It takes a force of 53 kN on the lead car of a 16-car passenger train with mass 9.1 × 103 kg to pull it at a constant 45 m/s (101 mi/h) on level tracks. (a) What power must the locomotive provide to the lead car? (b) How much more power to the lead car than calculated in part (a) would be needed to give the train an acceleration of 1.5 m/s2, at the instant that the train has a speed of 45 m/s on level tracks? (c) How much more power to the lead car than that calculated in part (a) would be needed to move the train up a 1.5% grade (slope angle ??? = arctan 0.015) at a constant 45 m/s?

Solution 97P Introduction We have to calculate the power required to pull the car with an constant velocity. We also have to calculate the power required to accelerate the car. Step 1 The force required to pull the car is F = 53 kN. The velocity of the car is v = 45 m/s. Hence the power required to pull the car is Step 2 3 The mass of the car is m = 9.1 × 10 kg. And the acceleration of the car is a = 1.5 m/s . Hence the force required to accelerate the car is Hence the total force required to accelerate the car is Hence the required power is So the power required to accelerate the train is 2.98 MW.