Question

The figure shows two thin beams joined at right angles. Thevertical beam is 15.0 kg and 1.00 m long and thehorizontal beam is 25.0 kg and 2.00 m long.

Find the center of gravity of the two joinedbeams. Express your answer in the form x,y, taking theorigin at the corner where the beams join.

Calculate the gravitational torque on thejoined beams about an axis through the corner.

Answer 1

    mass of horizontal beam , M1 = 25 kg
    mass of vertical beam, M2 = 15 kg
    length of horizontal beam, L = 2m
    height of vertical beam, H = 1m
    center of gravity of horizontal beam, ( X1, Y1 )= ( L/2 , 0 ) = ( 1 m , 0 )
    center of gravity of vertical beam , (X2, Y2 ) =( 0 , H/2) = ( 0, 0.5 m )
    center of gravity of the combination,
                         ( Xcm , Y cm ) = [ ( M1 X1 + M2 X2 ) / ( M1 + M2 ) , ( M1 Y1+ M2 Y2 ) / ( M1 + M2 ) ]
                                = [ ( 25 / 40 ) , ( 7.5 / 40 ) ]
                                = ( 0.625 m , 0.1875 m )
    Gravitational torque, τ = Force *perpendicular distance from axis of rotation
                                      = ( M1 g ) ( L/2 ) + ( M2 g ) ( 0 ) = 25 * 9.8 * 1 = 245 Nm