If two forces A and B are inclined to each other at an angle θ . Using triangle Law of vector addition, find the direction of resultant force.

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CONCEPT:

• Law of Parallelogram of forces: This law is used to determine the resultant of two coplanar forces acting at a point.
  • It states that “If two forces acting at a point are represented in magnitude and direction by two adjacent sides of a parallelogram, then their resultant is represented in magnitude and direction by the diagonal of the parallelogram which passes through that common point.”

• Let two forces F1 and F2, acting at the point O be represented, in magnitude and direction, by the directed line OA and OB inclined at an angle θ with each other.

Then if the parallelogram OACB be completed, the resultant force R will be represented by the diagonal OC.

\(R = \sqrt {F_1^2 + F_2^2 + 2{F_1}{F_2}cos\theta } \)

\(tan\alpha =\frac{F_{2}sinθ }{F_{1} + F_{2}cosθ }\)

EXPLANATION:

Here F1 = A and F2 = B

So angle, \(tan\beta =\frac{Bsin\theta }{A + Bcos\theta }\)