The sum of magnitudes of two forces acting at a point is 16N. If their resultant is normal to the smaller force and has a magnitude of 8N. Then the forces are

Explanation

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