Two forces whose magnitudes are in the ratio 3:5give a resultant35n.if the angle of inclination is 60°.find magnitude of each force
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Let the 2 vectors have magnitudes 3x and 5x respectively. Then by parallelogram law,
R² = A² + B² + 2ABcosθ
Ie,35² = (3x)² + (5x)² + 2(3x)(5x)cos60˚
ie 1225 = 9x² + 25x² + 30x²(1/2)
ie 1225 = 34x² + 15x²
ie 1225 = 49x² or x² = 25 or x = 5
So magnitude of first vector is 3x which is equal to 15N and that of the second vector is 5x which equals 25N.
R² = A² + B² + 2ABcosθ
Ie,35² = (3x)² + (5x)² + 2(3x)(5x)cos60˚
ie 1225 = 9x² + 25x² + 30x²(1/2)
ie 1225 = 34x² + 15x²
ie 1225 = 49x² or x² = 25 or x = 5
So magnitude of first vector is 3x which is equal to 15N and that of the second vector is 5x which equals 25N.
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