Riddle: You have a bike....

[JT!]

...that is freestanding* with no one on it. The right crank arm is at the 6 o'clock position. If you tied a piece of string to the pedal of that crank arm, held the string paralleled to the floor, and pulled backwards on the string, what would happen to the bike? Would it move forwards, move backwards or stay in the same place?

 

*it cannot fall.

[jeff costello]

i'd say the crank arm would move few degrees clockwise (hence a tiny amount of forward motion), then the bike would move backwards?

if friction was really high, it would not move at all?

(not 100% sure i got the initial situation right)

 

Edited April 22, 2017 by jeff costello

[Ali C]

the bike would move forward until the crank rotated 90 degrees then it would stop 

[jeff costello]

8 minutes ago, Ali C said:

90 degrees

are you pulling the strung from infinitely far away?

[Ali C]

wouldn't make any difference how long the string was would it? (within reason).

The string would naturally pull the crank to the centre of it's arc (9 o clock looking from the drive side) which is 90 degrees rotation. Rotating the cranks clockwise would drive the bike forwards until the crank stopped in said position. The string would then be trying to pull the whole bike backwards but the engagement system in the hub wouldn't let the rear wheel turn leaving the bike stationary unless enough force was put through the string to break the grip of the tyre.

Unless I've missed anything that seems right to me?

[JT!]

My first instinct was to say it pulled the bike backwards right away.

[jeff costello]

44 minutes ago, Ali C said:

wouldn't make any difference how long the string was would it? (within reason).

The string would naturally pull the crank to the centre of it's arc (9 o clock looking from the drive side) which is 90 degrees rotation. Rotating the cranks clockwise would drive the bike forwards until the crank stopped in said position. The string would then be trying to pull the whole bike backwards but the engagement system in the hub wouldn't let the rear wheel turn leaving the bike stationary unless enough force was put through the string to break the grip of the tyre.

Unless I've missed anything that seems right to me?

i think we are more or less thinking the same thing.  

if you pull the string parallel to the ground on pedal height, the crank can't go up all the way to 90°.

my train of thought was that after the initial movement upwards the crank arm should fall in line with the hypotenuse of a right-angled triangle. hence the crank would move upward as the string got longer.

[Ali C]

there was no bit saying the puling point of the string was a set height, if anything that description means the string is no longer being pulled horizontal as soon as the crank moves.

If the string is being pulled horizontal to the ground that means horizontal the whole way allowing the crank to rotate the 90 degrees  

[jeff costello]

16 minutes ago, Ali C said:

there was no bit saying the puling point of the string was a set height, if anything that description means the string is no longer being pulled horizontal as soon as the crank moves.

If the string is being pulled horizontal to the ground that means horizontal the whole way allowing the crank to rotate the 90 degrees  

"hold the string parallel to the floor and pull" does sound like a fixed height at crank level to me.

if you move your string upwards to stay level with the crank, it would of course go up to 90°, but you wouldn't have stayed parallel to the floor (the way i understood it)

[Ali C]

But it would be parallel. All parallel means is the angle of the string is fixed horizontal the same as the floor, nothing to do with start and end points or distance away from the floor. 

[JT!]

The string starts parallel to the floor, but the height can change and it still remain parallel. But that's really not the issue at hand.

 

^Ah you beat me to it.

Edited April 22, 2017 by JT!

[jeff costello]

ah, ok. that's true too.

i was more thinking in terms of the force applied should move parallel to the ground.

[Ali C]

it does  

[jeff costello]

16 minutes ago, Ali C said:

it does  

you b*****d! i'd put it on my english, but i'd struggle in german just as much. 

the angle point (or whatever to call that thing) moves upwards. "take a string & pull" sounds to me like you have a certain length where you grab the string. in my understanding both movement of angle point and string stayed parallel to floor. 

Edited April 22, 2017 by jeff costello

[manuel]

My first instinct - makes a big difference whether you are standing in front of or behind the bike....

[J.KYDD]

On 22/04/2017 at 0:40 PM, Ali C said:

the bike would move forward until the crank rotated 90 degrees then it would stop 

But surely the tension on the string would prevent the bike from going forward. Only if the string was slack could the bike move forward, but by pulling on the string, the bike is essentially leashed so could only either: 

stay in one place, if the tension put on the string equaled that of the forward pedalling force 

or, the bike would be dragged backward if the force pulling on the string exceeded the pedalling force. The rear wheel would indeed turn forward, the bike would not 

[JT!]

1 hour ago, J.KYDD said:

But surely the tension on the string would prevent the bike from going forward. Only if the string was slack could the bike move forward, but by pulling on the string, the bike is essentially leashed so could only either: 

stay in one place, if the tension put on the string equaled that of the forward pedalling force 

or, the bike would be dragged backward if the force pulling on the string exceeded the pedalling force. The rear wheel would indeed turn forward, the bike would not 

You're on the right track.

[Ali C]

That was such a good point I actually went and tied a string to my bike and got Jane to stop it from falling over.

I now know the answer! 

 

[Topsy]

12 hours ago, J.KYDD said:

But surely the tension on the string would prevent the bike from going forward. Only if the string was slack could the bike move forward, but by pulling on the string, the bike is essentially leashed so could only either: 

stay in one place, if the tension put on the string equaled that of the forward pedalling force 

or, the bike would be dragged backward if the force pulling on the string exceeded the pedalling force. The rear wheel would indeed turn forward, the bike would not 

 

Well, this would depend on the gearing wouldn't it?

Let's say you have a fixed point in the room, let's say where the BB is, and you'd have a sufficiently light gearing you could pull back on the crank and the crank would move away backwards from the fixed point faster than the bike would move forwards, leaving the bike traveling forwards with the crank actually traveling 'backwards' until it gets to the point Ali brought up?

 

On 22.4.2017 at 9:23 PM, manuel said:

My first instinct - makes a big difference whether you are standing in front of or behind the bike....

That is a good point too, you can tug backwards on the string whilst standing on the front of the bike too..

[JT!]

11 hours ago, Ali C said:

That was such a good point I actually went and tied a string to my bike and got Jane to stop it from falling over.

I now know the answer! 

 

You know an answer

[Greetings]

Thought I'd solved this, then went to check it on a real bike and...  came back to delete my answers. 

I think there's a 3rd / 4th (depend on how you look at it) scenario, and it's that the bike will move up.

Check out the Josephus problem if you're into such things. There's also one where you have 1000 bottles of wine, one is poisoned and you have 10 rats to test which bottle it is. Poison starts working after 1 hour and the party starts in an hour. You need to narrow it down to a single bottle.

[Mark W]

So what you're saying is it takes off?

[Greetings]

Not proposing a new way of interstellar travel, but if the bike can neither go forward nor backwards, the pulling force will cause the rear wheel to lift off the ground for a brief moment?

[Mark W]

It's all good, that post was essentially for JT's benefit

[Paperclip]

Love a good head scratch like this, actually did similar things at college.  

The more I think about this the more similar to a train question I was given in college as part of an exam and I nailed it I remember it being on a page of the exam labelled "Counteraction" (College exam's were pretty laid back :P)  so somewhere in the above something has to counteract, either the wheel would have to skid, the bike would move forward counteracting the tension of the pulling or that the bike would move backwards but the crank arm would have to technically move anti clockwise with the bike.