Question

Two forces of 80N and 70N act simultaneously at a point. Find the resultant force, if the angle between them is 150°?

Answer 1

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