- #1
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Homework Statement
http://img41.imageshack.us/img41/6579/mechanics2.jpg
Homework Equations
[tex]w=\frac{d\theta}{dt}[/tex] (1)
[tex]v=rw[/tex] (2)
[tex]F=ma[/tex] (3)
[tex]a=\frac{v^2}{r}[/tex] (4)
The Attempt at a Solution
For (i), from (2) and (4) I get [tex]a=rw^2[/tex]
and I'm thinking [tex]r=\frac{F}{cos\theta}[/tex] but I'm not too sure about it.
So then I'm left with [tex]cos\theta=mw^2[/tex] for the horizontal component.
For the vertical, I'm just completely stumped. I tried something, but I know it's probably so wrong that posting it would be to make a mockery out of myself
For (ii) I have [tex]N=mcos\theta(g-rw^2tan\theta)[/tex]
and since [tex]mcos\theta>0[/tex] since m>0,[tex]cos\theta>0 ,0<\theta<\frac{\pi}{2}[/tex]
I need to solve for w: [tex]g-rw^2tan\theta>0[/tex]
Hence, [tex]-\frac{g}{r}cot\theta<w<\frac{g}{r}cot\theta[/tex]
Is this correct?
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