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Answer: Six diesel units in series can provide 13.4 MW of
Chapter 6, Problem 96P(choose chapter or problem)
Problem 96P
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 × 106 kg. The average car in the train has mass 8.2 × 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 accelerating 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 α = 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 2.9 MW less power available how many cars can the six diesel units pull up a 1.0% slope a constant 27 m/s?
Questions & Answers
QUESTION:
Problem 96P
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 × 106 kg. The average car in the train has mass 8.2 × 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 accelerating 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 α = 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 2.9 MW less power available how many cars can the six diesel units pull up a 1.0% slope a constant 27 m/s?
ANSWER:
We have to first calculate the power required to pull one car at the specified speed. Now knowing the power of the engine we can calculate the total number of cars it can pull.
In the second problem we know the acceleration and the mass of the train. Hence we can calculate the extra force required to accelerate the train.
Knowing the extra force, we can calculate the extra power needed.
In the last part, we know the total power, force required to pull each cart in the level track and the force required to pull them in the slope. Hence we can calculate the total number of car it can pull.