Three identical train locomotives, on separate tracks, apply the maximum force needed to begin moving. The first train consists of a single empty freight car, the second train consists of 50 empty freight cars, and the third train consists of 50 equally loaded freight cars. Rank the accelerations of the trains. All of the freight cars, when empty, are identical.

Question

Three identical train locomotives, on separate tracks, apply the maximum force needed to begin moving. The first train consists of a single empty freight car, the second train consists of 50 empty freight cars, and the third train consists of 50 equally loaded freight cars. Rank the accelerations of the trains. All of the freight cars, when empty, are identical.

so the freight cars are 1 empty frieght car, 50 equally loaded freight cars, 50 empty frieght cars.

I have to rank the accelertion from large to small.

I think it's 1 empty car, 50 empty cars, and 50 equally loaded frieght car is the smallest.

am I right?

Answer 1

Right.

This follows from F=ma, or
a = F/m
When F is constant, then a is inversely proportional to m.
You have correctly ranked the three cases in the order of lightest to the heaviest loads.

Answer 2

To rank the accelerations of the three trains, we can consider Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

In this case, all three locomotives are applying the maximum force needed to begin moving and are identical, so the net force acting on each train is the same. However, the mass of the trains differs in each case.

Let's assume that the mass of each empty freight car is m, and each equally loaded freight car also has mass m.

1) 1 empty freight car: The mass of the train is m, so the acceleration will be the highest compared to the other two trains.

2) 50 empty freight cars: The mass of the train will be 50m, which is 50 times larger than the first train. Therefore, the acceleration will be smaller compared to the first train.

3) 50 equally loaded freight cars: The mass of the train will be 50m + 50m = 100m, which is twice the mass of the second train and 100 times larger than the first train. Consequently, the acceleration will be the smallest among the three trains.

Therefore, the correct ranking from largest to smallest acceleration is: 1 empty freight car, 50 empty freight cars, 50 equally loaded freight cars.