View Full Version : brain teaser



cooler
04-21-2005, 06:44 PM
someone gave me this brain teaser and i see a flaw in the answer but can't prove it wrong convincingly yet. Do u guys see the same as me or the answer is correct?

Brain Teaser
A twin railway track is constructed around the equator. Two identical trains travel at the same speed endlessly around the tracks in opposite directions. Assuming the conditions on both trains are the same at all times, which track will wear out faster?

Answer to Brain Teaser
As you look down onto the North Pole, the earth is constantly spinning counter-clockwise around its polar axis. Thus the train that is travelling from west to east will be rotating faster around the centre of the earth than the one travelling from east to west. This additional rotational velocity will increase the centrifugal force on the eastbound train, reducing the force it applies to its track. The track carrying the westbound train will therefore wear out faster.

Cengsc
04-21-2005, 09:29 PM
Hi,

correct me if i am wrong,
i thought the globe is rotating clockwise,
then i think the answer will be opposite.

ceng

Qidong
04-22-2005, 12:35 AM
Cooler is correct, it should be counter-clockwise. Note that in the morning New Yorkers see the sun before Californians. :)

cooler
04-22-2005, 02:46 AM
Cooler is correct, it should be counter-clockwise. Note that in the morning New Yorkers see the sun before Californians. :)


:D thanks but that was the supplied answer anyway :) I was just trying to verify whether the rate of wear of each train was sound & logical. I did some deep thinking and came to agree with that answer, even tho it doesn't work in the real world.

Neil Nicholls
04-22-2005, 03:38 AM
tricky.

if the eastbound train is faster and therefore presenting a lighter load on the tracks, does its wheels have less grip on the tracks? Does the engine have to drive the wheels harder to keep the same speed as the westbound train? Does this cause more wear on the track?

Does the eastbound train encounter less air resistance than the westbound train (on average)?

there is something else I can't quite put my finger on...

lorus_blue
04-22-2005, 05:07 AM
hmm..does the rotational velocity still apply even if they both travel at the same speed endllessly?

cooler
04-22-2005, 06:04 AM
tricky.

if the eastbound train is faster and therefore presenting a lighter load on the tracks, does its wheels have less grip on the tracks? Does the engine have to drive the wheels harder to keep the same speed as the westbound train? Does this cause more wear on the track?

Does the eastbound train encounter less air resistance than the westbound train (on average)?

there is something else I can't quite put my finger on...

yes, i had thought of those too :)
it is really a stupid theoretical teaser. They factor in only wheel friction (real world) with an ideal (unreal) world of perfectly straight tracks, exactly same trains, no air resistance, exact same speed, etc.

FEND.
04-22-2005, 10:42 AM
someone gave me this brain teaser and i see a flaw in the answer but can't prove it wrong convincingly yet. Do u guys see the same as me or the answer is correct?

Brain Teaser
A twin railway track is constructed around the equator. Two identical trains travel at the same speed endlessly around the tracks in opposite directions. Assuming the conditions on both trains are the same at all times, which track will wear out faster?

Answer to Brain Teaser
As you look down onto the North Pole, the earth is constantly spinning counter-clockwise around its polar axis. Thus the train that is travelling from west to east will be rotating faster around the centre of the earth than the one travelling from east to west. This additional rotational velocity will increase the centrifugal force on the eastbound train, reducing the force it applies to its track. The track carrying the westbound train will therefore wear out faster.
Do you factor in relative velocity?

Break-My-String
04-23-2005, 03:48 AM
Yes, what happens when we compare the velocties (V) of the trains when they are travelling at

(A) V = 1 inch per hour
(B) V = 1041 miles per hour (approx. earth's rotational velocity)
(C) V = 1042+ miles per hour

Cheers!

cooler
04-23-2005, 04:32 AM
Yes, what happens when we compare the velocties (V) of the trains when they are travelling at

(A) V = 1 inch per hour
(B) V = 1041 miles per hour (approx. earth's rotational velocity)
(C) V = 1042+ miles per hour

Cheers!

it seems that teaser is a hypothetical question, so in essense, any V > 0 will create frictional wear difference, even if it take billion years to wear down the trains. :o

bigredlemon
04-23-2005, 12:55 PM
Presuming your answer would be true, then if hypothetically the earth's rotation were accelerated to the speed such that the trains's experience no net up or down force and thus gravity would be balanced against the "centrifugal" force, then it would follow that a train travelling one direction would be pressed into the earth whereas the train travelling in the opposite direction would float into space.

cooler
04-23-2005, 03:12 PM
Presuming your answer would be true, then if hypothetically the earth's rotation were accelerated to the speed such that the trains's experience no net up or down force and thus gravity would be balanced against the "centrifugal" force, then it would follow that a train travelling one direction would be pressed into the earth whereas the train travelling in the opposite direction would float into space.

true, the teaser question didnt specified which speed. One dont need to accelerate earth rotational V, if the train can attain 1041+1 mph, the west to east train would be levitating :D

Robin (SWE)
06-07-2005, 11:12 AM
...the centrifugal force...

Doh! Everytime I hear or read "centrifugal force" the image of my higher level physics(I.B.) teacher, which is bald and has a heavy beard, apear in my head and says "the term 'centrifugal force' does not exist in physics!"

nice job Mr. Charters!

Neil Nicholls
06-07-2005, 11:45 AM
centrifugal force, centripetal force,
what's in a name?

" A centrifugal force is a force on an object that tends to move it away from a center of rotation and always results from the inertia of the object. Inertia is the property of an object proportional to mass that opposes acceleration. A centripetal force is a force on an object that tends to move it toward a center of rotation and can be a result of gravitation, electricity, or any other naturally occurring force. For example, if you hold a bucket of water by the handle and spin in a circle, you can feel the bucket pull your arms away from the center of your rotation. This is the centrifugal force and is a result primarily of the inertia of the bucket and the water. The effort that it requires to hold onto the bucket and keep spinning is the source of the centripetal force. You can “feel” the centrifugal force in this example, and you can observe (due to the circular motion) that a centripetal force is present. When Apollo 8 orbited the Moon in 1968, the centripetal force was provided by the gravitational attraction between the spacecraft and the Moon. The centrifugal force, which opposed gravity in this example, was provided by the inertia of the spacecraft and the astronauts. Because both gravity and inertia are proportional to the mass of an object, the astronauts could not “feel” either the centripetal or centrifugal force. This cancellation of effects that are proportional to mass is the source of weightlessness when in outer space."

wilfredlgf
06-07-2005, 12:16 PM
yes, i had thought of those too :)
it is really a stupid theoretical teaser. They factor in only wheel friction (real world) with an ideal (unreal) world of perfectly straight tracks, exactly same trains, no air resistance, exact same speed, etc.

You forgot about travel visa, immigration checkpoints, refuelling at stations and of course, the construction of rails across the ocean.