Question

Problem 1 Equilibrium of a Body in 3D (25pts) Determine the components of reaction at the ball-and-socket joint A and the tension at cables BC and BD necessary for equilibrium. Show Free body diagrams and all calculations for full credit. | 3 m ce 2 m 3 m BL X- 5 m (3 m Ē = 100î – 200Â N 400 N

Answer 1

Drace the Pree Boy diagsam At FBC FBo B Ay 200 N woite pcsiton vectons the - 3 BC E-8 233 C8 m E(5m AB

ectors unit Find the -81-3 3k NE&YC-33 Fa88i-3314033 BC 8 2 Jt 3k co CD 823 o.221 Je3u1 0.91 Find the fonce vecl os FBcec 0.22 33 33k) Fgo F. = F-0.91 it .2227 J+o.341

a bout A, 2MAO moment Take x Fec on, AB calcale Each tem. x Fec +o 33 K) - 2- 64 Fsc 2 64 Fsck

8i FeD-6.9u7+0221 o-34 J FBo - 2-128 FR + 1S16F Te 5ix C-400 ) 2000 be comes Noto Euation O 2-64 F8c 2-128 F J + 2000+ \600 2-64 Fk 816 FsD compece 2.128 Fn + 3 600 O sc - 2. Fes ニ3600 2.64 F8c t2.728

८) COmpare = ০ २६५ Fgc 1.६\৫ +gp 2 6५ fg८ ·৪\ 6 Fgo Fgp = |. ५53+ Fs F০০ ২ (५ Fgct २-1२8x [०५5 3अ F«] 3D 3600 = 5५5-५5 N P০ |०५531 x 5५5-५१ FsD Fop 1१२ १2 M

Find he force uec tors 0.33k t-c.88.3354.331) FBc Foc -0.88i-0.33 -419-111-91 i+19-11J |1१:११ = [- ५19-९१ - 11१. Fgr FeD-0+023 o. 227 +o.341 -122.35 + 179.99 t 240.38 k. eceiDi hstium, ZF=d fonce APply F+FFeo FeD t =0 BC (Ai+ AyJt Az k) Fsc

Comp aae A. u79.99-7 22.35 +100 =6 A 02- 34 N (1१॰११ + (77-११ Ay Ay Az t (79.9f210 38 - 200- 40 = O