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 tangential acceleration of the block as a function of the speed v .

Step-by-step solution

The normal force exerted by the cylindrical wall provides the necessary centripetal force for the block to move in a horizontal circle of radius R . N = mv^2 R The kinetic friction force from the wall acts tangentially, opposite to the direction of motion. f = N = mv^2 R By Newton's second law, the tangential acceleration a_t is given by: m a_t = -f m a_t = - m v^2 R a_t = - v^2 R