Determine the directional sense and the magnitude of the res

Determine the directional sense and the magnitude of the resultant moment about the origin by scalar analysis and vector analysis.

FA = 400cos30 i +400 sin30j = 346.4i + 200 j N

rA = 2i - 5j

FB = 260(5/13)i + 260(12/13)j = 100i + 240j N

rB = 6i + 0j m

resultant moment = rA x FA + rB x FB

= [ (2i - 5j) X ( 346.4i + 200 j )] + [ (6i + 0j) X (100i + 240j)]

= [ 400k + 1732k] + [ 1440k]

= 3572 k N m

Magnitude = 3572 N m

direction = couter - clock wise

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Or Horizontal distance of A form origin = 2 m

and vertical component = 400 sin30

moment1 = 400 N m ccw

vertical distance of A = 5 m

horizontal component = 400 cos30

moment2 = 5 x 400cos30 = 1732 N m ccw

vertical distance of B = 0

hence moment = 0

horizontal distance = 4 + 2 = 6 m

vertical component = 260 x 12 / 13 = 240 N

moment3 = 1440 Nm ccw

net moment = 3572 N m ccw