If anyone could help me with this statics/phisycs question I would greatly appreciate it! I need to find the magnitude, direction, and location of the equilibrant with respect to point A on the diagram (The diagram should be attached below).

Here's what I've got so far:

Force (kN) Hor. Component (kN) Vert. Component (kN) ƩMₐ Components (kN*m)
55 +42.1324 -33.6533
35 -33.6533 -9.6152
60 +45.9627 -38.5673
25 0.0000 -25.0000
15 +15.0000 0.0000

Ʃ= +69.4418 -108.5358


The column "ƩMₐ Components (kN*m)" is blank for the time being, that is, until I get some assistance with this problem! The reason some of the values in the table are negative is because of their relation to their respective axes (i.e. if a force on the x-axis is going left the value is negative, if a force is going down on the y-axis the value is negative). I know the values themselves are correct, but I'm not sure if I was supposed to change the polarity of them.

So far so good. The magnitude and signs of the horizontal and vertical components look right. I didn't check to see for sure that your magnitudes were correct, but I'll take your word for it. You've calculated the resultant force, so you know the equilibrant will be exactly opposite of that.

As you can see from your post, this forum doesn't handle copying and pasting very well, so it's hard to figure out what that last column was supposed to read. Regardless, I'm guessing that column is reserved for the torque values? To compute the resultant torque from each applied force, it's probably easiest to compute the individual torque contributions from the horizontal and vertical components. For example, for the 55 kN force, the horizontal component contributes -43.1324*6 kN*m of torque about point A. The negative sign is because I've arbitrarily chosen to call counter-clockwise torques positive and clockwise torques negative. Anyway, the torque from the vertical component of the 55 kN force is 0 because the moment arm (the perpendicular distance to A) is 0.

Once you fill in and add up the values for all of the torque contributions, it's just a matter of finding a location to apply the equilibrant force so that the resulting torque cancels. You have two variables (the x- and y-coordinates) with only one equation to fit, so there are an infinite number of solutions. To make it easy, I'd pick a point on the bottom of the rectangle (this would be the x-axis if you pretend that point A is the origin). That way, only the vertical component of the equilibrant is contributing to the torque. Then it's just a matter of computing the moment arm length to balance the torque from all the applied forces shown in the figure.

Does any of that make sense? :)