Question

Two forces whose resultant is 200N are perpendicular to each other. If one of them makes an angle of 60° with the resultant. Calculate it magnitude?

Answer 1

`100N`

Explanation:

Suppose,one of the force is `vec X` and the other is `vec Y`

so, `vec X + vec Y =vec R`

where, `| vec X|=X,|vec Y|=Y, |vec R|=200`

again, angle between `vec X` and `vec Y` is `alpha=90^@`

so, we can say, `R^2 =X^2 +Y^2 +2XY cos 90`

or, `200^2 =X^2 +Y^2....................1`

If,the `vec X` makes an angle of `theta=60^@` then,

we can write,

`tan theta = (Y sin alpha)/(X + Y cos alpha)`

putting the given values we find, `tan 60=Y/X`

or, `Y=sqrt(3)X...................2`

Putting `Y=sqrt(3)X` in `1` we get,

`X^2 +(sqrt(3)X)^2 =200*200`

or, `4X^2 =200*200`

or, `X^2=50*200=100*100`

or, `X=100N`