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Sum of magnitudes of the two forces acti...

Sum of magnitudes of the two forces acting at a point is `16 N` if their resultant is normal to the smaller forces and has a magnitude `8N` then the forces are .

Text Solution

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Let `vecF` be the resultant of two forces `vecF_(1)` and `vecF_(2)` as shown in figure with `F_(2)gtF_(1)`
`F_(2)sin theta=F_(1)`....(i) `F_(2) cos theta=F=8` ....(ii)
Squarting and adding Eqs (i) and (ii) we get
`F_(2)^(2)=F_(v)^(2)+64`....(iii)
Given `F_(1)+F_(2)=16`....(iv)
Solving Eqs. (iii) and (iv), we get
`F_(1)=6N` and `F_(2)=10N`
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