Question

Two equal forces are acting at a point with an angle of60"between them. If the resultant force is equal to 20 V3N Find the magnitude of each force.​

Answer 1

Correct Question :

Two equal forces are acting at a point with an angle of 60° between them. If the resultant force is equal to 20√3N. Find the magnitude of each force.

Answer :

the magnitude of each force is 20 N

Explanation :

The resultant of two forces P and Q at an angle θ is given by,

   $\boxed{\bf R=\sqrt{P^2+Q^2+2PQ cos \theta }}$

Given,

• Two equal forces are acting with an angle of 60° between them
• Resultant force = 20√3 N

Let the magnitude of each force be "F" N

Substitute

• P = Q = F

• θ = 60°

• R = 20√3 N

   20√3 = √(F² + F² + 2(F)(F) cos 60°)

   20√3 = √(2F² + 2F² cos 60°)

   (20√3)² = 2F² + 2F² cos 60°

   400(3) = 2F² (1 + cos 60°)

   1200 = 2F² ( 1 + ¹/₂ )

   1200/2 = F² ( 3/2)

    600 = 3F²/2

    3F² = 600 × 2

    3F² = 1200

     F² = 1200/3

     F² = 400

     F = √400

     F = √20²

     F = 20 N

Therefore,

the magnitude of each force is 20 N