Six diesel units in series can provide 13.4 MW of power to the lead car of a freight train. The diesel units have total mass 1.10 X 106 kg. The average car in the train has mass 8.2 X 104 kg and requires a horizontal pull of 2.8 kN to move at a constant 27 m/s on level tracks.
(a) How many cars can be in the train under these conditions?
(b) This would leave no power for acce1erating or climbing hills. Show that the extra force needed to accelerate the train is about the same for a 0.10-m/S2 acceleration or a 1.0% slope (slope angle a = arctan 0.010).
(c) With the 1.0% slope, show that an extra 2.9 MW of power is needed to maintain the 27-m/s speed of the diesel units.
(d) With 29 MW less power available, how many cars can the six diesel units poll up a 1.0% slope at a constant 27-m/s?