A 70 kg man stands in contact against the inner wall of a hollow cylindrical drum of radius 3 m rotating about its vertical axis with 200 rev/min. 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?
Given:
Mass of man, M = 70 Kg
Radius of the drum, r = 3m
Co-efficient of friction, � = 0.15
Frequency of rotation, v = 200 rev/min = 3.3 rev s-1
The necessary centrifugal force required for the rotation of man is provided by the Normal force (FN).
When the floor rotates, the man sticks to the wall of drum. So the friction between his cloth and wall prevents him from falling. i.e frictional force balances the weight.
Frictional force, f = � × FN
The man will not fall until,
Weight< f
mg<f
→ mg< �× FN
→ mg< �× mrω2
→ ω>( g/ �r )1/2
→ ωmin = (10/(0.15× 3) )1/2
→ ωmin = 4.71 rad/s
The minimum angular speed is 4.7 rad/sec.