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A locomotive accelerates a 23-car train along a level track. Each car has a mass of 48.6 metric tons and is subject to a drag force f = 243v, where v is the speed in m/s and the force f is in N. At the instant when the speed of the train is 34.5 km/h, the acceleration is 0.182 m/s 2 (a) Calculate the force exerted by the locomotive on the first car. (b) Suppose that the force found in part (a) is the greatest force the locomotive can exert on the train. What, then, is the steepest grade up which the locomotive can pull the train at 34.5 km/h? (1 metric ton = 1000 kg.)

A locomotive accelerates a 23-car train along a level track. Each car has a mass of 48.6 metric tons and is subject to a drag force f = 243v, where v is the speed in m/s and the force f is in N. At the instant when the speed of the train is 34.5 km/h, the acceleration is 0.182 m/s2 (a) Calculate the force exerted by the locomotive on the first car. (b) Suppose that the force found in part (a) is the greatest force the locomotive can exert on the train. What, then, is the steepest grade up which the locomotive can pull the train at 34.5 km/h? (1 metric ton = 1000 kg.)

Grade:upto college level

1 Answers

Deepak Patra
askIITians Faculty 471 Points
6 years ago
233-1431_1.PNG
Therefore, the force exerted by the locomotive on the first car is 2.57 x 105 N .

233-1847_1.PNG
Therefore, the maximum inclination at which the train can be pulled by the locomotive is 1.06° .

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