Consider the continuous rolling mill depicted in Fig.3.48. Suppose that the motion of the adjustable roller has a damping coefficient b, and that the force exerted by the rolled material on the adjustable roller is proportional to the material's change in thickness: F= c(T-x) Suppose further that the DC motor has a torque constant K, and a back-emf constant K, and that the rack-and-pinion has effective radius of R. (a) What are the inputs to this system? The output? (b) Without neglecting the effects of gravity on the adjustable roller, draw a block diagram of the system that explicitly shows the follow- ing quantities: V(s), lo (s), F (s) (the force the motor exerts on the adjustable roller), and X(s). (c) Simplify your block diagram as much as possible while still identifying output and each input separately. Thickness T CO000 Rack and Pinion Vertically adjustable roller Fixed roller Thickness x 1: N Gear ratio Motion of material out of rollers 1 La va(1) R v,(1)