Question

9. Two forces equal to F and 3 F newton act on a
particle. If the first force be tripled and the
second force be increased by 30 newton, the
direction of the resultant is unaltered. Find the
value of F.
(Ans. 5 N​

Answer 1

Let β be the angle which the resultant force make with the force F and θ be the angle between tow forces.

In first case, tanβ=3FsinθF+3Fcosθ

In second case : tane beta = (( 3 F + 30 ) sin theta)/( 3 F + 30 ) cos theta)Hence ( 3 F sin theta)/( F + 3 F cos theta ) = ( 3 F + 30 ) sin theta)/( 3 F + ( 3 F + 30) cos theta)or 3 /(1 + 3 cos theta) = ( 3 F+ 30)/( 3 F + F cos theta + 30 cos theta)or 9 F + 9 F cos theta = 90 cos theta= 3 F + 30 + 9 F cos theta + 90 cos theta or 9 F- 3 F= 30 or F = 5 N`.