z 1. Force F is 50 pounds upward. F A. Write the unit vectors for the forces on ring A A from the ropes to B, C, and D, as column vectors named ûp, ûc, and up ? ? 0 ? ? ? 3 ? ? ? ? ? ? -2 ? ? ? -3 R = ? 0 B RR = ? ? -2 ? R = ? -1 ? RD = ? 3 ? ? ? 1 ft ? ? 6 ? ? RBA= RB - RA= ? ? ? -2 ? ? ? LBA= V32 +22 +62 = 7 ? ? 0 ? ? ? 3 ? 0 ? ? ? ? 0 ? ? C 6 ft -y B ? -6 ? ? ? ? 3/7 ? ? 0.4286 ? 2 ft 3 ft R ? ? ? ? -0.2857 ? ÛR= BA = ? -2/7 ? = ? L BA ? ? ? ? ? -6/7 ? -0.8571 ? ? ? ? -3 ? x ? ? -3/146 ? ? Rca = Rc-R= - 1 ? -6 ? ? ? ? ? D 1 ft 2 ft 3 ft ? -0.4423 ? ? ? -0.1474 ? ? ? RCA = ? ? -1/V46 = CA = V32 + 12 + 62 = 46 UCLCA ? ? ? ? ? ? -0.8847 46 ? ? ? ? ? ? -2 ? ? ? -2/7 ? ? ? -0.2857 ? ? ?DA = RD - RA = ? 3 ? LDA= V22 + 32 +62 =7 ûp = RDA = ? ? -6 ? ? ? ? ? 3/7 ? = 0.4286 ? LDA ? ? ? -6/7 ? ? B. Write the equations for equilibrium using the above column vectors. Call the unknown tensions B, C, and D. ? ? ? ? ? ? -0.8571 ûp I B +uc IC tu, ID = - F ? ? ? 3/7 ? ? ? ? -3/ 46 ? -2/7 ? ? ? ? ? -1/746 ? -2/7 ? ? ? 3/7 ? ? ? ? ? ? ? ? ? -6/7 ? ? -6/7 ? ? ? -6/46 ? ? 0 ? ? ? ? 0 ? ? -50 ? ? ? C. Find the tensions in ropes B, C, and D. ? B C D ? ? 3/7 -3/V46 -2/7 ? ? -2/7 -1/V46 3/7 ? ? -6/7 -6/V46 ? ? -0 B = 25.67 lb 0 ? ? - C = 11.30 1b 0 -6/7 -50 ? ? ? ? D = 21.00 lb Page 1 of 2
! B H ! W ! 2. The 8 foot long strut AB has a pin joint at point A, and supports a 500 pound weight W from point B. Cable BC has unknown tension T. C 22! A 35! Fx 8 ft W A. What are the possible reactions on the strut at point A? Vertical force, horizontal force. (No moment reaction because it's a pin joint.)