Question

two cables attached to the pipe assembly each apply a force

Name: Date: Problem 1 (20 points) Two cables attached to the pipe assembly each apply a force, which will generate a moment about the support. (These forces are listed in Cartesian form in the diagram below). F:- (-101 + 25j + 2Ok] Ib F1 = 1-208-10j + 25k]}b T 12 It 15 2 211 -21 Part A: Calculate the resultant force Fr acting on pipe assembly. Express your answer as a Cartesian vector (2 points). Part B: At what angle (a) does the resultant force (FR) act relative to the x axis (4 points). Part C: Determine the resultant moment Mr about point 0. Express your answer as a Cartesian vector (14 points)

Answer 1

F = 1–207 – 107 + 25K] 16 F2 = (-107 + 25j +20K] 16 (A) FR=F1+ → Fr= (–207 – 107 + 25] + [-107 + 257 + 20% +F, = (–307 + 15j + 45k] lb (B) F. -30 cosa = |FR 302 + 152 152 = -0.53452 → a= cos-1(-0.53452) = 122.31°

(C) Position vectors ři = [1.57 + 2] ft r2 = [1.57 +41 + 2K] ft Resultant moment about O MR=ři x Ft + 72 x F2 MR = 1.5 2 0 + 1.5 4 2 -20 -10 25 |-10 25 20 → MR = [501 – 37.5j +25k] + [301 – 50j +77.5K → MR = [801 – 87.5j + 102.5k] lb.ft