Question

2 forces each of magnitude 8N act at point in the direction of OA and OB the angle between the forces is theta resultant of two force has component 9N in the direction OA find value of theta?

Two forces, each of magnitude 8 N, act at a point in the directions OA and OB. The angle between the forces is θ◦. The resultant of the two forces has component 9 N in the direction OA.
Find
(i) the value of θ
(ii) the magnitude of the resultant of the two forces.

Answer 1

Let direction `OA` represent `x`-axis, force along `OA` be `F_1`, force along `OB` be `F_2`, and `R` be their resultant.

(i) Resolving all three along `x`-axis and equating these we get

`F_(1x)+F_(2x)=R_x`

Inserting given values we get

`8\ cos0^@+8costheta=9`
`=>8+8costheta=9`
`=>theta=cos^-1((9-8)/8)`
`=>theta=82.8^@`

(ii) Resolving all three along `y`-axis and equating these we get

`F_(1y)+F_(2y)=R_y`

Inserting given values we get

`8\ sin 0^@+8\ sin 82.8^@=R_y`
`=>R_y=7.94\ N`
Now `R=sqrt(R_x^2+R_y^2)`
`:.R=sqrt(9^2+7.94^2)`
`=>R=12\ N`