Question

Mystery Problem 5. The uniform plate 26X28 shown weighs 200N and is supported in a horizontal position by a hinge at A at the center of the edge on the y-axis and a cable from B to C. Point B is 2 centimeters from both the edges on y and x-axis on the x-y plane. Point C is 20cm above the x-axis on the z-axis and the center of the edge on x-axis. Find the tension in the cable BC and the reaction forces at the hinge A. (14+6 pts) 20 cm 13cm 13cm A 2cm 2cm B 28cm

Answer 1

Answer' we want to find out cable BC C Tension in TBC Reaction force 13cm १ at hinge A 20cm Iw 28CM LCM B Х Civen a weight of Plate (w) = 200 N know) (This force will act in centraid of Plate that we ① locations of every required point in co-ordinates in also given b let the Methal! Only equilibrium equations. Note: Here A Point in linged so us first calculate Position of other pointa 13 s (end point of cable) with respect to & centroid (26-0) 웃 + (24-18) į + (0-0) e A SBIA 268 +lli SBIA cm 20 centimetess

tos + (13-13) i + (0-0) SIA (14-0) 1ч. cm Tension along calle: TEB Tx unit veetor = TX 64-26) i + (0-24) i (0-24) i + 20-0) I (24)² + Ta TBIC to magnitude (12)2 + (2012 TBC = T +/-128-249 +2012 33.466 TBC = T*(-0.358 i-onni tasan ie) in gonna act no, other left force in weight that downward Cin negative z dirn) W = -200k (în vector) moment at hinge A, Now we will calculate EMA = 0 MA i + MAZE) Lo component of moment in vector form, •B

(Mani + Maze la lrBIA * TBle) + (W x rain ) = 0 (Mayat MAZF) at (26érlli) FRC (-0.3588-000i +0.597ř +(-200 (e) x 14; MAX & + MAzle +6.573 Folce_ls.53 TBici 14.7 TBIL + 2800 20 (MAX +6.573) i +6.573) i + (+5.53 Tric +2800) i + (Az -14079 Compare i, i, k 1 coefficiente Mare + 6.573 TRIC=0 15.53 TBIC +2600 MAZ-14.7 TBIC * Magnitude. TBIC = +2800 +15.53 from @ ITBIC = 160.3 N Ay? Now for calculating reaction : EF 20 Cin the 3 dirn) Řt Teic & w 6 (Axe et Ay ; - + A3 (F) (Axi + Ay i + Az Fe) & 180,3 (-0.3501 -0.0172 +0.597 & w = 0 - 200 lc s

or (An it Ayit Az E) at 664.62 i-129.22; + 107.69%) 200 l = or (Age - 64.62) (Ay - 129.22) i +(Az +107.69) in علوم 2 Compare i, j, k ů, j, k coefficient 64.62 N An Ay A2 = 129.22 N 92.31 N or Reaction at H = (64.228 + 129,22 7 + 92.31 K) ni Answer: Note: 20 All forces nommat in z dirh in gero, and we only uned Tefz=0 EMA = 0 Moment about hinge a in zero.