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Net force of two forces in a ring

  1. May 8, 2013 #1
    1. The problem statement, all variables and given/known data
    Consider the following ring:
    DELETEME.JPG
    Considering that [itex]\theta = 30°[/itex], determine F1 and F2 in order for the net force to be oriented downards with magnitude 10^3 N and without any horizontal component.

    3. The attempt at a solution
    Alright, so, the problem is I find two conflicting solutions when solving this simple problem.

    Solution 1:
    [tex]
    \\
    \sum F_x = 0 \rightarrow F_1*Sin(20)-F_2*Sin(30)=0 \\
    \sum F_y = 0 \rightarrow F_1*Cos(20)+F_2*Cos(30)=1000
    \\ \rightarrow F_2 ({\frac{Sin(30)}{Sin(20)} + Cos(30)}) = 1000
    \\ \rightarrow F_2 = 429.56N | F_1 = 627.91N
    [/tex]
    PS: How do I fix my parenthesis in line 3 of my latex equation? It's lacking proportion.

    Solution 2(Book solution):
    Solution2.JPG

    So... In short, why aren't those two solutions agreeing?
     
    Last edited: May 8, 2013
  2. jcsd
  3. May 8, 2013 #2

    haruspex

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    Check that last step.
    Try using \left( etc. instead of just (.
     
  4. May 8, 2013 #3
    Ahh, got it, can't believe I made such a stupid mistake. I checked and re-checked many times but couldn't spot it myself.

    If anyone's wondering, it was supposed to be [itex]\frac{F_1*(Sin(30)*Cos(20)}{Cos(20)}+...[/itex]
     
    Last edited: May 8, 2013
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