What is M F x , the contribution to the moment about point O made by the x compo

Question

What is MFx, the contribution to the moment about point O made by the x component of the force F at point B? What is MFy, the contribution to the moment about point Omade by the y component of the force F at point B? What is the total moment Mdue to the force F about point O? Assume that moments acting counterclockwise about point O are positive whereas moments acting clockwise are negative.A rope is attached to a l=5.50m high shed that is to be relocated. A man pulls on the end of the rope at point A; the rope is attached to the shed at pointB.As the man pulls on the rope, it creates an angle ? with the horizontal. The end of the rope is located at x=2.70m from the shed and y=1.00m off the ground. The man pulls on the rope with a force of magnitude F=235N. MFx,MFy,M=

Explanation / Answer

F = 235 N

tan@ = (l-y) / x = (5.50 -1) / 2.70 =1.67

@ = 59.04 deg

moment due to any force = r x F ( cross product )

= |r||F|sin@
where @ is the angle between r and F .

Fx = Fsin@ = 235sin59.04 = 201.52 N

r = l = 5.50 m

@ = 90 deg

MFx = 5.50 x 201.52 x sin90 = 1108.35 Nm

nwo for MFy ,

Fy = 235cos59.04

r = l = 5.50 m

@ = 0 deg

Mfy = 0

total moment = MFx + MFy =1108.35 + 0 = 1108.35 N m

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