# 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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by indomitus

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by indomitus

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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__

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