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Author: Subject: Monday puzzle - which way will the little cart go?
craig1410

posted on 1/8/11 at 01:19 PM Reply With Quote
quote:
Originally posted by loggyboy
quote:
Originally posted by David Jenkins
This OP disagrees - there is no optical illusion - the ruler IS moving from left to right.

However, as I said earlier, the position of the ruler relative to the big wheel is right to left, which is why the cart does what it does.

I was not confused about what I saw - I was simply impressed by the mechanical aspects of the 'trick' (of course, it is no trick).


But you were wrong to say that craig and matt were correct. lol - this is getting complicated!


I disagree - matt and I were correct.

The hand IS pushing the ruler from left to right. This is the only external force. The ruler in turn is applying a force to the perimeter of the large wheel again from left to right. The fact the large wheel rotates in the opposite direction changes nothing.

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craig1410

posted on 1/8/11 at 01:20 PM Reply With Quote
quote:
Originally posted by russbost
If the ruler moves from left to right it must push the large wheel in a clockwise direct - that is NOT what is shown in the video! If the large wheel was rotating clockwise the cart would move to the left as the bobbins rotate counter clockwise, so I would say there is an optical illusion there, all to do with the gearing & therefore the perceived motion of the ruler surely! IMHO of course


If you use the paper as the frame of reference, both the hand, ruler and cart are moving from left to right. The only external force is also from left to right. (ie. the hand).

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loggyboy

posted on 1/8/11 at 01:24 PM Reply With Quote
quote:
Originally posted by David Jenkins
This OP disagrees - there is no optical illusion - the ruler IS moving from left to right.



The optical illustion is that it looks like the ruler is being pushed in the same direction as th cart is moving. In fact the ruller is being pulled in the same direction as the cart(by the cart/wheels but being pushed (by the the hand in the opposite direction.

quote:
Originally posted by craig1410
i disagree - matt and I were correct.

The hand IS pushing the ruler from left to right. This is the only external force. The ruler in turn is applying a force to the perimeter of the large wheel again from left to right. The fact the large wheel rotates in the opposite direction changes nothing.


Matt was distictly wrong is that he said 'Pushing on ruler will result in cart moving fast in the direction that ruler is pushed. '

When as i stated, the pushing of the ruler is not that in which the ruler is traveling in.

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craig1410

posted on 1/8/11 at 01:28 PM Reply With Quote
quote:
Originally posted by loggyboy
quote:
Originally posted by David Jenkins
This OP disagrees - there is no optical illusion - the ruler IS moving from left to right.



The optical illustion is that it looks like the ruler is being pushed in the same direction as th cart is moving. In fact the ruller is being pulled in the same direction as the cart(by the cart/wheels but being pushed (by the the hand in the opposite direction.

quote:
Originally posted by craig1410
i disagree - matt and I were correct.

The hand IS pushing the ruler from left to right. This is the only external force. The ruler in turn is applying a force to the perimeter of the large wheel again from left to right. The fact the large wheel rotates in the opposite direction changes nothing.


Matt was distictly wrong is that he said 'Pushing on ruler will result in cart moving fast in the direction that ruler is pushed. '

When as i stated, the pushing of the ruler is not that in which the ruler is traveling in.


I'd disagree again as it seems obvious that Matt was referring to the direction the ruler is being pushed by the **hand** which is left to right.

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craig1410

posted on 1/8/11 at 01:45 PM Reply With Quote
Here's a mathematical explanation:

http://www.cs.ucla.edu/~sahai/UnderFaster.pdf

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Miks15

posted on 1/8/11 at 02:24 PM Reply With Quote
before watching the video i was 100% againt craig on this and i couldnt see how it would do what he was saying. Ive just managed to watch it and now it makes sense and i agree with craig. There is no optical illusion at all. The ruler is moving to the right, the cart is moving faster to the right.
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splitrivet

posted on 1/8/11 at 02:29 PM Reply With Quote
Never mind all that stuff with the cart.
How did he make those cuddly toys talk when he asked them the question, thats what I want to find out.
Cheers,
Bob





I used to be a Werewolf but I'm alright nowwoooooooooooooo

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craig1410

posted on 1/8/11 at 02:29 PM Reply With Quote
If you look at the mathematical explanation, it all comes down the fact that the centre of the cotton reels are smaller than the bit which touches the ground. If the cotton reel was just one radius along its axis then the cart would not have moved at all and most likely would have come apart. If the centre section was larger radius than the bits which touch the ground (eg. if on rails) then it would have gone the opposite way to the ruler movement (ie. to the left).
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loggyboy

posted on 1/8/11 at 02:56 PM Reply With Quote
quote:
Originally posted by Miks15
before watching the video i was 100% againt craig on this and i couldnt see how it would do what he was saying. Ive just managed to watch it and now it makes sense and i agree with craig. There is no optical illusion at all. The ruler is moving to the right, the cart is moving faster to the right.


Im not arguing that the ruler is moving to the right, Im arguing that the hand is applying a force that moves the ruler to the left. Simply look at the direction that the large tyre moves!
The force applied to the ruler (to the left) makes the cart move to the right, but due to the gearing effect the ruler is CARRIED to the right by the motion of the cart, not the force of the hand.

You can see this clearly in the video when the ruler is replaced by a finger.

[Edited on 1/8/11 by loggyboy]

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craig1410

posted on 1/8/11 at 02:59 PM Reply With Quote
quote:
Originally posted by loggyboy
quote:
Originally posted by Miks15
before watching the video i was 100% againt craig on this and i couldnt see how it would do what he was saying. Ive just managed to watch it and now it makes sense and i agree with craig. There is no optical illusion at all. The ruler is moving to the right, the cart is moving faster to the right.


Im not arguing that the ruler is moving to the right, Im arguing that the hand is applying a force that moves the ruler to the left. Simply look at the direction that the large tyre moves!
The force applied to the ruler (to the left) makes the cart move to the right, but due to the gearing effect the ruler is CARRIED to the right by the motion of the cart, not the force of the hand.

You can see this clearly in the video when the ruler is replaced by a finger.

[Edited on 1/8/11 by loggyboy]


No, you are incorrect.

The cart has no power source of its own so the only way the ruler can move to the right is if the hand is pushing it to the right. The net resultant force on the ruler is to the right and the hand supplies this force.

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loggyboy

posted on 1/8/11 at 03:10 PM Reply With Quote
quote:
Originally posted by craig1410
No, you are incorrect.

The cart has no power source of its own so the only way the ruler can move to the right is if the hand is pushing it to the right. The net resultant force on the ruler is to the right and the hand supplies this force.


Where do I mention a power source of the cart, or allude to one?

the ruler and the cart dont touch directly, so therefore the force applied to the ruler can move in any direction that the cart is propelled in.

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craig1410

posted on 1/8/11 at 03:15 PM Reply With Quote
quote:
Originally posted by loggyboy
quote:
Originally posted by craig1410
No, you are incorrect.

The cart has no power source of its own so the only way the ruler can move to the right is if the hand is pushing it to the right. The net resultant force on the ruler is to the right and the hand supplies this force.


Where do I mention a power source of the cart, or allude to one?

the ruler and the cart dont touch directly, so therefore the force applied to the ruler can move in any direction that the cart is propelled in.


You didn't which is my point - Newton's first law states that and object at rest will remain at rest unless a force acts on it. Since the cart has no power source then the only place a force can come from is the ruler which is in direct contact with the wheel which is part of the cart. The hand supplies the force to the ruler. Every particle of the large wheel is moving to the the right as well regardless of the direction of rotation.

I just don't follow your logic.

Anyway, I'm going to duck out of this argument now if you don't mind. It doesn't seem like we are any closer to reaching any sort of agreement.

[Edited on 1/8/2011 by craig1410]

[Edited on 1/8/2011 by craig1410]

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loggyboy

posted on 1/8/11 at 03:18 PM Reply With Quote
So what your saying is, beacuse the cart is moving to the left, the force that powered the cart (ie the ruler) must be being forced to the left also?
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Liam

posted on 1/8/11 at 04:11 PM Reply With Quote
I think that's the gist of it. And you're saying the input effort is actually towards the left even though the buggy and ruler move right? I think that's quite fundamentally impossible, isn't it?
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sprouts-car

posted on 1/8/11 at 04:18 PM Reply With Quote
quote:
Originally posted by Liam
I think that's the gist of it. And you're saying the input effort is actually towards the left even though the buggy and ruler move right? I think that's quite fundamentally impossible, isn't it?


I'll second that, what you describe is impossible.





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loggyboy

posted on 1/8/11 at 04:27 PM Reply With Quote
Not impossible at all, just think of the old handcars they use on the train tracks. That 'converts' up and down motion to rotaty motion via series of connections and rods. Just beacuse the input force is up and down doesnt mean the output motion has to be the same. (same as an engine!)
The above cart converts a striaght line motion to roatory motion, then reverses the direction then coverts the rotary motion back to straight (recipricating, IIRC). Its theses changes in types of movement that allows the rulers input to be reversed.


Im gonna set this up myself with some lego when I get home to see it work with my own inputs!

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TheGiantTribble

posted on 1/8/11 at 05:12 PM Reply With Quote
It seems to me

and don''t all shoot at me all at once

the angle of the ruler is some what important, as in left hand down or right hand down, in the vid it didn't look exactly like the ruler was not constantly perdendicular (I'm sure that aint the right speeling of it) to the desk and actually a up down force was being applied.

Or at least I think that's what I'm saying???

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craig1410

posted on 1/8/11 at 05:14 PM Reply With Quote
quote:
Originally posted by TheGiantTribble
It seems to me

and don''t all shoot at me all at once

the angle of the ruler is some what important, as in left hand down or right hand down, in the vid it didn't look exactly like the ruler was not constantly perdendicular (I'm sure that aint the right speeling of it) to the desk and actually a up down force was being applied.

Or at least I think that's what I'm saying???


Good effort - but explain this then...

http://www.youtube.com/user/coolaun#p/u/0/bbF8jtej8jw


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russbost

posted on 1/8/11 at 05:18 PM Reply With Quote
There's an awful lot of confusion here & even more rubbish being spewed out!!!

Think about it, if you place the ruler on the top of the large wheel & push to the right, which way will the large wheel turn??? It would have to turn clockwise, otherwise it's defying the laws of physics & nature!, it cannot possibly turn in the opposite direction to that which the ruler applies a force to it.

I think I was wrong to say optical illusion b4, it's more a trick than an illusion as such. Surely it is actually that the ruler is not being pushed to the right at all but is, in fact being drawn to the left, this results in the large wheel moving counter clockwise & the 2 bobbins rotating clockwise, hence the cart moves to the right & a lot more quickly than the ruler is moving left due to the gearing, therefore the overall effect is that the ruler moves to the right even tho' it is being drawn to the left. For the large wheel to rotate counter clockwise the ruler has to be moving from right to left (relative to the centre of the large wheel), NOT vice versa - I reckon many of you have been had! Again all in my humble opinion of course!

Not sure how well I've explained that, but it must surely be more coherent than some previous explanations!!!





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David Jenkins

posted on 1/8/11 at 05:32 PM Reply With Quote
Here's something for all of you who say "the ruler is actually going to the left" - please note the very first line of the mathematical proof from UCLA quoted earlier:

"Suppose the ruler is moving at a velocity v to the right."

In other words, the whole mathematical proof starts with that basic fact...

(I think that a number of people are taking this far too seriously, and making it far harder than it really is! )






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Liam

posted on 1/8/11 at 05:35 PM Reply With Quote
quote:
Originally posted by loggyboy
Not impossible at all, just think of the old handcars they use on the train tracks. That 'converts' up and down motion to rotaty motion via series of connections and rods. Just beacuse the input force is up and down doesnt mean the output motion has to be the same. (same as an engine!)
The above cart converts a striaght line motion to roatory motion, then reverses the direction then coverts the rotary motion back to straight (recipricating, IIRC). Its theses changes in types of movement that allows the rulers input to be reversed.


Im gonna set this up myself with some lego when I get home to see it work with my own inputs!


Look at it this way - do you think it's possible for you to attempt to push, say, a big ball accross the floor, but for somehow your efforts to push the ball away from you to result in the ball actually moving towards you? No, hopefully! And whatever mechanism of wheels/pulleys/etc you might attach to that ball, and only to that ball, you are not going to change that impossibility.

The examples of a hand operated train thingy/engine are not comparable. There, a closed system does some work (the human effort or operation of the engine) and the result is motion in some direction against the reaction force of the ground. You're proposing that you can apply an external force to a system (the buggy and ruler system) and for the result to be acceleration of the system in the opposite direction to the external force. Impossible.

Good luck with the lego! I'd be doing exactly the same myself to confirm if obly it wasn't all 1000 or so miles away .

[Edited on 1/8/11 by Liam]

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Liam

posted on 1/8/11 at 05:38 PM Reply With Quote
quote:
Originally posted by David Jenkins
Here's something for all of you who say "the ruler is actually going to the left" - please note the very first line of the mathematical proof from UCLA quoted earlier:

"Suppose the ruler is moving at a velocity v to the right."

In other words, the whole mathematical proof starts with that basic fact...

(I think that a number of people are taking this far too seriously, and making it far harder than it really is! )


I dont think people are disputing that the ruler and buggy all move the same direction*. What loggyboy is actually suggesting is that the ruler (and buggy) moving right is not actually a result of pulling the ruler right, but in fact the guy is pushing it towards the left (yet it moves right). Quite impossible.

*edit: oh dear - russbost is

[Edited on 1/8/11 by Liam]

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craig1410

posted on 1/8/11 at 05:38 PM Reply With Quote
Let me try one last time to explain what is happening...

A couple of important predicates first:

1. There is no slippage between the ruler and large wheel, between the large and small wheels or between the small wheels and the ground.

2. The parts of the cart stay intact. ie. The cart components are considered to be held together firmly.

3. We are referring to left to right motion as viewed by the camera

When force is applied by the hand, and in turn the ruler, the force is applied to the cart as a whole (pred. 2) and therefore the cart as a whole wants to move to the right. Forget about wheels etc for a moment. This causes the small wheels to begin to rotate clockwise. This in turn makes the large wheel rotate counter clockwise. At this point, if there was no gearing involved, you would get a stalemate and the cart would not move. However, because the centre of the bobbins are smaller than the bit in contact with the ground, there is mechanical advantage (gearing) and this is enough to overcome the linear force applied by the ruler to the perimeter of the large wheel. Now because the large wheel is rotating against the linear motion of the ruler, the effect is to increase the speed of the cart beyond that of the ruler itself.

Crucially, there is no part of the cart which is moving to the left at any time. The part of the small wheels which are between the axle and the contact patch are at zero velocity wrt the ground but all other parts of the cart are moving to the right.

If the bobbins were of equal diameter along the axis of the bobbin then the cart would not move. And if you could create a bobbin that was fatter in the middle than at the ground contact patch and by necessity you would need to place the cart on rails to allow the fat part of the bobbins to remain off the ground, then the cart would move to the left when the ruler moves to the right.

Read over the mathematical explanation I posted earlier if you don't believe me.

Cheers,
Craig.


I hope this helps.
Craig.

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russbost

posted on 1/8/11 at 05:49 PM Reply With Quote
"This in turn makes the large wheel rotate counter clockwise" Ok, so you are pushing to the right with the ruler, but the large wheel is rotating counter clockwise - please explain how this could be possible without slippage being present between the ruler & the large wheel???





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blakep82

posted on 1/8/11 at 05:50 PM Reply With Quote
i think the little video where he moves the paper explains how it all works best for me





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