Question

Two forces of 20 N and 25 N act on an object at an angle of 30°. Determine the equilibrant of these two forces.

Answer 1

1. resolve the vectors into their x and y components

x component: Fcos(theta)
y component: Fsin(theta)

2. add the x components
3. add the y-components
4. put the sums into a new vector
<x component sum, y component sum>

5. find the magnitude and direction of this new vector
6. since the "equilibriant" is the force that acts in exact opposition to the original vectors, it will have the exact opposite direction (so just add 180 degrees to the original direction)

hope that helps, lmk if you need some help with the intermediate steps

Answer 2

Okay, so for the x-component and y-component the Fsintheta and Fcostheta there is 20 N and 25 N. Which should be the F? 

Answer 3

there are two forces so you must consider both of them and add them up

x components = 20cos(30) + 25cos(30)
y components = 20sin(30) + 25sin(30)

Answer 4

Aha, I see. Ty

Answer 5

(45√3/2 , 45/2) 

√((45√3/2)^2+(45/2)^2)

= 45 

Using the Sine law: 

Sin (30)/25 = sin x/45 

x = 64.16° 

Is that correct?

Answer 6

magnitude = good

angle = not quite, you only took into account the 25sin(30) vector not the 20 vector

there's a much easier way to do this, it's just direction = arctan(y/x) = arctan[45sin(30)/45cos(30)], and if you notice, sin(30)/cos(30) = tan(30) so

arctan(tan(30)) is just 30 giving 30 degrees as the direction

Answer 7

anyway, since the sum vector has magnitude 45, direction (30 degrees) we just add 180 to the degrees to get a vector with magnitude 45 and direction (210 degrees) as the solution

Answer 8

I found this answer that said:
The equilibrant has a magnitude of 43.49 N. It makes an angle of 167° with the 25 N force and of 163° with the 20 N force.
Which one is correct?