A block of mass m travels in a horizontal circle against the wall of a cylindrical room of radius R . The floor of the room is smooth, while the friction coefficient between the wall and the block is . The block is imparted an initial speed v₀ . Determine the frictional force exerted by the wall on the block as a function of the speed v .

Step-by-step solution

The normal force exerted by the cylindrical wall on the block provides the required centripetal force for the circular motion. N = 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 = N Substituting the expression for the normal force, we get the frictional force as a function of speed v : f = mv^2 R