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

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

    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