[Ldobry7554]

Find the force, which, together with the following forces, will produce equilibrium when they all act in a plane of a particle: 15 Newtons due North, 20 Newtons Northwest, 30 Newtons South, and 40 Newtons Southeast.

Help!

[ebaines]

To do this problem you need to convert each of the four forces into two perpendicular components - one in the north/south direction and one in east/west direction. Do you know how to do that? For the north-south forces, I suggest you define north as positive and south as negative. Similarly for the east-west forces define east as positive and west as negative. Then sum up all the north-south force componets to get one total north-south, and then sum up all the and east-west forces to get one total east-west force. These are the two components of the total force that is caused by the four initial forces. To counteract this, you need one force of the same magnitude but opposite direction of this composite force. I hope this explanation is clear - post back with what you get for an answer, and we'll check it for you.

[Ldobry7554]

I'm not quite sure what you are saying. Would I just make it 45 N and 60 N once I sum them up? Sorry I'm really awful at physics it doesn't make sense to me.

[ebaines]

OK, I'll give you an example. Suppose you had a force of 20N northeast and a second force of 30N southeast.

Step 1: make a drawing (see step 1 in the figure).

Step 2: break each force up into two perpendicular pieces . The first force's two components are 20 sin(45) north and 20 cos (45) east -- do you see why that is? The second force can be broken up into 30 sin(45) south and 30 cos(45) east.

Step 3: now add together the north/south components: 20 sin(45) - 30 sin(45) = -10 sin(45). Note the minus sign, which indicates that the force is heading south. And then add together the two east/west forces: 20 cos(45) + 30 cos(45) = +50 cos(45). Here the plus sign tells you that it's to the east. Now you have your two components of the resultant force.

Step 4: Combine these two perpendicular forces into one resultant - you use the pythagorian theorem to find the magnitude, and trigonometry to find the direction.. First, the magnitude is:



And the direction is:



This direction is 11.3 degrees south of east, so to convert to a compass directoin add 90 (since compass headings are measured from north, not east), to get 101.3 degrees.

If you want to add a single force to counteract this, you would add a force of 36.05N heading up and to the left - at a compass bearing of 101.3 + 180 = 281.3 degrees.

Hope this helps!