# Thread: Need help with this forces question

1. ## Need help with this forces question

A particle is acted upon by the following four forces: 25 N pulling east, 30 N pulling west, 54 N pulling north and 42 N pulling south.

Calculate the resultant and equilibrant of these forces.

2. Originally Posted by Soul to soul
A particle is acted upon by the following four forces: 25 N pulling east, 30 N pulling west, 54 N pulling north and 42 N pulling south.

Calculate the resultant and equilibrant of these forces.

let east/west be the x-direction ...

25N - 30N = -5N ... west component

north/south be the y-direction ...

54N - 42N = 12N ... north component

resultant magnitude, $\displaystyle |R| = \sqrt{(-5)^2 + (12)^2} = 13N$

resultant direction, $\displaystyle \theta = \arctan\left(\frac{12}{-5}\right) + 180 = 112.6^{\circ}$ counter-clockwise from east (the +x-axis), or $\displaystyle 67.4^{\circ}$ north of west.

If $\displaystyle R$ is the resultant vector, then $\displaystyle -R$ is the equilibrant vector.