Fig. P$4\mathrm{.}71$

$4\mathrm{.}72$ A $40-N$ roller, of diameter $80$ mm $,$ which is to be used on a tile floor, is resting directly on the subflooring as shown. Knowing that the thickness of each tile is $3$ mm $,$ determine the force $P$ required to move the roller onto the tiles if the roller is $(a)$ pushed to the left, $(b)$ pulled to the right.

Fig. P$4\mathrm{.}72$