Lift the rod
Determine the minimum coefficient of friction between a thin rod and a floor at which a person can slowly lift the rod from the floor, without slipping, to the vertical position, applying at its end a force always perpendicular to its length.
Details and Assumptions:
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Mass of the rod =
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Minimum coefficient of friction = , here is square free.
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Submit your answer as .
The answer is 36.
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1 solution
Relevant wiki: Torque - Equilibrium
the form of answer was confusing me , but then i rationalized , hey write the a b are integers btw one can easily see if a and b are not integers the answer will not be an integer. so, it may be okay :P the question is simple but i spent 2 days on it . why ? because i made it excessively difficult by taking angular acceleration , eliminate it , eliminate force from equation , but now it's easy see that force must be such that the rod is just moving upwards. get that condition and find normal reaction and write friction as N* μ , the expression for mew is - ( 2 − c o s x ∗ c o s x ) c o s x ∗ s i n x , derivate to find min mew as 4 2