2-13, 2-40, 2-61, 2-86 - ENGINEERING MECHANICS - STATICS....

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Unformatted text preview: ENGINEERING MECHANICS - STATICS. 2nd. Ed. W. F. RILEY AND L. D. STURGES Determine the magnitude of the resultant R and the angle 6 between the x axis and the line of action of the regultant for the two forces shown in Fig. P2-13. SOLUTION 1i ‘1‘ 1 From Eqs. 2-1 and 2*2: ¢ = tan- - tan- 54.160 2 2 2 , R — F_l + F2 + ZFle cos ¢ 6002 + 5002 + 2(600}{500] 005 54.160 980.4? lb 3 980 lb 51" ¢ ‘ -1 500 sin 54.160 = Sin —"'— . o R 980.4? ‘ 34'42 B + 21.30 = 24.42 + 21.30 = 46.22 a 46.2 fl = 980 1b a 46.20 Ans. 2-40* Two forces Fu and Fv are applied to a bracket as shown in Fig. P2-40. If the resultant R of the two forces has a magnitude of 375 N and a direction as shown on the figure, determine the magnitudes of forces F and ? . u V SOLUTION Fu Fv 375 sin 70.35° sin 42.27° sin 67.33° 3?5 sin 67.380 375 sin 67.38o sin ?0.35° 333 N sin 42.27° 273 N For the force shown in Fig. P2—61 F=lflmm {a} Determine the x, y. and z scalar components of the force. lb} Express the force in Cartesian vector form. SOLUTION {a1 d = {(-4}2 + {12)2 + (7)2 = {209 = 14.45? F cos 9x = 1500i-4/V209} = -415.03 lb 3 ~415 lb F cos 6y 1500(12/{209} = 1245.09 lb 3 1245 lb = F cos 6 = 1500(7/{2091 = 726.30 lb 3 726 1b 2 {b} F = —415 i + 1245 j + 726 R lb 2-86 Determine the magnitude R of the resultant and the angles 9 , 9 , and 6 between the x y 2 line of action of the resultant and the positive x-, y-, and z- coordinate axes for the three forces shown in Fig. P2—86. SOLUTION Rx = 10 cos 26° cos 42o - 16 cos 40° sin 350 + 20 cos 50° cos 60° = 6.077 kN Ry = - 10 cos 26° sin 42° - 16 cos 40° cos 35° + 20 cos 50° sin 00° = -4.921 RN R = 10 sin 26° + 16 sin sin 40° + 20 sin 50° = 29.989 kN R = .19: + a: + 2: = {6.077)2 + (-4.921)2 + (29.999)2 = 30.992 RN 2 31.0 kN Ans. _1 Rx -1 9.07? o 0 9x = cos —E = cos 30.992 = 78.69 a ?8.7 Ans. —1 Rx -1 -4.921 0 o 9y = cos -E = cos 30.992 = 99.14 B 99.1 Ans. -1 Rx -1 29.989 0 o 9 = cos - ‘ = 44.06 H 44.1 Ans. 2 R ‘ COS 30.992 ...
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2-13, 2-40, 2-61, 2-86 - ENGINEERING MECHANICS - STATICS....

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