Question

A block of mass $m$ slips on a rough horizontal table under the action of a horizontal force applied to it. The coefficient of friction between the block and the table is $\mu$. The table does not move on the floor. Find the total frictional force applied by the floor on the legs of the table. Do you need the friction coefficient between the table and the floor or the mass of the table?

Answer 1

Because the block slips on the table, maximum frictional force acts on it.

From the free body diagram

$R=\mu g$

$F-\mu R=0$

$F=\mu R=\mu mg$

But the table is at rest, so frictional force at the legs of the table is also $\mu R_1$

Let $f$ be the frictional force, from free body diagram.

$f-\mu R=0$

$f=\mu R=\mu mg$

$\therefore$ The total frictional force on the table by floor is $\mu mg$