Question

determine the resultant R of the two forces shown by a) applying the parallelogram rule for vector addition and b) summing scalar components.

Answer 1

PART A)

Resultant of two forces by using parallelogram law

as per parallelogram law sum of two vectors is given by formula

$R = \sqrt{F_1^2 +F_2^2 + 2F_1F_2cos/theta}$

here we know that

$F_1 = 600 N$

$F_2 = 400 N$

$\theta = 60 degree$

now plug in all values in it

$R = \sqrt{600^2 +400^2 + 2*600*400cos60}$

$R = 871.8 N$

PART B)

By component method

Two components of first force F1 = 600 N is given by

$F_{1x} = 600 sin60 = 519.6 N$

$F_{1y} = 600cos60 = 300 N$

similarly for other force F2 = 400 N

$F_{2x} = 0$

$F_{2y} = 400 N$

now net force in each direction is given by

$F_{x} = F_{1x} + F_{2x} = 519.6 N$

$F_{y} = F_{1y} + F_{2y} = 700 N$

now net force is given by

$F_{net} = \sqrt{F_x^2 + F_y^2}$

$F_{net} = 871.8 N$