Question

The friction coefficient between the board and the floor shown in figure (6-E7) is $\mu .$ Find the maximum force that the man can exert on the rope so that the board does not slip on the floor.

Answer 1

Let the maximum force exerted by the man is T.
From th free body diagram,
$R+T=Mg\Rightarrow R=Mg-T$
Again $R_1-R-mg=0$
$\Rightarrow R_1=R+mg$
and $T-\mu R_1=0$
From equation (ii), $T-\mu (R+mg)=0$
$\Rightarrow T-\mu R-\mu mg=0\Rightarrow T-\mu (Mg-T)-\mu mg=0T-\mu Mg+\mu t-\mu mg=0$

$\Rightarrow T(1+\mu )=\mu Mg+\mu mg\Rightarrow T=\frac{\mu (M+m)g}{1+\mu }$
Maximum force exerted by man is $\frac{\mu (M+m)g}{1+\mu }$