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Math Help - Odd net forces in a circle = 0

  1. #1
    RAz
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    Odd net forces in a circle = 0

    I proved that all even vectors in a circle than pull outwards have a net force of 0. I'm having trouble with odd vectors.

    What I've managed to do so far:

    sin\frac{2k\pi}{n}-sin\frac{2\pi}{n}(n+k)<br />
=sin\frac{2\pi}{n}-sin\frac{2\pi}{n}(k)=0

    I'm having trouble with doing it for cos, plus I don't know if I'm solving it correctly. Thanks
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    Quote Originally Posted by RAz View Post
    sin\frac{2k\pi}{n}-sin\frac{2\pi}{n}(n+k)<br />
    Was this equation given to you?

    Wrong factorization.
    Last edited by dwsmith; May 27th 2010 at 01:14 PM.
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  3. #3
    RAz
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    Well kind of, that is the one I used. We can use any one necessary. We weren't given any equation, we were just asked to prove it.

    I proved it for n=3 with real angles, and by adding the vectors it's net force is 0. I also did this for n>3 when n is even. It's when n>3 and odd that I'm having trouble with.
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    Quote Originally Posted by RAz View Post
    Well kind of, that is the one I used. We can use any one necessary. We weren't given any equation, we were just asked to prove it.

    I proved it for n=3 with real angles, and by adding the vectors it's net force is 0. I also did this for n>3 when n is even. It's when n>3 and odd that I'm having trouble with.
    sin\left(\frac{2\pi}{n}(n+k)\right)

    Is everything supposed to be part of sine function?
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  5. #5
    RAz
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    Quote Originally Posted by dwsmith View Post
    sin\left(\frac{2\pi}{n}(n+k)\right)

    Is everything supposed to be part of sine function?
    No it doesn't have to be, as when I was proving when N was even I broke it up.

    The question was this: All vectors exert forced of the same magnitude F. Calculate the net force on all the vectors when N is any integer greater than 3.

    So yeah, I've done if for N=3 and N>3 when N is even. We can do anything to make it work. Thanks for your help so far ;D
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    Quote Originally Posted by RAz View Post
    No it doesn't have to be, as when I was proving when N was even I broke it up.

    The question was this: All vectors exert forced of the same magnitude F. Calculate the net force on all the vectors when N is any integer greater than 3.

    So yeah, I've done if for N=3 and N>3 when N is even. We can do anything to make it work. Thanks for your help so far ;D
    Use math induction to prove it.
    start by showing p(3)
    assume p(k)
    show p(k+1)
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