00:01
In this problem, we are given a diagram of a particle subjected to four forces, where one of the forces has an unknown magnitude and an unknown direction.
00:11
We want to find the magnitude and direction of this unknown force that will ensure that our particle is in equilibrium.
00:17
So for a particle to be in equilibrium, we need to have that the sums of forces is equal to zero.
00:25
And the sums of forces vectorial like this we write as two equations.
00:30
The sums of the forces along the x component must be equal to zero.
00:37
And the sums of forces along the y component must be equal to zero.
00:42
Let's go ahead and decompose all of our vectors here along the x and y component.
00:49
So this first vector, 8 kn, pointing 30 degrees towards the negative x axis, above the negative x axis, can decompose as a negative x component and a positive y component.
01:14
Where the negative x component will be equal to minus 8 times the cosine of 30 degrees.
01:28
The second vector here will also decompose as a negative x component, but also a negative y component.
01:41
Where the negative x component will be equal to 4 times the cos of 60 degrees.
01:55
We also have on the x component a positive vector of 5 kn, which is only along the x component.
02:03
So we don't need to decompose this one.
02:06
It is already decomposed naturally along its x component.
02:18
So plus 5...