If the coefficient of friction between an ant | vedclass

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Question

(A) For an object to remain at rest on an inclined surface,the angle of inclination $\alpha$ must be less than or equal to the angle of repose $	heta

Vedclass · Accepted Answer

$\cot \alpha = 3$

Vedclass · Answer

(A) For an object to remain at rest on an inclined surface,the angle of inclination $\alpha$ must be less than or equal to the angle of repose $	heta$,where $	an 	heta = \mu$.Here,the surface is curved,and the angle $\alpha$ is measured with the vertical.The forces acting on the ant are gravity ($mg$ downwards),normal force ($N$ perpendicular to the surface),and friction ($f$ along the tangent).At the point of slipping,the friction is limiting,so $f = \mu N$.Resolving forces along the tangent and normal to the surface:$mg \sin \alpha = f = \mu N$$mg \cos \alpha = N$Dividing the two equations:$	an \alpha = \mu$Given $\mu = 1/3$,we have $	an \alpha = 1/3$.Therefore,$\cot \alpha = 1/	an \alpha = 3$.

If the coefficient of friction between an ant and the surface is $1/3$,find the maximum value of $\alpha$.

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