Two forces equal to P and 2P newton act on a particle . If the first be doubled and the second be increased by 20 newton, the direction of the resultant is unaltered . Find the value of P .

Explanation

Let the resultant make angle `beta` with the force P .
`:.` In first case,
`tan beta = (2 P sin theta)/( P + 2 P cos theta)`
In second case,
`tan beta = ((2P + 20) sin theta)/(2P + (2P + 20) cos theta)`
Hence,
`((2P + 20) sin theta)/( 2 P + (2P + 20) cos theta) = (2P sin theta)/(P + 2 P cos theta)`
(or) `(2P sin theta)/( P +2 P cos theta) = (2 0 sin theta)/( P + 2 0 cos theta)` [ `:' (a)/(b) = (c)/(d) = (a-c)/(b-d)` ]
From the above equation , 2P = 20
(or) P = 10 N