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## Homework Statement

A locomotive accelerates a 24-car train along a level track. Every car has a mass

of 50000 kg and is subject to a frictional force f = 250 v, where the speed v is in

meters per second and the force f is in Newtons. At the instant when the speed of

the train is 28 km/h, the magnitude of its acceleration is 0.3 m/s^2. (a) What is the

tension in the coupling between the first car and the locomotive? (b) If this tension

is equal to the maximum force the locomotive can exert on the train, what is the

steepest grade up which the locomotive can pull the train at 28 km/h?

## The Attempt at a Solution

F-25(250v) = 25(50000)a

v=7.778

F = 24(50000)(0.3) + 24(250*7.778)

F= 360000 + 46,668

F = 406.7 kN

T = 406.7N x 10^3

T= mg*cos(theta)

406.7x10^3/24(50000)(9.81) = cos(theta)

theta = 1.98

am i correct?? second part was a mystery, i just tried so many things till the answer seemed right.