Problem $6).$

A train consists of $4900$hp locomotives with $4-$axles weighing $165$ tons $(.....2,000$ lbs$/$ton$)$ and has a cross$-$

sectional area of $135f{t}^2.$ The train must haul $18$ four$-$axle passenger rail cars which each weigh $50$ tons on

average. The train must be able to ascend a $4\mathrm{.}5\%$ grade with a $3$ curve at $55$ mph $.$

a$).$ How many locomotives are required for the train to maintain this speed up the hill and around

the curve?

b$).$ What is the maximum speed of this train on a level and straight section of track?