Question

Two forces of 400N and 600N act at an angle of 60° to each other such that smaller forces is directed along positive x axis . determine the resultant in magnitude and direction​

Answer 1

The magnitude of the resultant is 871.78 N.

The direction of the resultant is 36.59°.

Given:

Two forces, F₁ = 400N and F₂ = 600N

The angle between two forces, θ = 60°

Small force (F₁) acts along the positive axis.

To Find:

The resultant of the two forces in magnitude and direction​.

Solution:

We are required to find the resultant magnitude and direction​ of the two forces.

According to parallelogram law, The resultant of the two forces is given as

R² = F₁²+F₂²+2F₁F₂Cosθ ------(1)

    = 400²+600²+2×400×600×Cos60°

    = 160000+360000+480000×(1/2)

    = 520000+240000

    = 760000

|R| = 871.78 N

Therefore, The magnitude of the resultant is 871.78 N.

The direction of the resultant from the picture given below is

tan α = F₂sin θ/(F₁+F₂cos θ)

         = 600sin 60°/(400+600cos 60°)

         = 600×(√3/2)/(400+600(1/2))

         = 300√3/700

         = 519.61/700

         = 0.7423

α = tan⁻¹(0.7423)

  = 36.59°

Therefore, The direction of the resultant is 36.59°.

#SPJ1