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 1.- El mástil está sometido a las tres fuerzas mostradas. Determine los angulos directores coordenados de alfa, beta y delta de F1 de manera que la fuerza resultante que actua sobre el mástil sea cero  F1= ? F2= 200 N F3= 300 N  F2= (-200i+0j+0k)  F3= (0i-300j+0k)  F1+F2+F3=0  F1=-F2-F3 F1= - (0i+0j-200k) - (0i-300j+0k)  F1= (i+300j+200k) F1 = F1= 360.55 N   500 cos a= 0 a = cos inv (0/500) a= 90°  500 cos b= 300 a = cos inv (300/500) a= 53.1°  500 cos c= 200 a = cos inv (200/500) a= 66.42°  2.- Si F3=9Kn, d=30°, p=45°, determine la magnitud y los angulos conectores coordenados de la fuerza resultante que actua sobre la junta de la rotula  F1= 10kN F2= 8kN F3= 9kN  F1= 10 cos60°sin30°(-i) + 10 cos60°cos30°(+j) + 10 sin60(-k)  = ( -2.5i + 4.33j – 8.66k) kN  F2 = 8(3/5)(-i)+ 8(4/5)(k)  = (-4.8i +6.4k)kN <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: -25px; width: 1px;"> F3 = 9 cos45°sin30°(+i) + 9 cos45°cos30°(-j) +9 sin45°(-k) <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: -25px; width: 1px;"> = (3.182i -5.511j -6.364k) <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: -25px; width: 1px;"> FR= F1+F2+F3 <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: -25px; width: 1px;"> = (-4.118i -1.181j -8.624k) kN <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: -25px; width: 1px;"> FR = = 9.630 kN  <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: -25px; width: 1px;"> a = cos inv (-4.118/9.63)= 115.31° <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: -25px; width: 1px;"> b = cos inv (-1.181/9.63)= 97.04° <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: -25px; width: 1px;"> c = cos inv (-8.624/9.63)= 153.57° <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: -25px; width: 1px;"> 3.- Determine la magnitud y los angulos directores coordenados de la fuerza resultante que actua en A <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: -25px; width: 1px;"> Fg = 900 N Fc = 600 N <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: -25px; width: 1px;"> ug= <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: -25px; width: 1px;">{ .4243i -.4243j - .8k} <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: -25px; width: 1px;"> uc = <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: -25px; width: 1px;">-1/3 i - 2/3 j - 2/3 k <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: -25px; width: 1px;"> Fg= fg*ug= 900(.4243i -.4243j - .8k) = 381.84 i – 381.84 j – 720k <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: -25px; width: 1px;"> Fc = fc*uc=600(-1/3 i - 2/3 j - 2/3 k) = -200 i – 400 j - 400 k <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: -25px; width: 1px;"> Fr=Fg+Fc = (381.84 i – 381.84 j – 720k) + (-200 i – 400 j - 400 k) = (181.84 i – 781.84 j – 1120 k) N <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: -25px; width: 1px;"> Fr = = 1377.94 N  <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: -25px; width: 1px;"> a = cos inv (181.4/1377.94)= 84.41° <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: -25px; width: 1px;"> b = cos inv (-781.84/1377.94)= 124.595° <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: -25px; width: 1px;"> c = cos inv (-1120/1377.94)= 144.42°