A small block of mass m is on a horizontal frictionless surface as it travels around the inside of a hoop of radius R. The coefficient of friction between the block and the wall is mu; therefore, the speed v of the block decreases. In terms of m, R, mu, and v, find expressions for: a. the frictional force on the block. I got this part, friction is the centripetal force or mv^2/R. b. the block's tangential acceleration, dv/dt. c. the time required to reduce the speed of the block from an initial value v0 to v0/3. I haven't formally taken calc yet (this is an APC mechanics free response), but I think I have a good enough understanding of it. The thing that hangs me up is that friction is not proportional to weight as usual. The only friction is caused by the hoop. The force on the hoop at an instant is the velocity. Does this mean friction = mu x v?. I think I'm on the right track, the sliding causes a friction force which lowers the velocity which in turn lowers the friction force, lowering the velocity, etc. But how do I express this mathematically and answer the last two parts?