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

(please explain the steps aswell)



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When two forces or more act on one object, the net force or the resultant force is found by using the parallelo gram law of forces or vectors. If P & Q are forces, construct a parallelogram with the sides proportional to their magnitudes, and the angle between them equal to the angle Ф betwen the forces.

Then the resultant of the two forces is the diagonal passing the intersection of the two forces.
so the length of the diagonal = resultant force = R
R² = P² + Q² + 2 P Q cos Ф
the angle made by R with P is given by :  tan α  =  Q sin Ф / (P+Q cosФ)

R = 20√3 Newton          Ф = 60 deg         cos Ф= 1/2
forces are equal P = Q
So (20√3)² = P² + P² + 2 P P 1/2    
=>  400 * 3 =  3 P²  => P² = 400    So  P = 20  newotns

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