Question

For the composite length shown below, determine the total length [units] given that X = 77, Y = 120 units b) Determine the position of the x-centroid [units] c) Determine the position of the y-centroid [units] d) Determine the position of the Z-centroid [units] 60° с B 12

Answer 1

E 3 Scanned with CamScanner

Let mass per unit length be in?, Now we will to safe cenfond of segonants AD, De, arco C to B SAB 212 (1) AD; Coordinate of C.G.. @,y, (@,120, 38.5) (8) rector to C.G. of AD = 19 = 0.3 + 120 + 38.5k. De, Co-ondinate of G.G = (0, 912, 2) = (0,60,77) Vector to C. G. of Death oft bo] + 836 Angle=29=60°07/3 Asclength Rsind 2 Ž TX 77 3 ga for are to B src = 9 = 77 cout "76. (in roadjans 60 30 = 2 X2 o 77 * sin 80° = 73.566 endt. 1/6 Comoroinate = 10 ÉJ COS 30 = 63.710 unit. 2- Co-ordinate - 10€ sin 30 = 36.783 unit. Scanned with CamScanner

Vector to O.G.E - F = 36.483 +0j +63.71ok. ( ) 13 AB - 1912+y? = 142-579 units. (OB) singo ر 33-342 - Coordinate 2- Co-ordinate les y ces coº: 19.25 Y123 (20 -60 unit y - Consinate 2 Vector of CG. of AB s Fly = 33.3489 + + 19-25K be as? geren Now cenfroid can from m, & + micemia + murcing N me + m2 +3 + my E M XAD) F, & Cox DC ) x 2 + x Arc etoB) x F3 T(hxM3 brey M X D C + Aro C to B t AB * 1 #9 x rg + 120xi + x 13 + 142. 5aquity on & A + Ph*DC 0777 3 &7 + 1207 11x77 3 + 142.979 Scanned with CamScanner

Com - 79(+ 12023.6k) +1800 + 44% Oxbor (36.78314 0j + 63-710 of 142.589*( 33.34 22 + bolj + 19.25k 1.25€). 1 210k) 1 3 420-122 & (47X0 C 77X0 +620x0 + x 7 x 36.783 H 142.579x 33342 3 ㅓ j( *7120 + 120 x 60 + 5*93 xo + 142.539x cos * (*** 27 x 38.5 + 120x77 & 7 x 63.710f 142.5798) 3 19.25 4720:192 2 *( 18.369) +j (59.487) + K (49.7988 Total length 20.199) 2 4- Centrald 18. 869 enot forom o 59.487 9 1 7 11 47.7988 Scanned with CamScanner