Question

1. The 6-m pole ABC is acted upon by a force Pos shown. The pole is held by a ball-and-socket joint at A and by two cables BD and BE. If the tension in cable BE is 158 N and if a : 3m, determine the reaction at A along the y-axis. 3 m P 3 m 15 1.5 m 2. | The 6-m pole ABC is acted upon by a force P as shown. The pole is held by a ball-and-socket joint at A and by two cables BD and BE. If the tension in cable BE is 250 N and if a : 3m, determine the tension in cable BD 3 m P 3 m 1.5 m F 3 1.5 m

Answer 1

co-ordinates of points AB = (0,3,0) TA (0,60) CF = ? - Z w = (-5, -6,2) B = (0,3,0) as A-(0/0-0). To C = (01610) E = (15,0.3) OBEE-B = (1.5,-3,3) F=(-3,0,2) ABD = B = (155) 3) o D = (1.503) P = 1P1 C ICFL 1 158 158 FBE - 250 B 1B티 IPI ( -34 – 65+212) how 32+62+4 IP) (-32-67 +22) 7 250 (1.si - 3} +32) 32+32 +1.52 Ish-39 +3 it) N ( 15 î - 39 - 3R) 5 32+32 +1.52 T (1.51-39-32) N 4.5 158 us TBD - T. BD BP CF MA=0 AB XFBE + AB TBD + CAXB=0 3- so 0 30 To 0 6 0 - 3 - 6 2 158 0 30 1.5-33 + 4.5 1.5-3-3 4.5 - 1 (9-0)x158 1 4.5 k x 4.5 x 158 + ?(-9)x I - î x 4.5 x1 4.5 mot 4.50 mar 4.5 IPL êx 12 + 18 20 IP) 7 + 7 -2T +121P1 k 158-1] → [ 158 18 IPL 7 21 0.5 Each parto 15892 -- 2T-121PL -T + L81P) - 158

Solving (EG) T-43-203166 (P/= +24007 184.33 Ain y dian Ay SP 4.5 184.33 13 1201-3) =0 word 4.5 4.SAN to 1711-51-39 - 3k) w i 3100 Let reaction along for Stanic equilibrium {fy=0 Hy + 4(-6) + 1583 (-3) + T (+3) Ay + 124.44 (-6) 158(-3) py 4740 N (2) FBF 4:53 (SLOUSE + 7 32.20 N VA Bosco B = 181 (- 3 2 - 67 + 2) - 250 (1.51-39 + 3Q ) 'N 4.5 31

MAFO -ABFBE AB x TBD + CA x P = 0 + * + o 3o ГИ 71-3-62 O 3 o 1.5 -33 4.5 45 7.5-3-3 î.9x250 4.5 - 2 x 4.5 x 250 - 2 xqx1T) - î x 4.5 x T) 4.5 4.5 + 1P1 x 12 2 + 111x18? 4.5 7 -D [ 500 - 2171+1242] + [ 18 -250 -til- fu) 121P1 - 2111 - Soo 7 181PL - IT +250 7 Solving ① & 1 = 18 291.67 500 Tension in Cable BD = SOON Ano