Question

Three forces P, Q and R act at the same point and are in equilibrium. The forces P and Q have magnitudes 30 N and 20 N respectively, and there is an angle of 20° between their directions. Calculate the magnitude of the force R?

Answer 1

Three forces `vecP, vecQ and vecR` act at the same point and are in equilibrium.
Given forces `vecP and vecQ`.
`=>` Resultant of `vecP and vecQ` is equal and opposite to `vecR`

By Parallelogram Law of vectors, magnitude of resultant `vecR_r` of two vectors `vecP and vecQ` is given by the expression

`|vecR_r|=sqrt(|vecP|^2+|vecQ|^2+2|vecP||vecQ|cos alpha)`
where, `alpha` is the angle between the two.

Inserting given values we get

`|vecR_r|=sqrt(30^2+20^2+2xx30xx20\ cos 20^@)`
`=>|vecR_r|=sqrt(900+400+1200xx0.93969)`
`=>|vecR_r|=49.3\ N`
`:.|vecR|=49.3\ N`