Question
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. 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?
Solution
The centrifugal force experienced by the man, when the drum rotates = mrω2 , in outward direction which is normal to the wall of cylinder.
When the floor is removed, due to the weight of the man he has tendency to fall from the drum.
But, the man will not fall down as,
μN = μmrω2, opposes it.
The man remains stuck to the wall without falling when the floor is suddenly removed if the force of friction is greater or equal to the weight of the man.
i.e.![<pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
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i.e.,
, is the minimum rotational speed.
When the floor is removed, due to the weight of the man he has tendency to fall from the drum.
But, the man will not fall down as,
μN = μmrω2, opposes it.
The man remains stuck to the wall without falling when the floor is suddenly removed if the force of friction is greater or equal to the weight of the man.
i.e.
i.e.,
, is the minimum rotational speed.
