A harmless little riddle

malmo wrote:

Wrong. The riddle was worded correctly. It's real simple if you imagine it another way. You have a treadmill in front of you. In your hand you have a model car, which you hold at arms length at one end of the treadmill. Now, make some "vrrrooom, vroooom" noises and move your arm so that the car moves towards the other end of the treadmill. What speed the treadmill moves opposite of the direction of the movement of the car is irrelevant: if the treadmill moves at half the speed, three quarters the speed, the same speed or faster than the speed that you move the model car, the result is EXACTLY the same. The car moves down the treadmill because it is being propelled by your arm -- NOT THE WHEELS.

The play will fly, of course.

VRRRROOOOOOM- VROOOOOOM!

like the movie Clue, "that's how it could happen, but what about this?"

under a different interpretation you would not even be able to move your toy car forward on the treadmill. because if you did so that would mean that the speed differential between the car and treadmill is greater than the speed of the treadmill to the ground, so the treadmill would speed up. it would speed up until the speed differential between the car and treadmill was the same speed differential between the treadmill and ground. the only speed of the car relative to the ground that satisfies that condition is a speed of 0. the car remains still. to help you understand this, imagine how fast the treadmill would have to be moving so that you would have to use all the arm strength you had to keep the car from moving backwards with the treadmill. say this speed is 500mph. that's the speed that makes it impossible for you to overcome the treadmills force due to friction. at that speed the car is moving over the treadmill at 500mph while the treadmill is moving backwards at 500mph, but the car relative to the ground is perfectly still, satisfying the riddle. if the treadmill slowed and you were then able to push the car forward then the speeds would not match.

like i said, both solutions are correct, depending on your interpretation of the riddle.

wadsworth wrote:

under a different interpretation you would not even be able to move your toy car forward on the treadmill. because if you did so that would mean that the speed differential between the car and treadmill is greater than the speed of the treadmill to the ground, so the treadmill would speed up. it would speed up until the speed differential between the car and treadmill was the same speed differential between the treadmill and ground. the only speed of the car relative to the ground that satisfies that condition is a speed of 0.

THE SPEED OF THE TREADMILL IS IRRELEVANT.

The wheels of the model car, or airplane, spin freely.

not so malmo. in the real world there is something called friction. if you really think that you could move a toy car forward against a treadmill going 100000000 miles per hour then you don't understand physics very well.

you are adding a sliding force + rolling force to give the plane lift; the rolling force is neglible if we assume the treadmill matches the speed of the wheels of the plane.

the rolling force is produced by the thrust of the engines.

hence you are wrong

the plane will not fly

wadsworth wrote:

not so malmo. in the real world there is something called friction. if you really think that you could move a toy car forward against a treadmill going 100000000 miles per hour then you don't understand physics very well.

I understand physics well enough to spot a red herring when I see it.

I work for an airline and put this little riddle up on the whiteboard.

It started some serious arguments so I was forced to remove it.

The only concensus you can reach, within a group of people, is that the riddler is indeed a Complete Assole.

Congratulations.

malmo wrote:

I understand physics well enough to spot a red herring when I see it.

god damn it you are so stupid. do you not agree that there exists a speed of the treadmill that will make it impossible for you to overcome with your flimsy arm? wheels dont eliminate friction, they just reduce it to a negligible force. however the friction force is still there. and if the treadmill speed was high enough this force could counteract your attempt to push the car forward. its as simple as that.

wow i thought this thread was done a while ago. malmo is correct, the plane will fly. the thrust is produced by the engines, creating a pressure gradient across the engines that "sucks" the plane's wings forward. NO force is applied through the wheels to the runway pavement. a treadmill that matches the airplane's speed relative to the ground around the treadmill will not prevent the airplane from flying. true, the frictional force will slow the acceleration of the airplane, but as long as the wheels and tires can withstand the centripital forces due to their spinning more than twice what they would normally need to take off, the plane will indeed fly. now let's alld drop this conversation and move onto something else. when is the next treadmill marathon attempt going to take place? i'm getting anxious.

If you want to start a fight in a bar/pub without actually being there.

o.k you take the ass kisser award

beauford wrote:

wow i thought this thread was done a while ago. malmo is correct, the plane will fly. the thrust is produced by the engines, creating a pressure gradient across the engines that "sucks" the plane's wings forward. NO force is applied through the wheels to the runway pavement. a treadmill that matches the airplane's speed relative to the ground around the treadmill will not prevent the airplane from flying. true, the frictional force will slow the acceleration of the airplane, but as long as the wheels and tires can withstand the centripital forces due to their spinning more than twice what they would normally need to take off, the plane will indeed fly. now let's alld drop this conversation and move onto something else. when is the next treadmill marathon attempt going to take place? i'm getting anxious.

malmo is correct that the plane will fly under ONE interpretation. the thing that neither he nor you understand is that there are multiple interpretations of this riddle.

wadsworth wrote:

god damn it you are so stupid. do you not agree that there exists a speed of the t readmill that will make it impossible for you to overcome with your flimsy arm? wheels dont eliminate friction, they just reduce it to a negligible force. however the friction force is still there. and if the treadmill speed was high enough this force could counteract your attempt to push the car forward. its as simple as that.

Yes, I'm an idiot wadsworth.

For arguments sake, lets just say that friction, instead of being negligible, is a major factor here. Lets assume that the takeoff speed of an airplane is 150mph, and friction of the wheels is ten percent. If you put enough thrust to move the plane 170 mph, the friction reduces the speed to 153, The plane flys. At takeoff, the treadmill was moving 153, the wheels 306mph, but the plane has lift. Game over...The idiot.

The most convincing argument so far.

wadsworth wrote:

malmo is correct that the plane will fly under ONE interpretation. the thing that neither he nor you understand is that there are multiple interpretations of this riddle.

The Riddle:

"An airplane is sitting on an enormous treadmill. As the plane starts its engines, the treadmill runs in the opposite direction at the same speed the plane is moving. Can the plane take off?"

I don't understand where there are any different interpretations to be made. Parse the riddle down to the components and you have:

1)An airplane is sitting on an enormous treadmill.

2)As the plane starts its engines, the treadmill runs in the opposite direction at the same speed the plane is moving.

This is a straightforward question. It's hardly a riddle at all.

Now if the riddle read: "An automobile is sitting on an enormous treadmill. As the automobile is put in gear, the treadmill runs in the opposite direction at the same speed the automobile is moving. Can the automobile get to the end of the treadmill?" -- then you'd have a different answer.

Same answer.

malmo wrote:

Yes, I'm an idiot wadsworth.

For arguments sake, lets just say that friction, instead of being negligible, is a major factor here. Lets assume that the takeoff speed of an airplane is 150mph, and friction of the wheels is ten percent. If you put enough thrust to move the plane 170 mph, the friction reduces the speed to 153, The plane flys. At takeoff, the treadmill was moving 153, the wheels 306mph, but the plane has lift. Game over...The idiot.

you are forgetting that the riddle can be interpreted differently, and that was my main point. your example here still follows your interpretation, not another permissible interpretation.

the speed is not defined. the way the riddle is worded the treadmill speed relative to the ground might be understood to match the speed of the plane relative to the treadmill. in that case it would be impossible for the plane to move. because if the plane ever started moving then the planes speed over the treadmill would be the treadmills speed relative to the ground PLUS the planes speed relative to the ground, and that does not satisfy the riddle, so the treadmill would have to speed up. it would speed up as fast as it needed to to halt the plane. you have a case where T=T+P which is only possible if P equals zero.

malmo wrote:

The Riddle:

"An airplane is sitting on an enormous treadmill. As the plane starts its engines, the treadmill runs in the opposite direction at the same speed the plane is moving. Can the plane take off?"

I don't understand where there are any different interpretations to be made. Parse the riddle down to the components and you have:

1)An airplane is sitting on an enormous treadmill.

2)As the plane starts its engines, the treadmill runs in the opposite direction at the same speed the plane is moving.

there are different interpretations because speed is a RELATIVE value and the reference frame is not defined in the riddle. is the riddle referring to the planes speed relative to the surface of the treadmill? or is it referring to the planes speed relative to the ground?

even with your interpretation, if you assume that the wheels are indestructable then the plane will still fly. you continue to forget that unlike in a car, THE WHEELS DON'T SUPPLY THE DRIVING FORCE, the air in front of the engines "sucks" the airplane forward. matching the velocity of the airplane relative to the treadmill will only make the wheels on the airplane reach some ridiculously large rotational velocity, while the air still pulls the airplane up to a sufficient speed as to produce the lift.

of course, this is an idealized situation. first, there is an amount of friction that exists between the axle and the tires. although it is negligible at the spinning speeds required during a normal takeoff, at the speeds now required the frictional force will become significant. secondly, at the rotational velocity required to carry the airplane down this treadmill, the tires would most likely tear themselves apart. i don't know of any airplane tire today that can carry an airplane as fast as it would on this treadmill.

so...

INTERPRETATION 1: THE TREADMILL MOVES OPPOSITE THE VELOCITY OF THE AIRPLANE RELATIVE TO THE GROUND

-the airplane flies. the tires must rotate twice as fast, though. no-brainer.

INTERPRETATION 2: THE TREADMILL MOVES OPPOSITE THE VELOCITY OF THE AIRPLANE RELATIVE TO THE TREADMILL AT THAT MOMENT IN TIME

-if you idealize the friction and the integrity of the tires, it flies. in a real-world situation, though, the tires would blow out before reaching takeoff speed. the plane does not fly.

you still do not understand interpretation 2.

if we idealize the tire integrity but keep the axle friction then the only condition that satisifies the riddle is one where the airplane has zero ground speed. the airplane could not ever begin to move forward. as soon as it would start to move forward we have a situation where planes speed to treadmill is positive. this would cause the treadmill to speed up to the same speed. so if the plane started to move forward over the treadmill at 1mph the treadmill would start to move backward at 1mph, but this would mean that the speed differential is now 2mph, which would cause the treadmill to speed up to 2mph, which would cause the speed differential to be 3mph.....and on and on. now if there is friction with the axle this would continue (instantaneously) until the plane slowed to 0mph. the plane would never take off.

now lets say there is no friction with the axle. the plane still would not take off, but the reason has nothing to do with the plane. the reason is that the riddle now becomes a paradox and doesnt make sense. if the plane started moving forward at 1mph the treadmill would move backward at 1mph but this would have no effect on the plane so the differential would be 2mph casuing the treadmill to speed up to 2mph, and on and on, except this time since the treadmill doesnt act to slow down the plane the treadmill is constantly trying to catch up to the speed differential which is impossible. T cannot equal T + P if P is a positive number.