Question

There are three identical train locomotives on separate tracks. Each applies equal force 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.

Answer 1

From lowest to highest acceleration:

3rd train

2nd train

1st train

Step-by-step explanation:

The acceleration of an object can be found by using Newton's second law:

`a=(F)/(m)`

where

a is the acceleration

F is the net force on the object

m is the mass of the object

We notice that for equal values of the forces F, the acceleration a is inversely proportional to the mass, m. Therefore, greater mass means lower acceleration, and viceversa.

So, the train with lowest acceleration is the one with largest mass, i.e. the 3rd train consisting of 50 equally loaded freight cars. Then, the 2nd train has larger acceleration, since it consists of 50 empty freight cars (so its mass is smaller). Finally, the 1st train (a single empty car) is the one with largest acceleration, since it is the train with smallest mass.