A body rests on a horizontal piece of metal. 

The coefficients of friction between the body and the metal
surface are 

µ_{s} = 0.3 and
µ_{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}

