Given the vectors below, determine the resultant and the equilibrant using trigonometry.

Question

230.0 newtons @ 125 degrees
175.0 newtons @ 60.0 degrees

Answer 1

1. Find the x- and y-components of both forces.

2. Add the x- and y-components separately.

3. Find the total force (magnitude and direction).

 

1.    F_1x = 230 cos(125)     F_1y = 230 sin(125)

       F_2x = 175 cos(60)       F_2y = 175 sin(60)

2.    F_x = -44.4 N                F_y = 340. N

3.    F = sqrt (44.4² + 340²) = 343 N, 

       θ = tan^-1(340/-44.4) = -82.6°+180° = 97.4°

This is the resultant force. The equilibrant force has the same magnitude but opposite direction:

       F = 343 N, θ = 97.4°+180° = 277°

 

You should draw a picture and verify this result graphically (tip-to-tail rule).

Answer 2

Hi Meg;

Andre is correct.  I apologize.