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HW9 - PROBLEM 3.70 Two 60—mm-diameter pegs are mounted on...

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Unformatted text preview: PROBLEM 3.70 Two 60—mm-diameter pegs are mounted on a steel plate at A and C. and two rods are attached to the plate at B and D. A cord is passed around the pegs and pulled as shown, while the rods exert on the plate lO-N forces as indicated. (9) Determine the resulting couple acting on the plate when T = 36 N. (b) If only the cord is used. in what direction should it be pulled to create the same couple with the minimum tension in the cord“? (c) Determine the value of that minimum tension. SO LUTION (:1) Have (11) Have M = £(Fd) : (36 N)(0,345 m) - (10 N)(0.380 m) z 8.62 N~m M = 8.62N-m ) 4 M : Td : 8.62N-m For T10 be minimum, 51 must be maximum. and (c) Have where . T min must be perpendicular to line AC = 1.33333 19 : 53.130o or 3:53.1°‘ M=T mindmax M = 8.62 N-m [ (0.380)2 + (0.285)2 + 2(0.030)] m 2 0.535 m 8.62 N-m = 3.40.535 m) T min =16.ll2lN or Tmin : 16.11 N 4 PROBLEM 3.81 A landscaper tries to plumb a tree by applying a 240—N force as shown. Two helpers then attempt to plumb the same tree, with one pulling at B and the other pushing with a parallel force at C. Determine these two forces so that they are equivalent to the single 240-N force shown in the figure‘ SOLUTION Based on ER: —(240 N)cos30° = 4‘]; cosa — Fccosa or —(FB + Facesa = 7(240 N)cos30° (I) SF); (240 N)sin30“ : ngina + china or (F3 + Fdsina : (240 N)sin30° (2) From _—:2:::::: ((213: tana = tan 30° or : 30° Based on ZM(-: [(240 N)cos(30° — 20°)](0.25 m) : (F3 cos10°)(0.60 m) F5 2 100 N or F3 : 100.0N :t. 3004 From Equation (1), 7(100 N + E-)cos30° : 7240c0530° Ff. = 140 N or PC : 140.0 N L‘s. 30” ‘ PROBLEM 3.90 An eccentric, compressive 270-11) force P is applied to the end of a. cantilever beam. Replace P with an equivalent force-couple system at G. SOLUTION Have 2F: —(2701b)i = F F : 7(2701b)i4 Also, have EMU: rAEG x P = M i j k 270 0 —4 —2.4 lb-in. : M 71 0 0 M z (270 lb-in.)[(72.4)(—l}j —(—4)(71)k] or M = (643 lbvin.)j —(]080 lb-in.)k4 ...
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