Question

Two forces equal to f and 3f newton act on a particle .if the first force be triplled and the second force be increased by 30 newton .the direction of the resultant is unltered .find the value of f

Answer 1

Let the resultant make angle x with the force f

So, in first case

tan x = 3f sin Ф / (f + 3f cos Ф)

In second case,

tan x = [ (3f + 30) sin Ф ] / [ 3f + (3f + 30) cos Ф ]

So

3f sin Ф / (f + 3f cos Ф) = [ (3f + 30) sin Ф ] / [ 3f + (3f + 30) cos Ф ]

3f sin Ф / (f + 3f cos Ф) = 30 sin Ф / f + 30 cos Ф

[as a/b = c/d = (a-c)/(b-d) ]

So, from above equation,

3f = 30

f = 10 N