Compute algebraically the resultant of the
following coplanar forces: 100 N at 30O
, 141.4
N at 45O
, and 100 N at 240O
. Check your
answer graphically.
Fx=F1cosα1+F2cosα2+F3cosα3=136.6 N,F_x=F_1\cos\alpha_1+F_2\cos\alpha_2+F_3\cos\alpha_3=136.6~N,Fx=F1cosα1+F2cosα2+F3cosα3=136.6 N,
Fy=F1sinα1+F2sinα2+F3sinα3=63.4 N,F_y=F_1\sin\alpha_1+F_2\sin\alpha_2+F_3\sin\alpha_3=63 .4~N,Fy=F1sinα1+F2sinα2+F3sinα3=63.4 N,
F=Fx2+Fy2=150.6 N,F=\sqrt{F_x^2+F_y^2}=150.6~N,F=Fx2+Fy2=150.6 N,
ϕ=arctanFyFx=25°.\phi=\arctan\frac{F_y}{F_x}=25°.ϕ=arctanFxFy=25°.
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