Question

2 forces each of magnitude f and resultant of the same magnitude f the angle between them

Answer 1

Let the magnitude of the forces, f = x

Angle between the forces = t


magnitude of resultant = x


x^2 = x^2 + x^2 + 2×x×x × cos t

=> x^2 = 2x^2 + 2x^2 cos t

=> x^2 = 2x^2( 1 + cos t )

=> x^2 / 2x^2 = 1 + cos t

=> 1/2 = 1 + cos t

=> 1/2 - 1 = cos t

=> -1/2 = cos t

=> cos t = -1/2 = cos (120°)

=> t = 120°

So angle between the forces is 120°

Answer 2

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Let the magnitude of the forces, f = x

Angle between the forces = t

magnitude of resultant = x

x^2 = x^2 + x^2 + 2×x×x × cos t

=> x^2 = 2x^2 + 2x^2 cos t

=> x^2 = 2x^2( 1 + cos t )

=> x^2 / 2x^2 = 1 + cos t

=> 1/2 = 1 + cos t

=> 1/2 - 1 = cos t

=> -1/2 = cos t

=> cos t = -1/2 = cos (120°)

=> t = 120°

So angle between the forces is 120°