A small locomotive of mass 30 tons is used to push a train up a mountain railroad whose steepest portion has an inclination of 8 degrees. The friction coefficient between the locomotive's wheels and rails is u=0.35.
a) Find the maximum allowable mass for the train (the mass at which the locomotive would be barely able to maintain constant speed without slipping).
b) If the locomotive pushes a train of mass 30 tons, what is the magnitude of the normal reaction between locomotive and the first car?

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