Forces in equilibrium

1. Oct 25, 2004

jamie_o

Hello, this isn't technically a homework, but its something I'm trying to figure for myself. As shown in the diagram (in the attachment), there are three forces acting on a particle. The particle is in equilibrium. I have to find the magnitude of S and the angle theta (which ill write as x, because I dont know how to type theta on a computer screen) Now what I would do is solve it horizontally and vertically.
so horizontally: 6 - Scosx = 0
vertically : 2.5 - Ssinx = 0

My problem is where do I go from here? I know I could make it 6 = Scosx and likewise for the other, but it won't help me solve it. Since they are both equal to 0 I tried setting them equal to each other in the hope that the S would cancel and I would get sinx/cosx which is equal to tanx = to a number and then work from there. However I can't get the equation into that form. Any ideas on how I would solve this? Any help is very much appreciated :)

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2. Oct 25, 2004

Staff: Mentor

Try writing your equations like this:
(1) 6 = Scosx
(2) 2.5 = Ssinx

Now how can you get the S to cancel?

3. Oct 25, 2004

jamie_o

Thank you for the reply. I can see a link there and use Ssinx/Scosx to cancel S and leave tanx = 2.5/6, then use inverse tan of 2.5/6 = x. Then working out S would be straightforward from there. Why would I do this though? Why would I divide the horizontal equation into the vertical equation? Is there theory behind doing this? I don't like being 'monkey sees, monkey does' :) Thanks for the help.

4. Oct 25, 2004

jamie_o

Oh and if possible, could someone please tell me why setting the two equal to each other does not work? I might have a serious hole in my understanding of it all. Thanks.

5. Oct 25, 2004

Staff: Mentor

You're just solving two equations with two unknowns. There are many ways to approach it; here are two:
(1) Solve for S in one equation, then plug that in to the second. That's a standard approach.
(2) Square both equations and add them. Take advantage of $sin^2\theta + cos^2\theta = 1$.

Your skill in math often depends on picking up various little "tricks of the trade". Try to have as many "tricks" in your bag as possible.

6. Oct 26, 2004

jamie_o

Thank you. I should have spotted that since I am much further on in maths now, from when I got this question. I did try to take advantage of https://www.physicsforums.com/latex_images/35/352887-0.png [Broken] previous to posting the first time. However I came out with a very large sum, what I had before was incorrect I think.

Last edited by a moderator: May 1, 2017