Two forces of magnitudes 3N and 4N respectively are acting on a body. Calculate the resultant force if the angle between them is : (i) `0^(@)` (ii) `180^(@)` (iii) `90^(@)`

Explanation

(i) `theta=0^(@)`, both the force are parallel, `R=A+B`
`therefore` Net force or resultant force `R=3+4=7N`
Direction of resultant is along both the forces
(ii) `theta=180^(@)`, both the forces are antiparallel, `R=A-B`
Direction of net force is along bigger force means along 4N
(iii) `theta=90^(@)`, both the forces are perpendicular
then `R=sqrt(A^(2)+B^(2)+2ABcos 90^(@))`
`=sqrt(A^(2)+B^(2))=sqrt(3^(2)+4^(2))=5N`
`tan alpha =(3)/(4)` or `alpha=tan^(-1)((3)/(4))=37^(@)`
magnitude of resultant is 5N wich is acting at an angle of `37^(@)` from 4N force.