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If cofficient of friction between an insect and bowl is mu(u) and the radius of the bowl is r, find the maximum height to which the insect can crawl in the bowl

If cofficient of friction between an insect and bowl is mu(u) and the radius of the bowl is r, find the maximum height to which the insect can crawl in the bowl

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Grade:11

2 Answers

Arun
25750 Points
5 years ago

Let angle subtended at the centre of bowl in limiting case=θ
mgcosθ=μmgsinθ

μ=tanθ .This implies cosθ=1√μ2+1

Let h be the height which is given by h=R-x
where x=Rcosθ

h=R-Rcosθ
h=R(1-cosθ)
h=R(1-1√μ2+1)

 

Regards

Arun (askIITians forum expert)

Eshan
askIITians Faculty 2095 Points
5 years ago
Let\thetabe the angle the line joining insect and point C makes with vertical.

The componnent of weight of insect along tangent to the bowl at its position ismgsin\theta.
The maximum amount of fricition possible=\mu mgcos\theta.

Under equilibrium,mgsin\theta= \mu mgcos\theta\implies tan\theta=\mu

Hencecos\theta=\dfrac{r-h}{r}=\dfrac{1}{\sqrt{\mu^2+1}}
\implies h=r(1-\dfrac{1}{\sqrt{\mu^2+1}})

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