2-11. As shown in the figure, a train consists of an engine and three cars. The wheels of the engine provide a resultant frictional tractive force F, which gives the train forward motion. The wheels of the cars roll freely. The train starts from rest, and it takes to increase its speed uniformly to. If the mass of the engine follows a normal distribution , and the masses of the three cars are the same, , which also follows a normal distribution . Determine the distributions of frictional tractive force F and the force T developed at the coupling between the engine and the first car.

Solution

System

Therefore,. Ans.

Three cars

Thus . Ans.