Question

Consider the situation shown in figure (6-E9). Suppose a small electric field E exists in the space in the vrticall upward direction and the upper block carries a positive charge Q on its top surface. The friction coefficient between the two blocks is $\mu$ but the floor is smooth. What maximum horizontal force F can be applied without disturbing the equilibrium?

Answer 1

$R_1+QE-mg=0\Rightarrow R_1=mg-QE$

From Equation (i) ,
$F-T=\mu (mg-QE)$

$\Rightarrow F-T-\mu mg+\mu QE=0T-\mu R_1=0\Rightarrow T=\mu R_1=\mu (mg-QE)$
From equation (ii) ,
$F-\mu mg+\mu QE-\mu mg+\mu QE=0\Rightarrow F-2\mu mg+2\mu QE=0\Rightarrow F=2mumg-2\mu QE\Rightarrow F=2\mu (mg-QE)$
Maximum horizontal force that can be applied is $2\mu (mg-QE)$