Question

4.) Determine the force T required to balance the system shown, and the pin reactions at points C and B. Assume pulleys at A and D are small relative to the members shown. 6A 2' 7' 75lb/ft A 55 5' T 6' 31

Answer 1

free body diagram for pulley system

T

as the distance is small forces  can be assumed to act at center of pulley

free body diagram of arm CDE is

T TK Re 6¢
as it is hinged at c taking moments about c zero we get
Moment abot point c Tue 2r (Cos 6)13') Cato) -T C3) aT Sino Re F(3) 0:4a 9-53-130 - ar Co6)(3')-2aT 0s (3') 0 Re Ca)-T3 3.6T -4.8T-O Re -3T 114T -0 9 Re 11-4 Re: T 1-2666 T Re

now free body diagram of leaver is

f8 o the (ave 75 blft 6 It aT Re

now taking moments about B we get

so the value of T is found and minimum of that value is required to maintain equilibrium .

ON Equilibhum Condtonu momont abat B' -2T Cooe Cs') +5**') (2+35') Re (a) (S.S txst 3994T 1-2666 T () Co-6) 50 S.t880 T 165.94 88 ib - 6T