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Sign up with GooglePlane on a treadmill
- Thread starter Nuro
- Start date
It doesn't matter at all, provided the engines have enough for to over come the friction- which we know they do, because planes take off all the time!
#$%#$%#$%$#$ me - who ever did that diagram as per hammell's post should offer me a job. My formula was much simpler and I was right
Your formula can remove any reference to the treadmill's speed since the wheels are "free spinning" as they said. I did not understand what they meant with "free spinning" but it means no/little friction in the bearings... so it makes sense then.
Nerfherder
Honorary Master
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Its fairly simple... take an airplane, elevate it off the ground and smack the tires so that they spin really fast.... that is the exact same thing as putting it on a treadmill.
Aint gonna fly
Aint gonna fly
Yes but the plain is moving backwards so you obviously still need to get the plain moving forward, overcome the backwards kinetic energy you gained from the treadmill. But I suppose in a perfect world where there was no friction in the bearings the plain would not be moving backwards to begin with.
You're close to being right, but you are wrong. Your analogy almost works, but you need to imagine the place being elevated yet still free to move. Then it's clear to see that no matter how fast the wheels are spinning, it will have no influence on the ability of the engine to push the plane through the air.
Wow... Ok last try courtesy of a previous post:
The treadmill is acting tangential to the (assumed) free-spinning wheel. A force acting tangential to a free-spinning object can not cause any force on the axis, only a rotational force causing the object to spin about its axis. Therefore the only thing that the treadmill can do is cause the wheels to spin.
The engines on the other hand, are causing a thrusting force which is acting on the wings (or whichever part of the plan that the engine happens to be connected to). Since it is rigidly connected, the force is carried by the member it is connected with towards the CoM (Center of Mass). This transposed force on the Center of Mass causes an acceleration (F=ma). Basic physics principles will explain why and when a force can be translated to a different point. If you read and understand these principles you will note that the force can be translated from its origin to the CoM in a rigid body. Note, also, that on a free-spinning object, a force acting tangent to this object can not be translated to the axle which is the only part of the wheel assembly that is considered to be part of the rigid body of the plane.
Hence, if you use the basic theory of F=ma you will note that the sum of the forces acting on the rigid body of the plane is the thrust and only the thrust. Therefore, the thrust is directly proportional to the acceleration without regard to the force of the treadmill.
Now that was in a "perfect physical world." Very few things change when converting that logic to the real world. These are the following forces that should be taken into account:
Force of friction due to the wheel touching the ground: This can be assumed zero as the tire in both the stated question as well as in real life does not slip relative to the treadmill. If the tire did slip (as if it was locked up) the tire would be considered part of the rigid body and the force of the treadmill would effect the CoM and thus the acceleration. Whether the plane would be able to take off in such a situation would depend on the coefficient of friction between the locked wheel and the ground (very similar to how a seaplane is affected by the water it is in).
Force of friction due to rotation of the wheel about the axle: Most people would agree that a spinning wheel, especially if properly lubricated and fastened as it would be on a plane, causes very little friction on the axle. This friction, however, will add a force that is counteracting the thrust. Once again, though, for this force to cause a plane to not reach take-off speed, the wheel would have to have very high friction, and even then it would still depend on how powerful the engines are (once again, imagine a seaplane and the friction/drag caused by the water, yet it is still able to take off). Therefore, except in extreme rare cases, this will not substantially affect the motion of the plane.
Drag force: The plane is submitted to drag force caused by the air whether it is on a treadmill or not. Airplanes are built with aerodynamics in mind as to minimize this drag force. The only difference might be if the treadmill is causing a velocity in the air, however this would be similar to a breeze in the wind which would cause higher drag forces, but also would move more air over the wings causing higher lift forces. Therefore, in this problem this can also be assumed zero.
Hence, even in a non-perfect physical world, the plane still has a very overwhelming net force moving it forward and will thus fly.
I hope that this clears up any misunderstandings about this problem, and if you made it this far in the post: congratulations. If you made it this far and still don't believe it will fly, go outside and play sports or find something else to do because you are too stubborn to learn physics.
The treadmill is acting tangential to the (assumed) free-spinning wheel. A force acting tangential to a free-spinning object can not cause any force on the axis, only a rotational force causing the object to spin about its axis. Therefore the only thing that the treadmill can do is cause the wheels to spin.
The engines on the other hand, are causing a thrusting force which is acting on the wings (or whichever part of the plan that the engine happens to be connected to). Since it is rigidly connected, the force is carried by the member it is connected with towards the CoM (Center of Mass). This transposed force on the Center of Mass causes an acceleration (F=ma). Basic physics principles will explain why and when a force can be translated to a different point. If you read and understand these principles you will note that the force can be translated from its origin to the CoM in a rigid body. Note, also, that on a free-spinning object, a force acting tangent to this object can not be translated to the axle which is the only part of the wheel assembly that is considered to be part of the rigid body of the plane.
Hence, if you use the basic theory of F=ma you will note that the sum of the forces acting on the rigid body of the plane is the thrust and only the thrust. Therefore, the thrust is directly proportional to the acceleration without regard to the force of the treadmill.
Now that was in a "perfect physical world." Very few things change when converting that logic to the real world. These are the following forces that should be taken into account:
Force of friction due to the wheel touching the ground: This can be assumed zero as the tire in both the stated question as well as in real life does not slip relative to the treadmill. If the tire did slip (as if it was locked up) the tire would be considered part of the rigid body and the force of the treadmill would effect the CoM and thus the acceleration. Whether the plane would be able to take off in such a situation would depend on the coefficient of friction between the locked wheel and the ground (very similar to how a seaplane is affected by the water it is in).
Force of friction due to rotation of the wheel about the axle: Most people would agree that a spinning wheel, especially if properly lubricated and fastened as it would be on a plane, causes very little friction on the axle. This friction, however, will add a force that is counteracting the thrust. Once again, though, for this force to cause a plane to not reach take-off speed, the wheel would have to have very high friction, and even then it would still depend on how powerful the engines are (once again, imagine a seaplane and the friction/drag caused by the water, yet it is still able to take off). Therefore, except in extreme rare cases, this will not substantially affect the motion of the plane.
Drag force: The plane is submitted to drag force caused by the air whether it is on a treadmill or not. Airplanes are built with aerodynamics in mind as to minimize this drag force. The only difference might be if the treadmill is causing a velocity in the air, however this would be similar to a breeze in the wind which would cause higher drag forces, but also would move more air over the wings causing higher lift forces. Therefore, in this problem this can also be assumed zero.
Hence, even in a non-perfect physical world, the plane still has a very overwhelming net force moving it forward and will thus fly.
I hope that this clears up any misunderstandings about this problem, and if you made it this far in the post: congratulations. If you made it this far and still don't believe it will fly, go outside and play sports or find something else to do because you are too stubborn to learn physics.
Nerfherder
Honorary Master
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- Apr 21, 2008
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Were the engines running ?
It's the magnitude of the velocity that matters, ie the speed. Why are you stressing this distinction? I'm sure we all assume the plane's motion is constrained to the forward-backward direction anyway.
Scooby_Doo
Executive Member
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This is silly, the engines on the plane will push the aircraft off the treadmill and it will speed down the runway and take off. there is no force being exerted on the treadmill so it will not be pushed backwards so it will not turn.
The end
The end
This treadmill is infinitely long.
Scooby_Doo
Executive Member
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It can be as long as it wants the power is in the air around it not the treadmill. If the treadmill is upto speed ie electrical then the wheels will spin as fast as the treadmill and the power from the engines will push it faster over the treadmill surface so it can go as fast as it wants too. The power in the wheels will be treadmill speed - friction from contact + power from engines. Therefore the plane will always be moving forward over the treadmill. If it was a person it would be like using your arms on the sides to move yourself forward not your legs. There is no force pushing the aircraft coming from the wheels.
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Let's say this plane is a Boeing 747
747 Take off speed = 290Km/h
The only way the plane is going to be able to take off, is if it reaches a speed of 290km/h
Doesn't matter if this is on a treadmill or whatever.
If the treadmill reduces speed by 100km/h, then the 747 will have to reach 290km/h on the treadmill by adding enough power for 390km/h on a strip through the engines
Then the 747 will take off just as it would on a strip although it needs a little more power
Dont know if this is correct but It sounds right enough and I wanna get back to my pizza
747 Take off speed = 290Km/h
The only way the plane is going to be able to take off, is if it reaches a speed of 290km/h
Doesn't matter if this is on a treadmill or whatever.
If the treadmill reduces speed by 100km/h, then the 747 will have to reach 290km/h on the treadmill by adding enough power for 390km/h on a strip through the engines
Then the 747 will take off just as it would on a strip although it needs a little more power
Dont know if this is correct but It sounds right enough and I wanna get back to my pizza
Yes it will still take off, from the treadmill...just saying for our scenario the treadmill is very long.