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

Explanation

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