# Two trains that cross

Two absolutely identical trains that weigh exactly 3,500 tons each travel at 72Km / h on a track that runs along the 60th parallel land. One of the trains goes west and the other east.

At one point they cross, Which of the two weighs more?

#### Solution

The heaviest of the two, that is, the one that exerts the most pressure on the track, is the train that travels contrary to the direction of rotation of the Earth, that is, the train that moves west since moving slowly around the Earth's axis, due to the centrifugal effect, it loses less weight than the train heading east.

In parallel 60, the earth moves around its axis at a speed of 230 meters per second. If we know that the speed of the train is 72 km / h (= 20 m / s) we have that the train that travels to the East has a total speed of 230 + 20 m / s = 250 m / s and the one that travels towards the west, it does so at a speed of 210 m / s.

Taking into account that the radius of the circumference of the Earth in parallel 60 is 3,200 km = 320,000,000 cm
The centrifugal acceleration for the first train will be:

And for the second train it would be:

The difference in centrifugal acceleration value between the two trains is:

Since the direction of the centrifugal acceleration is at an angle of 60 ° with respect to the direction of gravity, we will consider only the appropriate fragment of that centrifugal acceleration:.

This gives a gravity acceleration ratio of 0.3 / 980 or approximately 0.0003.

Therefore the train that goes east is lighter than the one that goes west for a fragment of 0.0003 of its weight and the difference in weight between one and the other would be 3,500,000 kg * 0.0003 = 1,050 kg, just over a ton.