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If the coefficient of friciton between a...

If the coefficient of friciton between an insect and bowl is `mu` and the radius of the bowl is r, find the maximum height to which the insect can crawl up in the bowl.

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The insect will crawl up the bowl till the component of its weight along the bowl is balanced by limiting frictional force. So, resolving weight perpendicular to the bowl and along the bowl,

`N=mg costheta,f_(1)=mgsin thetaimpliestan theta=(f_(L))/(N)impliestantheta=mu[becausef_(L)=muN]`
`impliessqrt(((r^(2)-y^(2)))/(y))=mu impliesy=(r)/(sqrt(1+mu^(2)))So h=r-y=r[1-(1)/(sqrt(1+mu^(2)))]`
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