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Laws Of Motion

Question
CBSEENPH11016760

Define angle of repose and find the relation between angle of repose and angle of friction.

Solution

Angle of repose is the angle that an inclined plane makes with the horizontal when a body placed on it just starts sliding down.
Let a body of weight W be placed on rough inclined plane and the body just starts sliding when angle of inclination is ϕ.

W can be resolved into two components:
(i) W sinϕ along the plane.
(ii) W cosϕ perpendicular to the plane.
When body is just at the point of sliding, then 
                Wsinϕ equals straight f equals μWcosϕ 
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#6 {main}</pre>                      ...(1) 
We know the relation between angle of friction<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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#6 {main}</pre> is,
                         tanθ space equals straight mu                ...(2) 
So, from (1) and (2), 
                         tan space straight theta space equals space tan space straight ϕ 
rightwards double arrow                           straight theta equals straight ϕ