Question

The two ropes attached to the hook in the figure below are pulled on with forces of F1 = 150 N and F2 = 300 N. What size single force acting in what direction would produce the same effect?
F1 45 Degrees
F2 30 Degrees
F1 = 150 N. @ 45 Deg.
F2 = 300 N. @ 30 Deg.

X = hor. = 150*cos45+300*cos30 = 366 N.
Y = ver. = 150*sin45+300*sin30= 256 N.

tanA=Y/X = 256/366 = 0.6996,
A = 35 Deg.

F = X/cosA = 366/cos35=447 N. @ 35 Deg.

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