.2 Ans. 61.77° 60.380 ENGINEERING MECHANICS - STATICS, 2nd. Ed. W. F. RILEY AND L. D. STURGES 2-84 Determine the magnitude R of the resultant and the angles 8 , 9 , and 9 between the x y z line of action of the resultant and the positive x—. y—, and z— coordinate axes for the three forces shown in Fig. P2-84. SOLUTION A a = 2 1 + 5 + 0 ﬂ = 0.3714 3 + 0.9285 3 + 0 E 1 . 1212 + (5)2 + (0)2 A a = ~—3—l—i—§—l—i—3—E—— = 0.5298 3 + 0.8823 3 + 0.5298 E 2 V1472 + {512 + (4}2 0 + 2 + 4 E = 0 i + 0.4472 3 + 0.8944 R E = ____l__a__Ja.m__.__. 3 x” 2 2 2' (0} + (2) + {4} 10(0.3714 i + 0.9285 3 + 0-1?) = 3.714 T + 9.285 3 kN 12(0.5298 i + 0.6623 3 + 0.5298 E) A = 6.358 1 + 7.948 3 + 6.358 E kN F = 5363 = 8(0 3 + 0.4472 3 + 0.8944 E1 = 3.578 3 + 7.155 E kN ﬁ = F1 + F2 + F3 10.072 3 + 20.811 3 + 13.513 E lb (10.072)2 + (20.811}2 + (13.51312 kN a 26.8 kN 0 57.91° s 87.9 = 39.00° G) H O O 6‘) II 0 O 0‘) II 01 to a: 9 cos = cos ' = 59.700 Ans. ‘7? ENGINEERING MECHANICS - STATICS, 2nd. Ed. ’ RILEY AND L. D. STURGES A homogeneous cylinder weighing 500 lb rests against two smooth planes that form a trough as shown in Fig. P3-3. Determine the forces exerted on the cylinder by the planes at contact points A and B. SOLUTION From a free-body diagram for the cylinder: + T 2F = F cos 30o - W y B FB cos 30 5'7.35 '77 lb . 0 FA — FB Sln 30 FA - 577.35 sin 30° = 0 288.68 lb E 289 lb = 289 lb —+ A ENGINEERING MECHANICS - STATICS, 2nd. Ed. W. F. RILEY AND L. D. STURGES The collar A shown in Fig. P3—7 is free to slide on the smooth rod BC. Determine the forces exerted on the collar by the cable and by the rod when the force F = 900 lb is applied to the collar. SOLUTION From a free—body diagram for the collar: + /” ZFx, = T cos 50o - 900 cos 600 = 0 = 700.08 lb a 700 lb T = 700 lb E 20.00 = FA - 900 sin 60° — T sin 50° FA - 900 sin 60° - 700.08 sin 50° 0 1315.71 lb 3 1316 lb FA = 1316 lb E 60.00 ...
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