An insect crawls up a hemispherical surface v | vedclass

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(A) Let the mass of the insect be $m$. The forces acting on the insect are:$1$. Weight $mg$ acting vertically downwards.$2$. Normal reaction $N$ actin

Vedclass · Accepted Answer

$\cot\,\alpha = 3$

Vedclass · Answer

(A) Let the mass of the insect be $m$. The forces acting on the insect are:$1$. Weight $mg$ acting vertically downwards.$2$. Normal reaction $N$ acting radially outwards from the centre.$3$. Frictional force $f$ acting tangentially upwards along the surface.Resolving the weight $mg$ into two components:- Along the radius: $mg \cos \alpha$ (acting inwards).- Tangential to the surface: $mg \sin \alpha$ (acting downwards).For equilibrium in the radial direction:$N = mg \cos \alpha$For equilibrium in the tangential direction:$f = mg \sin \alpha$Since the insect is crawling very slowly,the frictional force is at its maximum limit,$f = \mu N$.Substituting the expressions for $f$ and $N$:$\mu N = mg \sin \alpha$$\mu (mg \cos \alpha) = mg \sin \alpha$$\mu = 	an \alpha$Given $\mu = 1/3$,we have:$	an \alpha = 1/3$$\cot \alpha = 3$

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