Odd net forces in a circle = 0

• May 27th 2010, 03:12 AM
RAz
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:

$sin\frac{2k\pi}{n}-sin\frac{2\pi}{n}(n+k)
=sin\frac{2\pi}{n}-sin\frac{2\pi}{n}(k)=0$

I'm having trouble with doing it for cos, plus I don't know if I'm solving it correctly. Thanks :D
• May 27th 2010, 08:12 AM
dwsmith
Quote:

Originally Posted by RAz
$sin\frac{2k\pi}{n}-sin\frac{2\pi}{n}(n+k)
$

Wrong factorization.
• May 27th 2010, 01:04 PM
RAz
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.
• May 27th 2010, 01:15 PM
dwsmith
Quote:

Originally Posted by RAz
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?
• May 27th 2010, 01:19 PM
RAz
Quote:

Originally Posted by dwsmith
$sin\left(\frac{2\pi}{n}(n+k)\right)$

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
• May 27th 2010, 01:24 PM
dwsmith
Quote:

Originally Posted by RAz
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)