Insects

An insect crawls up a hemispherical surface very very slowly. The coefficient of friction between the insect and the surface is 1/3. If the line joining the centre of the hemisphere to the insect makes an angle of \alpha with the vertical, the max possible value of \alpha is ?

Well I made the FBD of the insect and since it's moving quite slowly, I assumed net force on it is zero. I got

Fr + mgsin\alpha = 0 (Both friction and mgsin\alpha are in the same direction, maybe here my diagram is wrong)
I'm getting cot\alpha = -3. The answer is +3. Can someone help out? Fr is friction btw.

2 Answers

24
eureka123 ·

""Fr + mgsinα = 0"" .....hows htat possible ??
friciton will act in opp direction....so u will get cotα=3

39
Pritish Chakraborty ·

Yeah I got the mistake in my diagram. Thanks :)

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