Two forces of 80N and 70N act simultaneously at a point. Find the resultant force, if the angle between them is 150°?
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The resultant force C of the two forces A and B acting at a point is obtained by vector addition formula.
A = 80 N
B = 70 N
θ = 150°
Magnitude of C = A^2 + B^2 + 2 A B Cos angle
= 80× 80+ 70×70+2×80×70× Cos 150°
C = 6400+4900- 11200×sqrt(3)/2 N
C = 11300 - 5600 sqrt3. Newton
Angle of the resultant C with 70N = θ
Tan θ = 80×1/2 / (70 - 80×sqrt(3)/2 )
= 40/0.72
= 500/9
θ = 88.9° nearly
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