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?
1 Answer
May 15, 2018
Three forces
Given forces
By Parallelogram Law of vectors, magnitude of resultant
#|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#