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Friction Example
A body rests on a horizontal piece of metal.  
The coefficients of friction between the body and the metal surface are  
s = 0.3 and d = 0.22  
One end of the piece of metal is lifted up.  
   
a) What is maximum angle of inclination for which will the body will not slide down the slope?  
b) What will be the acceleration of the body down the slope once it as started moving?  
Assume that the angle of the slope is equal to (or very close to) the maximum angle calculated in part a).  
     
In the following statements we consider just the magnitudes of the forces.  
a) The body will not slide down the slope as long as  
 
Therefore, at the maximum angle  
 
   
Also, as the forces acting perpendicular to the slope are in equilibrium, we have  
 
   
and, from the definition of the coefficient of friction, we have  
 
Dividing the first equation by the second gives  
 
so  
 
which gives maximum angle of slope about 16.7  
   
b) The net force acting down the slope is equal to the component of the force of gravity acting down the slope minus the force of friction.  
 
 
and as the forces acting perpendicular to the slope are still in equilibrium, we have  
 
Therefore  
 
and, as acceleration = force/mass, we have  
 
which gives a = 4.88ms-2  
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