Question

1.0 Consider the forces applied to the object shown below. All connections are rigid. rx=200 mm, ry=400 mm, r = 300 mm. (a) (3 points) if FD = {-10i +40j - 50k} N. Calculate the CVN of the moment Mo created at O by FD; (b) (5 points) Ignore the information in question (a), if the moment created at O by Fp is Mo= {10i + 20j -30k} Nm, and the object is only able to rotate about OC, what are the magnitude and CVN of the component moment along OC? When the object starts to rotate, will point A move approximately upward or downward (explain your answer briefly)? (c) (2 points) If the magnitude of FB is 100 N, to maximize the moment caused by FB about O in the positive y direction, which of the following should be the coordinates of point B? (0,ry, r:), (0, ry, -r-), (Ix, ry, 0), or (Tx, ry, -2r-) Use scalar formulation (i.e. M=Fd) to calculate the magnitude of the moment BOB, B., B.)mm F

Answer 1

soln (a) = 200mm = 0.2m ty = 400 mm = 0.um r = 300 mm = 0.3m Fo=(-10 i +407 -50%)N CUN = Cartesian rector Notation. To = va êtry ] - rz 2 = (02? +0.49 - 0:3R) m > no = ŏ * = (0.2i toy}-03R)x(-10 i +40 sole) 102 oy -03 1-10 40 -50 = 04(-50) - (03)40(-1)] + /603)E10) – 10-2)(+50)J + [ [02(40) – (6-4) (-10)] - î (-20 +12)+ Î ß+10) + Ě (8+4) ño = rî + 139 +121 To Bus

Sale (6) Grinen & Mo= (10ê +207-308) Nm oc = reg ] - rze OT 0:41 -03 Ể anit rector ñ along oc = oča ay 9 -0.312 310C) roygl +1033 I r = 0.4 Î 10.3 0.5 L magnitude then component of no along oc - ñ o mo = (0.47 -0.3). (rol +20-30R) - 0.5 Mon = (0.4) (20) +(-03)(-30) (0-5) (8 + 9) = 134 Nm Ans (NN of año along or = 34 ņ pele. = 39 (wy -0.38) -- And [68 (ory) - 0:32) O 'S 05 eo)

- When Blo, ry, z) & then f is along AB = B Ă = (b ) + r ) - (vai tryj - rE) AB = rei+ZER FB = - ozir og A AB= -0.zitor rozkroto M = OR 0632 =(ry]tre Rx 100 (-okî to GÊ (0.2124(0.622 = (0.4 g + 0.3% 100 (-0.2i to off) = 100 [loy) (2002) gxi +(0.49(06) } XE + (0.3) (-0·2) Exł to ] = 100 -008(-) + 0.24 Î +(0-3) (-0,2)(+2) - 100 oogk tozu 2-0.06 } ] 0-632 I aty=( 100 ) - 086) = -9.5) | My = 9.5) 0-632 L o 632 when Bo, ry, rz) = 3-² = (oîtry 3-rak) - ñs OB FO ! = (by]-re R) x 100 (1) = (0.49 - 0-3K ) (1 ou

Tua (0.47-03 R) & look? = 100 [=com) } xi to3 Rxi] = 100 (on tÊ +0.3 } , My = (100kf0:3) } = +30] When B(ra, ty, B) AB = Bo = (reftryj) - (raît ry jrg El Panel R M = 0B Fo - (x 2 try ) x (100 I) = (azîro 4 x love = 100 [ 0.2 î x C + 0.4 j x2] = 100 (+0-2) -} + 100 (0.4) î My = -20 } ] - My) = 2 )

When B (re ry, 22) ore on = (raîtry ) -2 12 12) - (raîtry jakk) = (-222 +82) AB = -t = OB XF = (beltry} -282K) x 100 (-E) (co zł +o-74 -0.6Ê ) x 1006 €) = 100 [ (0-2) ê x (12) + ou (î x-) fo) = 100 (0.23 -0.42) My z lou Corza ġ = 20) - 1|My) = 20 as maginum magnitude of moment in y direction is my =0 which corresponds to B(0, ry, ore) ire whon point B coincides with e point t then Foo is along x dirn and as B concides with C B lies in y z plane.

Because I lies in yz plane Fo in perpendicular to ob or on then magnitude of moment m=rd = |f8] Doll = loo v (ry? ² + (re)? , &y= 0.4 = 100 ſ (0.9% +63 180 r 0,16+0.08 - 100 xos = so nm + M = 50 Non & Ang r₂ = 0.3