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Anonymous Poster

Interesting Brain Teasers

03/29/2007 3:34 PM

Here are some interesting brain teasers, especially the last two.

http://varatek.com/scott/feynman_problems.html

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#1

Re: Interesting Brain Teasers

03/30/2007 2:15 AM

Ok the first two are relatively easy.

  • Left and right are reversed in a mirror because they are relative to the direction you are facing, while, up and down are relative to the earth and not dependant on the direction you are facing. The direction left and right describe are dependant on the way you are facing and therefore will be affected by the reversal of the image in the mirror. The light being reflected by the mirror has changed in direction by 180° but the image has not altered therefore the plane of reference has not changed. Change in direction with no change in the plan of reference results is a reversal of the relative directions of left and right. Up and down on the other hand are not dependent on the way you are facing, therefore, the reversal of the direction in the mirror has no affect.
  • Because the two wheels are linked together, with a common rigid axle, and have the same diameter, they must both travel the same distance. This means the train must travel in a straight line. This however falls down when going around a corner or if the wheels have separate bearings.

The other two I need to think about a litter more before I give my answers.

You do intend to give the answers some time in the future don't you? Not giving the answers could be hazardous to you ongoing health and future wellbeing.

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#4
In reply to #1

Re: Interesting Brain Teasers

03/30/2007 6:10 AM

2.) Train wheel rims (ignoring the flange) are slightly conical (larger diameter on the inside than the outside). If the train moves slightly to the left on the rails the larger diameter "tries" to "drive" the left hand side of the train faster i.e. steers to the right.

3.) The "other way" surely, but, I suspect a catch I haven't thought of here.

4.) Again, it seems obvious that the total torque on the coil will be equal and opposite to the torque on the balls, so, the disc remains still. But, I'd like to see if I'm wrong.

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#5
In reply to #4

Re: Interesting Brain Teasers

03/30/2007 6:25 AM

In no.4, the induced torque will only have an effect for a tiny length of time - like an ignition circuit in a car. The disc will start to move, but then be stopped by the induced effect in the charged balls - resulting in a tiny jerk, but in no obvious direction.

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#8
In reply to #4

Re: Interesting Brain Teasers

03/30/2007 8:56 AM

Actually what it is doing is letting both sides stay it sync relative to the actual distance both must travel as the train goes around the curve. Stagger between the wheels does make the axle want to turn you are correct about that. The old trains of Europe used to have single wheel sets on each end of the car. Most trains in today use the twin axle trucks that actually have a truck frame and bolster that connects a pair of axles. The axles are linked together by the bolsters and must remain parallel to each other as long as the flanges are engaged with the rails. They could have independent rotation and still stay on the track because the axles are prevented from skewing to each other and the rectangle they form will not let them rotate far enough to leave the rails within the normal gauge of the track.

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#2

Re: Interesting Brain Teasers

03/30/2007 5:08 AM

#2 - Outer train tracks are raised to give a camber at corners, so the mass of the train helps it turn. There is a maximum speed for each bend, greater speeds putting excess pressure on the flanges and causing derailments.

#3 - The sprinkler will turn in the opposite direction if sufficient suction is available, as that will reduce the pressure at the side with the holes.

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#3

Re: Interesting Brain Teasers

03/30/2007 5:57 AM

#2

The train wheels is formed like a trapezium.

on a bend the train is forced to one side.

The running diameter of the inside wheel is smaller than the outside wheel and the different distances can be covered. A flat faced wheel Will have to slip around corners (bends) causing excessive wear.

I think they use a tiny hammer to get it in shape again.

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#7
In reply to #3

Re: Interesting Brain Teasers

03/30/2007 8:41 AM

"The train wheels is formed like a trapezium."

I really hope that's in a section view Hendrick !

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#29
In reply to #7

Re: Interesting Brain Teasers

04/02/2007 1:38 AM

Yes definitely, maybe i should have used another word.

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#6

Re: Interesting Brain Teasers

03/30/2007 6:28 AM

Mirror

Your eyes are spaced horizontal with left eye looking at the left side (right side of image).

But up will be up and down will be down for both eyes

if you Lay on your side the up/down direction will be disturbed.

The reverse effect can be removed by placing 2 mirrors at 90degrees and view from 45 degrees.

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#9
In reply to #6

Re: Interesting Brain Teasers

03/30/2007 11:51 AM

the sprinkler will not move at all. Water is heavier than air. the force of the water coming out of the sprinkler is heavier than the air that surrounds the tubing. therefore it spins. In an underwater setting the water is being sucked into a tube that is surrounded by water already. It might start to move at first suction and then stay put once the tube is full of water.

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#10
In reply to #6

Re: Interesting Brain Teasers

03/30/2007 12:41 PM

Hendrik -

I don't think the placement of the eyes is important. If you cover one eye, you still see right and left reversed.

Another point: Front and Back are reversed in the mirror, as well as Right and Left. And if you put the mirror on the ceiling, Up and Down are reversed!

I've been playing with this concept since I was a kid. I've always had trouble with Right and Left anyway.

:)

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#30
In reply to #10

Re: Interesting Brain Teasers

04/02/2007 2:05 AM

I think the placement do play a part of how the image is perceived.

I had a back operation and had to Lay down for a long time.

Looking at the same mirror the horizontal then was ok but the vertical was reversed.

The perception will therefore always change relative to the placement of your eyes.

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Anonymous Poster
#11

Re: Interesting Brain Teasers

03/30/2007 3:15 PM

OK, I'm the troublemaker who posted this thing. Here's my take on the answers:

1. The mirror doesn't reverse top-bottom or left-right. It reverses front-back (imagine someone standing in front of the mirror).

2. As has been pointed out, train wheels are not flat but tapered, smaller on the outside, and locked together on the axle. If the train gets off to one side, that side rides on a larger part of the wheel and the train steers itself back toward the middle. In turns, it would be slightly off center until the track was straight again.

3. This one is tricky. I tried simulating it (as suggested by someone on the web) by punching holes in an angle into a can, and weighting it so it would sink into the water. The can definitely turns one way and the water inside the can turns the other (conserving angular momentum). So I believe that if the water had to come to a stop (as in a sprinkler) there wouldn't be any rotation. If the water was still swirling as it left the sprinkler and went up the hose, there might still be some rotation. Someone with a swimming pool and a sprinkler could adapt the pool vacuum to the garden hose and give this a try (any takers?).

4. The electric and magnetic field are crossed and in this configuration store angular momentum as well as energy, so the initial momentum is non zero. If we started with a charged disk and no magnetic field and turned on the magnet, it would start to turn. To stop it would require a torque which would give the disk an initial angular momentum, even with it stopped. (Google "Feynman disk paradox").

Now the spooky thing (I read somewhere) is that if you have a charged (insulating) disk and you bring a magnet to the face of the disk, the disk will feel a torque and start to turn, but there will be no corresponding reverse twist on the magnet. (It's the same situation, except without the magnet on board). This is totally counter-intuitive.

Being able to "hide" momentum in an electromagnetic field excites folks who want to build a "reactionless" spaceship drive. Unfortunately, I think its been proven that it won't work. Nature is not very nice sometimes.

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#12
In reply to #11

Re: Interesting Brain Teasers

03/30/2007 3:37 PM

About the mirror - I came to the same conclusion during a discussion at lunch! (Shoulda posted it faster, I guess.) The key is to look at things from your own point of view, not from the point of view of your reflection.

Right and left aren't reversed from your point of view. If you have a table on your left, the reflected table is still on your left. Your reflection would see the table on its right! But your reflection is only an illusion, after all, and doesn't "see" anything.

Front and back are reversed from your point of view. If there is a window behind you, the reflected window is now in front of you. On the other hand, your reflection has a reflected window behind it.

Finally, if the mirror is on the ceiling, it does not reverse anything, from your point of view, except Up and Down.

The bottom line is that the mirror reverses things in the same direction that it reflects light. Perfectly logical - as long as you don't try to see things from the point of view of that pleasant and attractive person in the mirror!

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#13
In reply to #12

Re: Interesting Brain Teasers

03/30/2007 3:47 PM

I like to imagine this - I'm nose to nose with a mannequin . I unzip my back , and fold the skin onto the mannequin . It confirms your point , in a rather sick sort of way. If you imagine your eyeballs moving the same way , it reveals that your reflection is not how others see you . I was kind of twisted to start with though. Kris

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#14
In reply to #13

Re: Interesting Brain Teasers

03/30/2007 3:57 PM

"I like to imagine this..."

...you DO?? You like to imagine peeling off your own skin??

"rather sick" ... "kind of twisted"

Well, OK, if you say so...

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#15
In reply to #14

Re: Interesting Brain Teasers

03/31/2007 2:00 AM

You may be taking me a bit too serious Astronut . Comprehending an unusual viewpoint is a bit like the process of remembering useless information. For instance I can reel off Countries around the Equator by a daft sentence using the first letters. The more absurd the mnemonic the better it works (It's a fact) .Brits are not quite the flaggellants you imagine . Kris

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#17
In reply to #15

Re: Interesting Brain Teasers

03/31/2007 12:38 PM

Kris, I'm not taking you seriously at all - just poking fun at your choice of words. Guess I should've included an emoticon.

:p

I do get a kick out of exploring unusual viewpoints. Science fiction is a great venue for that; one can safely explore alien ideologies that would be terrifying if encountered in real life!

Speaking of absurd mnemonics - everyone seems to have one for sine, cosine, and tangent. My teacher used this one:

"Try our apples, cold and hot! Sample our huckleberries!"

Translated: Tan = Opposite / Adjacent, Cos = Adjacent / Hypotenuse, Sin = Opposite / Hypotenuse

What did you use?

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#18
In reply to #17

Re: Interesting Brain Teasers

03/31/2007 1:45 PM

Thanks Astronut ,

Words have so much ambiguity , you're right . For what it's worth ; "Some Of Harry's Cows And Horse's Trod On Arthur".

Weird , hmm . That was a chosen phrase of my first mentor . Stupid , but works yes.

Science Fiction ? - even the odd has is place. Punctuation changes all in meaning. Meaning and intent can be confused . Have you seen the person who has not yet spell-checked their name ? If not , look around - I was tempted to point it out but thought 'woh' (honest , it's great !), they probably just haven't realised yet. I don't usually bother too much with spelling and grammar - the result usually ends up in understanding if both sides have humour and understanding . You may have got a FOAD reply here, but I smile and like the potential repartee / understanding. One of my favourite people speaks in metaphor (many languages do).Vive la difference.

Kris

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#19
In reply to #18

Re: Interesting Brain Teasers

03/31/2007 2:04 PM

...FOAD?

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#20
In reply to #19

Re: Interesting Brain Teasers

03/31/2007 2:19 PM

It wouldn't google , and it is a touch blunt to spell out . 'Go forth and do not trouble me again' is a rough translation. I did not mean it to yourself literally so didn't spell it out. My intent was more a jokey 'fair enough' etc. It's the kind of comment that can either leave you laughing or mad depending on how it's said/how well you understand the other person. I meant the former .

Kris

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#21
In reply to #20

Re: Interesting Brain Teasers

03/31/2007 2:47 PM

OK, then, I'll take it in the spirit it was intended.

:)

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#22
In reply to #21

Re: Interesting Brain Teasers

03/31/2007 2:55 PM

+=

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#23
In reply to #18

Re: Interesting Brain Teasers

03/31/2007 3:44 PM

Hi Kris

"Have you seen the person who has not yet spell-checked their name ?"

Thought you may find this link interesting.

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#24
In reply to #23

Re: Interesting Brain Teasers

03/31/2007 4:23 PM

Hey , I know royalty ! Mind you , I may be fewer steps removed from Bush (which is worrying ). Your namesakes didn't meddle - no sense of fun !

I have two dopplegangers on a UK search - odd 'cos I used three initials + surname . I didn't leave any tracks during my wayward student days. The surname is more common in Ireland than England (which surprises many). Even stranger the associated names (ie same address) were ones of family members . I have a large family tree , but it was a bit jaw-dropping. It's like the question of how many people need to be in a room for 2 to share a birthday - comes out as something like 21 for a 50% chance . A sure fire pub bet . I had to tear up bits of paper and put them in a hat to show my wife - she still didn't believe ! You can make a killing on this principle - a bit like lots of carny games (many of which boil down to quick binary maths).

Dare you - bet a mate that if you ask 25 people in a bar , 2 will have same day+month of birth . You will win in the long run (probably first time ).

Kris

ps -the name check was serious - somebody placed a derogatory response to another person , and my spell-checked reply said it all (at the name )! I had to ignore it's suggestion for fear of offence.

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#26
In reply to #24

Re: Interesting Brain Teasers

04/01/2007 5:29 AM

The name MASU is actually a contraction of two names. I originally used a different contraction but somebody developed a drug to treat migraines that had the same name so I needed to change it. Even so in the US MASU is sometimes used as an acronym for Minimum Access Surgical Unit. Everybody else calls this endoscopic or laproscopic surgery but you know how the US loves the use of acronyms.

A classic is the use of AMD by IBM. AMD stands for Air Movement Device, otherwise known as a fan. Only IBM could invent a three letter acronym to replace a three letter word.

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#25
In reply to #12

Re: Interesting Brain Teasers

03/31/2007 9:34 PM

"...if the mirror is on the ceiling..."

I hope you're not one of those guys who have a mirror on their bedroom ceiling, and the words on the mirror are "Objects in the mirror appear larger than they are"!

S

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#31
In reply to #11

Re: Interesting Brain Teasers

04/05/2007 3:56 AM

"2. As has been pointed out, train wheels are not flat but tapered, smaller on the outside, and locked together on the axle. If the train gets off to one side, that side rides on a larger part of the wheel and the train steers itself back toward the middle. In turns, it would be slightly off center until the track was straight again."

- just like a toboggan going down an ice run.

The angle of coning is about 1 in 20. Rails are canted inwards by this figure too, except at modern switch-and-crossing formations where the rails are vertical so as to save on the number and type of baseplates required to secure the rails to the crossing timber.

As regards curved track, there are whole chapters dedicated to this subject in permanent way engineering manuals. It is common practice to put on only about 2/3 of the equilibrium cant for the top speed. If the full equilibrium cant is applied, then the increased angle of attack causes more rail- and flange-wear. In addition, more force is applied to the outer wheel at the equilibrium cant, thereby accelerating the wear process. Wear reduction and energy saving are important considerations on high-speed lines. The technique is called 'cant deficiency', and there are certain limits to the provision that are absolutely necessary to achieve the safe passage of a rail vehicle round a curve.

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#16

Re: Interesting Brain Teasers

03/31/2007 9:56 AM

You all missed the point about the reflection in the mirror, Light travels in straight lines and the light from you left or right side strikes the mirror in front of its self the brain inteprets this as an image reversal. When you read text in a mirror it is seen as reversed because it is reversed in you hands look down at the letters then in the mirror. All will be made plain to you, the illusion is in fact real.

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#27

Re: Interesting Brain Teasers

04/01/2007 10:31 AM

Mirror Case: mirror doesnot change anything in the image but it shows the image as it is i.e. left side on the left side and the right side on the right side. But since our body is symmetric around longitunal plane and our perception (making of image at ratina and its analysis by brain); we feel that the image's side has got changed. actually our left side and right side are just mirror image of each other. If we lie down in front of the mirror then if we are lieing on right side the image will rest on left side but the head and feet will be on the same side wrt mirror.

Rail case: it is partly due to its flange but mainly due to, mentioned by some body that the wheel is little conical which forces the wheels inside and since the inward force is on both the wheels, the train keeps on straight.

Sprinkler case: When a fluid is going out it pushes the nozzle/ outlet. The moving fluid also creates some ripples in the surrounding fluid. In open air case ( squirting), the outgoing fluid is water and the surrounding fliud is air here the momentum created by the outgoing water cannot be equally countered by the moving air so the sprinkler rotates. But in the second case, where the outgoing fluid and the surrounding fliud are all same i.e. water so I feel that the sprinkler will not rotate but will be stationary. There may be some swinging thisside that side due to the ripple in the water but no clear rotation as in first case.

Fourth riddle: no clue.

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#28
In reply to #27

Re: Interesting Brain Teasers

04/01/2007 5:59 PM

Mirror Case: I think the confusion about the mirror results from the following scenario. If you take a book, for example, and hold it in front of the mirror, the text looks backwards. However, to see it in the mirror, you turned it around. It is backwards compared with what the book looked like before you turned it around. If you take a transparent stencil, the kind that are commonly stuck on back windows of cars, you can read it correctly in the mirror without turning it around. Only its front and back side have been reversed.

Train case: Yes, hopefully it doesn't get to the flange. That's when sparks start flying.

Sprinkler case: When the water comes out it makes no difference whether it is in water or air except in water it will turn slower due to drag forces. When the water squirts out the sprinkler heads, their orientation causes the water to have a net angular mementum as it leaves the sprinkler. Because of conservation of angular momentum, the sprinkler has to turn in the opposite direction.

If water goes in, the question is: Does water going into the nozzles impart an angular momentum to the fluid around it? If it does, then the sprinkler should turn to cancel out this momentum. I don't think there is concensus one way or the other. I'm still waiting for someone with a swimming pool to try it out.

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