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Two forces whose magnitudes are in the r...

Two forces whose magnitudes are in the ratio `3:5` give a resultant of 28N. If the angle of their inclination is `60^@`, find the magnitude of each force.

Text Solution

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Let `F_(1)` and `F_(2)` be the two forces.
Then `F_(1) =3x, F_(2) =5x,R = 28N` and `theta=60^(@)`
`R = sqrt(F_(1)^(2) + F_(2)^(2) + 2F_(1)F_(2)cos theta)`
`rArr 28= sqrt(9x^(2) +25x^(2) + 15x^(2))=7x`
`rArr x=28/7=4`
`therefore F_(1) =3 xx 4 =12 N,F_(2) =5 xx 4=20 N`
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