The greatest and the least resultant of two forces acting at a point ared ` 14 M` and ` 4 N` respectively. If each force is incerased by `2 N`1 find the resultant of two new new forces acting at an angle of ` 60^@` to ach other.

Explanation

Let (A) and (B) be two forces and ` A gt B`. Then
` A+ B 14 N`…(i)
and ` A - B= 4 N` …(ii) ltBrgt Solving (i) and (ii) , we get
when each force is increased by ` 2 N`, then ltbRgt ` A_1 = 9 + 2 = 11 N` and ` B_1 = 5 + 2 = 7 N`
Angle between these two forces ` theta= 60^@`
Resultant force,
` R_1 = sqrt ( A-1^2 + B_^2 + 2 A_1 B_1 cos 60^@)`
` = sqrt ( 11^2 + 7^2 + 2 xx 11 xx 7 1//2 )`
` = sqrt( 121 + 49 + 77 ) = 15. 72 N` ltbRgt Let ` vec R_1` maken an angle ` beta` with the force ` vec A_1` , then ltbRgt ` tan beta= ( B_1 sin 60^@)/( a_1 + B_1 cos 60^2) = ( 7 xx sqrt 3//2)/( 11 + 7 xx 1//2 ) = 0. 4180` ltbRgt ` beta = 22^2 41'`.