Photo:
THE MIRROR
The bicycle is a sophisticated means of transportation.
With only a little effort, it moves people much faster than when they walk.
Cycling can only be torture uphill and against the wind.
However, no one is sitting on the bicycle, which is the subject of this puzzle.
It leans against a table, on the edge of which it can be easily pushed forwards or backwards.
One of the pedals points vertically downwards, the other upwards.
A leash is attached to the bottom pedal.
You stand behind the rear wheel and gently pull on the leash as if trying to pull the bike backwards towards you.
What's happening with the bike?
Does it roll backwards or forwards?
Or is it not moving at all?
Note: We assume that the tires have good contact with the ground and do not slide on it.
The bike rolls backwards.
This riddle appears in various books, sometimes with a wrong solution.
At first I didn't want to believe that the wheel was moving backwards.
I bet it wouldn't move.
Then I went into the basement with a piece of string and was amazed to find out: Yes, it really rolls backwards!
It is relatively easy to show that the wheel cannot roll forward, even though we are moving the pedal in one direction as in normal forward driving.
The chainring, which is firmly attached to the pedals, usually has more teeth than the sprocket on the rear wheel.
If the chain ring rotates once, the pinion and thus the entire rear wheel rotates two or three times, depending on the gear ratio.
The bottom pedal moves backwards relative to the bike when riding forward.
The wheel as a whole naturally moves forward when riding.
Because of the high gear ratio and the large diameter of the rear wheel, the lower pedal always moves forward in relation to the ground – albeit not quite as fast as the bike as a whole.
Thus, forward movement of the wheel is associated with forward movement of the lower pedal.
If I pull the bottom pedal backwards, the wheel cannot move forward.
But what does the wheel do instead?
Doesn't it move at all?
Or backwards?
It moves backwards - and the pedals turn backwards too.
It's not exactly easy to understand.
I found a clear explanation in a video by the mathematician George Hart.
As explained above, when driving forward, the pedals always move forward in relation to the ground, regardless of whether they are straight up or down.
If, on the other hand, the pedals are moved backwards and the bike rolls backwards (this works with a track bike without a freewheel – also called a fixie), the pedals are constantly moving backwards in relation to the ground.
Hart demonstrates this reversal of forward motion in his video by simply playing a forward motion clip backwards.
Incidentally, there is also a constellation in which the wheel does not move backwards when you pull the pedal backwards, but forwards.
The translation must be so small that the backward movement of the pedal relative to the wheel is greater than the total forward movement of the wheel.
In case you missed a mystery from the past few weeks, here are the most recent episodes:
Every dash a dot
The split cube
The missing tile
A bridge, four people and a flashlight
All A's
A card makes the difference
The domino duel
Fairness at the coffee table
Magical 45
Perfectly arranged
