Answer to Question #314064 in Atomic and Nuclear Physics for roy

Question

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.

Answer 1

$F_x=F_1\cos\alpha_1+F_2\cos\alpha_2+F_3\cos\alpha_3=136.6~N,$

$F_y=F_1\sin\alpha_1+F_2\sin\alpha_2+F_3\sin\alpha_3=63 .4~N,$

$F=\sqrt{F_x^2+F_y^2}=150.6~N,$

$\phi=\arctan\frac{F_y}{F_x}=25°.$