Determine the maximum ratio h//b for which the homogenous block will side without tipping under the actionof force P. The coefficient of static friction between the block and the incline is mu_(s).

Determine the maximum ratio h//b for which the homogenous block will s

1.	Determine the maximum ratio h//b for which the homogenous block will side without tipping under the actionof force P. The coefficient of static friction between the block and the incline is mu_(s).
Answer» Solution :Block has to slide WITHOUT tipping, which implies that block is in translational as well as rotational equilibrium. From conditions of equlibrium, Along SLOPING surface. `F+muN=mgsintheta` ..................i Perpendicular to the sloping surface `N=mgcostheta` .............ii Balancing torque about point `P`, `Fxxh=mgcosthetab/2` .................iii when the block is on the verge of tipping, the normal reaction will pass through the edge of the block. from EQN i, ii and iii `F=mgsintheta-mumg cos theta`........IV On substiting `F` in eqn ii we obtain `(mgsintheta-mumgcostheta)h-mgcosthetah/2=0` Which on solving for `h//b` yields `h/b= 1/((2mu_(2)-tantheta))`