Thevertical beam is 15.0 kg and 1.00 m long and thehorizontal beam
is 25.0 kg and 2.00 m long.
joinedbeams. Express your answer in the form x,y, taking
theorigin at the corner where the beams join.
thejoined beams about an axis through the corner.
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