Question

Prob. 3 A slender uniform homogeneous bar of total mass 2 kg is used to stiffen the 4 kg rectangular plate, as shown, along all its four sides. Determine a) The total length of the bar b) The total mass of the assembly c) Its center of mass location, G. d) determine the moment of inertia e) and radius of gyration about G. 300mm A 300mm + 400mm Prob. 4 The stiffened plate described in Prob 3 above, and supported at the hinge at A is released from rest in the vertical position shown. Determine, immediately after release: a) The magnitude and sense of the angular acceleration, and b) The reaction components at A. Prob. 5 Consider when the stiffened plate in Prob 4 above has rotated through 90°, determine: a) its angular velocity and acceleration; and b) the reaction components at A

Answer 1

pevimeter af the vettanulay Prob tolal ingth of bar 2(600+400) m 2000 mm Omele 0Total mass of assembly moss of clesidey Vin Rectugular ptoles bn=la(u+) t ilocolion of hinge A is arigin then with vespect to hs (20omm,o) mm (0.2m ,0 m(a't bi 200m 2 gamm 1:2 where 1a moment of inerta a bout total mass 400mm 0 4m 0.6 m 60omm (e-4)+ (0-6'} 12 +0.36) +91.0 1eg m 0-26 eg mi k is the rad of gfration. it mk fhen 261gim O.26 Scanned with ehhstane

Prob Meem Conven han Mament of iner tia abaut hinge A + m co-2)2 from paralll anis thearem 60omb O 26 t 6 X O-04 IA 0.m 400mm d is angular accelerelration mgxo-2 Nm 6(9.8)X0-2 Nm 1176 Nm 23.52 vads clockwise Sense from free body cliogram Ny Since bedy is in translation equlibrium hence NyMg Nn N6xg.8 N 58.8 N Scanned with GamScanner

Drob o5 0.6m From mechani cal energy Ny Conseruation wrt center of the plate 0-4m loss in potentral energy Gain in Kinetic Energy M Co-2) w2 mgco 2) 2mg(o.2) Yadis A 2X6X9.8x0.2 6.86 radls O.5 hecaune heferces Rasgis fh dO from figure it was cleay fhat 6xg. 6 x0-2x (6.6 115.27N be cause line of action of forces passeas T=0 ,ブ=0 CS Scannphroih anis of roa tion A imamScanne