A block of mass m travels in a horizontal circle against the wall...

The normal force exerted by the cylindrical wall on the block provides the required centripetal force for the circular motion.

$N = \dfrac{mv^2}{R}$

Since the block is sliding against the rough wall, the kinetic frictional force acts tangentially opposite to the direction of motion. The magnitude of this frictional force is given by:

$f = \mu N$

Substituting the expression for the normal force, we get the frictional force as a function of speed $v$:

$f = \dfrac{\mu mv^2}{R}$