What keeps a train on the tracks going round a bend?

Do you think it is the flanges on the wheels? Sorry, not right! Ok, it must be a differential. Sorry, not right again! But there must be a differential because the outside wheel travels further going round the bend. Sorry, there is no differential! What’s more the axle between the two wheels is solid. So what is going on?

Let the late Richard Feynman explain. Among the many awards he received he won the Nobel Prize for Physics in 1965. Feynman’s ability to explain something is amazing. Click here. Enjoy. Also click here for another explanation.

The lesson of the trains and the fly

When you are faced with solving a problem make sure you choose the best method to solve it.

Often there is more then one way to get the correct answer.

And, often one way is more difficult that another.

Always ask: Are there several ways to get the answer?

Do you remember the famous example of the fly flying between two oncoming trains?

  • Two trains are approaching each other.
  • Each train is travelling at 50 mph.
  • They are on the same single track.
  • They are 100 miles apart.
  • A fly is on the front of the engine of one of the trains.
  • As the trains approach each other, the flies to and fro between the two approaching trains – going from engine to engine.
  • The fly flies at 72.7 mph.
  • The trains crash and the fly is killed.
  • The total distance the fly flies is the total of the diminishing distances between the two trains up to the moment of impact.

The question is: What is the total distance flown by the fly?

There are two ways of working out the answer

The first way is mathematical.

Good luck doing it this way. You are going to struggle. Unless of course you have a brain like John Newmann the physicist and mathematician who apparently worked it out mathematically in seconds.

The second way is to use logic.

  • How long does it take for the trains to collide? Answer: 1 hour
  • How fast is the fly flying? Answer: 72.7 mph.
  • How far does the fly fly in one hour: Answer: 72.7 miles
  • And that of course is the answer: 72.7 miles

(Tough luck John Newmann)

So, what is the lesson of the trains and the fly problem?

The lesson

When you are faced with solving a problem make sure you choose the best method to solve it.

Finally. Just for fun.

Have a look at what may gone through mathematician John Newmann’s head in seconds https://mathworld.wolfram.com/TwoTrainsPuzzle.html