A wagon is being pulled behind a tractor around a curve on a rural highway. The wagon when empty weighs $600$ LB and $4300$ LB when fully loaded and has a track width of $5$ ft$.$ The center of gravity of the wagon is $6\mathrm{.}5$ ft above the roadway when fully loaded and when empty it is $3$ ft above the roadway. The sharpest curve in the highway section over which the wagon is being pulled has a $200$ ft$.$ Radius of curvature and a superelevation of $0\mathrm{.}06$ ft$/$ft$.$ The maximum coefficient of friction on an icy day is $0\mathrm{.}05,$ the maximum on a wet day is $0\mathrm{.}3$ and on a dry day it is $0\mathrm{.}5.$

What is the maximum speed that the wagon can be pulled along the highway:

a$)$ When the pavement is wet?

b$)$ When the pavement is dry?

c$)$ Is there a minimum speed the wagon must be pulled when the pavement is icy? If so$,$ what is that speed?

d$)$ At what speed is no steering effort required? How does pavement condition affect this speed?