Here's something to think about...
Look at this picture:
It shows a little cart made with a couple of bobbins that that can rotate freely. A big wheel sits on top of the bobbins - if you push the cart, the
big wheel rotates in the opposite direction to the bobbins. OK so far?
Now if a ruler is put on top of the big wheel and is pushed to the right, which way will the cart move, and how fast (roughly)?
I'll post the answer in a couple of hours!
Depending on the coefficient of friction between the different materials the piece of paper inder the cart should move in the same direction as the ruler is moving and the cart will stay where it is.
does it goes left, roughly 3 times faster than you move the ruler?
no, change my mind, it doesn't move at all! go with that, because the little wheels won't have enough power to them to overcome you dragging
the whole thisng the other way with the ruler
[Edited on 1/8/11 by blakep82]
Looks to me like it will move towards the hand
it will move to the left and the monkey gets his nose cutoff
Whizz to the lion?
Top of wheel moves in same direction as the cart, but way slower.
Pushing on ruler will result in cart moving fast in the direction that ruler is pushed.
Ratio distance move is the same as the ratio bobbin diameter to bobbin-outer minus bobbin-inner diameters.
Go on show us the video
depends if you intend to be on Penn and teller next weekend ?
Best bit of Saturday TV that IMHO
regards
Agriv8
quote:
Originally posted by blakep82
does it goes left, roughly 3 times faster than you move the ruler?
It will move in the same direction as the ruler, to the right and at a faster rate than the ruler is moving in relation to the ground. I had to think
about it for a minute though...
My thinking goes like this:
1. There is only one external force - that of the ruler applying a force from left to right.
2. This will apply a clockwise force to the bobbins which will in turn apply a counter-clockwise force to the big wheel.
3. The force on the big wheel is working against the external force from the ruler but because of the gearing the force on the bobbins will
"win".
4. Therefore the cart will move right but at several times the speed of the ruler due to the large wheel rotating against the ruler's tangential
direction.
I hope that makes sense...
[Edited on 1/8/2011 by craig1410]
quote:
Originally posted by craig1410
It will move in the same direction as the ruler, to the right and at a faster rate than the ruler is moving in relation to the ground. I had to think about it for a minute though...![]()
Opposite direction to ruler, same speed.
Assuming that the paper doesn't move the cart must go left if the ruler is pulled to the right.
ETA I think that the ruler will not move in absolute terms (i.e. in relation to the table), but it will move to the right relative to the top of the
wheel at the same speed as the cart moves to the left (relative to the table). Make sense? It does in my mind!
[Edited on 01.08.2011 by Humbug]
Matt & Craig have got it right!
Video of cart
(the video's a bit stupid, but he does demonstrate how it works - and it looks weird!)
quote:
Originally posted by Humbug
ETA I think that the ruler will not move in absolute terms (i.e. in relation to the table), but it will move to the right relative to the top of the wheel at the same speed as the cart moves to the left (relative to the table). Make sense? It does in my mind!
quote:
Originally posted by David Jenkins
Matt & Craig have got it right!
Video of cart
(the video's a bit stupid, but he does demonstrate how it works - and it looks weird!)
quote:
Originally posted by loggyboy
quote:
Originally posted by David Jenkins
Matt & Craig have got it right!
Video of cart
(the video's a bit stupid, but he does demonstrate how it works - and it looks weird!)
The ruler IS being pushed to the opposite diection, however the travel of the cart makes it looks like the ruler is being pushed in the same direction.
quote:
Originally posted by craig1410
quote:
Originally posted by loggyboy
quote:
Originally posted by David Jenkins
Matt & Craig have got it right!
Video of cart
(the video's a bit stupid, but he does demonstrate how it works - and it looks weird!)
The ruler IS being pushed to the opposite diection, however the travel of the cart makes it looks like the ruler is being pushed in the same direction.
Eh? The ruler is being pushed/pulled/whatever from left to right and the cart is moving from left to right. How is that opposite?
quote:
Originally posted by craig1410
Eh? The ruler is being pushed/pulled/whatever from left to right and the cart is moving from left to right. How is that opposite?
Cool video David
[Edited on 1/8/2011 by craig1410]
Okay I think I get you now - I was thinking in terms of motion not force. Sorry.
The only way that could've been more awesome would be if Johnny Ball did the voice over...
No need to be sorry!, I love this sort of discussion.
But the wording of the OP is if 'you' move the ruler to right.
Sadly the OP was looking at the optical illiusion and assuming the input of the hand is moving the ruler in the direction of the cart, when in fact
its the cart that is moving the ruler, but the input of force from the hand is in fact pushing the ruler in the opposite direction to that in which it
'appears' to travelling in.
[Edited on 1/8/11 by loggyboy]
[Edited on 1/8/11 by loggyboy]
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).
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).
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
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!
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
quote:
Originally posted by David Jenkins
This OP disagrees - there is no optical illusion - the ruler IS moving from left to right.
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.
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.
Here's a mathematical explanation:
http://www.cs.ucla.edu/~sahai/UnderFaster.pdf
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.
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
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).
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.
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]
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.
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.
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?
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?
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?
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!
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???
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???
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!!!
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! )
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!
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!)
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.
"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???
i think the little video where he moves the paper explains how it all works best for me
quote:
Originally posted by russbost
"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???
lol, i love a nice argument.
My input, apart from agreeing with craig (for once, since we're not talking f1 ), is that all that counts is that the ruler cannot slip on the
big bobbin and the table cannot slip relative to the little bobbins. Then the cart can go in any damned direction it likes, irrespective of which way
the ruler goes, so long as nothing has to slip. It is entirely down to the gearing and the fact that once the cart moves relative to the table, it
also moves relative to the ruler in additon to the existing motion of the ruler (relative to the table). This thus adds a new dimension to how the
cart moves relative to the table, and both aspects must be worked out simultaneously to decide how it moves overall. And this is why its difficult to
predict before watching the video, because it appears that it should move left - but this left motion would have an effect on the big bobbin that
causes the cart to move right anyway.
Skip this bit if you want...
if the ruler moves 2cms to the right, the big bobbin turns 2cms round, causing the little centres to go 2 cms the other way, which equates to maybe
3cms at the rim. So the cart moves 3cms left, but that 3cms left rubs the ruler on the bobbin, which causes the small rim to turn 4.5cms back towards
the right, or 1.5cms further right than it started. Obviously it doesnt move left then right because nature solves both equations at once. That 1.5cms
would have an additional effect too...
A similar concept is how a large boat with turbines instead of sails, can go directly up wind, even though that seems impossible.
[Edited on 1/8/11 by JoelP]
quote:
Originally posted by russbost
"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???
and it is alarming nonsense, the suggestion that the ruler is being pulled left but moves right.
What we should all be thinking is how can we make use of this phenomenon to make our Locosts faster????
Imagine what you could do if you had a 1/4 mile long ruler attached to an engine which was on the ground next to the drag strip start line. You would
then have a super light car (no engine) with a huge wheel sticking out the sunroof and touching the ruler. Then you just need a remote control between
your throttle pedal and the engine beside the track!
2 second 1/4 mile here we come..............oh yeah, you might need a parachute too...splat! Too late!
quote:
Originally posted by craig1410
Here's a mathematical explanation:
Only on Locost builders, you see something with your very eyes and still theres 30 odd posts disagreeing with it.
Sheesh.
Still trying to work out how the teddies could answer questions.
Cheers,
Bob
opp direction as ruler and same speed as the smallers bobbins are just acting as Idler gears.. 1:1 ratio !?!?!?!?
quote:
Originally posted by splitrivet
Still trying to work out how the teddies could answer questions.
Cheers,
Bob
quote:
Originally posted by splitrivet
Only on Locost builders, you see something with your very eyes and still theres 30 odd posts disagreeing with it.
Sheesh.
if u disregard the the ruler being pushed or pulled and in fact the ruler could somehow balance itself on the large wheel by itself.
then push the white connecting plate things then the mechanics, ratios, motions would all be the same.
it doesn;t matter if the ruler is being pulled or pushed...the idea is the same.
u gys should know better as its exactly the same as say a cam belt with anchilary wheel on it..
quote:
Originally posted by MikeRJ
quote:
Originally posted by splitrivet
Only on Locost builders, you see something with your very eyes and still theres 30 odd posts disagreeing with it.
Sheesh.
I think most people haven't grasped the idea (or at least the importance of the idea) that the bobbins have two different diameters, the part that touches the table and the part that touches the big centre wheel. This is absolutely fundamental to the operation of this gadget, if the bobbins were simple cylinders it would not work at all.