a 70 kg man stands in contact against a wall of a cylindrical drum of radius 3 m rotating about its vertical axis with 200 rpm. the coefficient of friction between the wall and his clothing is 0.15. what is the minimum rotational speed of the cylinder to enable the man to remain stuck to the wall (without falling) when the floor is suddenly removed? please explain it with diagram.

Asked by ABHINAVSINGH | 11th Dec, 2013, 07:06: PM

Expert Answer:

The man is standing in contact with the wall as shown below.
 
 
The normal reaction N provides the necessary centripetal force
 
N = mv2/r = mrω2
 
The frictional force balances the weight of the man
 
fs = mg
 
Now, the man will remain stuck to the wall after the floor has been removed when
 
fs ≤ μ N
 
That is,
 
mg ≤ μ N
 
mg ≤ μmrω2
 
ω2 ≥ g/μr
 
Thus, the minimum rotational speed is
 

Answered by Romal Bhansali | 12th Dec, 2013, 10:14: AM

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