A block of mass m moves on a horizontal circle against the wall of a cylindrical room of radius R. The floor of the room onwhich the block moves is smoth but the friction coefficient between the wall and the block is `mu`. The block is given an initial speed `v_0`. As a function of the speed v write a. the normal force by the wall on the block. b. thefrictional force by the wall and c. the tangential acceleration of the block. d. Integrate the tangential acceleration `((dv)/(dt)=v(dv)/(ds))` to obtain the speed of the block after one revoluton.

Answer

(a) `(mv^(2))/R` (b) `(mumv^(2))/R` (c) `(-muv)/(R^(2))`(d) `v_(0)e^(-2pi mu)`