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Adsy
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Homework Statement
A ceiling fan is turning at a rate of 100 revolutions per minute. A spiders is clinging to a blade of the fan. If the spider experiences a centripetal acceleration greater than 0.3g, it will lose its grip on the blad and be flung off. How far from the centre of the fan can the spider safely go?
[tex]Rate = 100 rev/sec[/tex]
[tex]a = 0.3g[/tex]
[tex]r=?[/tex]
Homework Equations
[tex]\omega=\frac{\Delta\theta}{\Delta t}[/tex]
[tex]\omega=\frac{2 \pi}{T}[/tex]
[tex]v= \omega r[/tex]
[tex]T= \frac{2 \pi}{\omega}[/tex]
[tex]a=\frac{v^{2}}{r}[/tex]
[tex]a=\omega^{2}r[/tex]
The Attempt at a Solution
I've worked out that the time period, [tex]T = 0.6s[/tex]
[tex]a=0.3g=2.94 ms^{-2}[/tex]
then use: [tex]\omega=\frac{2 \pi}{T}[/tex]
[tex]\omega=\frac{2 \pi}{0.6} = 10.47 rad s^{-1}[/tex]
then I rearrange this formula: [tex]a=\omega^{2}r[/tex]
[tex]r= \frac{a}{\omega^{2}}[/tex]
then put in the known values to find r
[tex]r= \frac{2.94}{10.47^{2}} = 2.7*10^{-2}m[/tex]
*fixed*
This is incorrect. What am I doing wrong?
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