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 normal force exerted by the wall on the block as a function of the speed v .

Step-by-step solution

The block moves in a horizontal circular path of radius R with an instantaneous speed v . The centripetal acceleration required for this circular motion is directed towards the center and has a magnitude of a_c = v^2 R . This centripetal acceleration is provided entirely by the normal force N exerted by the cylindrical wall on the block. Applying Newton's second law in the radial direction gives: N = m a_c = mv^2 R