Plane on a Treadmill
- Thread starter Warder60
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Actually, if you want to really figure out how this would work, let's not forget the treadmill, let's forget the thrust provided by the jet engine. Let's not attach bungees or stings to a car or anything like that. Let's put a car with free rotating wheels (where the friction on the wheels is negligible) on a perfectly level treadmill. Mark the original "absolute" location of the vehicle before you turn the treadmill on as "zero. When you turn on the treadmill, the vehicle will not move from the absolute zero location, because any force exerted on the vehicle will be negated by the wheels rotating at the exact same speed that the treadmill is moving. It doesn't matter how fast you get that treadmill going - you could get the tread going at 100 mph, but the wheels on the vehicle are going to spin at 100 mph and the vehicle is not going to go anywhere. That is why if you apply any kind of thrust to the plane it will move forward no matter the speed of the treadmill. If the takeoff speed of a plane is 100 mph, and you get the treadmill going at essentially a -100 mph, and you apply enough thrust to the vehicle to allow it to go 5 mph, the vehicle will travel at 5 mph and the wheels will spin at 105 mph (100 mph to accommodate the tread going in the opposite direction, as proved earlier in the post, and 5 mph to accommodate the thrust applied to the vehicle). The same thing applies if you have the treadmill going -100 mph and apply enough thrust to get the plane going at 100 mph, the assumed takeoff speed. The vehicle will travel at 100 mph, but the wheels will spin at 200 mph (100 mph to accommodate the -100 mph treadmill speed and 100 mph to accommodate the thrust). Essentially, the treadmill is negligible in determining the final speed of the vehicle, as you can get the tread moving as fast as you want - the vehicle will not move, that is, until you apply thrust to the vehicle, then it will move as fast as the thrust will push it. To answer the question of wind resistance needed to take off, because you have the plane traveling at 100 mph, you will have all of the wind resistance necessary for the plane to take of BECAUSE the plane is traveling at 100 mph.
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It would be the same if the plane were being propelled forward by the wheels. Then the plane's forward motion is a result of the friction of the tires on the road/treadmill. But the plane is propelled by the jet engines, so the forward motion is a result of friction with the air and has nothing to do with the treadmill or ground. If it did as soon as a plane became airborne it would no longer accelerate and in fact decelerate and crash to the ground.
This principle is sound. A few holes in your example, as it still takes a force to accelerate an object, even in a friction free world. In a friction free world, the treadmill wouldn't apply any force at all, and neither could the tires on a car.
In a world with friction, the car in your example would have to apply a force to counteract this force of friction, otherwise the car would accelerate in the same direction of the treadmill belt. It would not instantly go from zero to the speed of the belt, but it would accelerate at a rate dependent on the coefficient of friction between the car/treadmill and the mass of the car, until their speeds matched.
Acceleration is defined as a change in velocity, positive or negative. However, in a friction free world the treadmill would have no effect on anything, as it would apply zero force to anything, wheels or otherwise. THe car would just sit on the treadmill. You also would not be able to walk, crawl, etc.
Keep in mind though it doesn't matter in a frictionless world if its wheels, skids, etc. (wheels would just slide in a frictionless world.
It all goes back to how you define the speed of the treadmill vs. speed of aircraft.
After all that, I still say that the question needs clarification. Otherwise, both sides can be right.
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Yes, but while on the ground/treadmill, it wouldn't matter in the manner of how the force is applied, as they are all additive in the direction they are applied.
Assuming any amount of friction, the faster the treadmill moves, the more backward acting force is applied to the wheels. The plane would then accelerate (in this case, backwards) due to that change in force, assuming that the plane does not counter that force with more forward acting thrust. This is true if there is any friction, irregardless of the amount.
It does make a difference take the following example copied and pasted from cmoneyr's post earlier in the thread.
"Let me try this scenario:
Take a shopping cart, a treadmill and a length of rope. Tie the rope to one end of the shopping cart, like you were pulling it behind you. Put the cart on the treadmill and turn it on with the rope slacked. The cart would be stationary, the wheels of a shopping cart do not produce and power and are there only to spin as the pusher provides thrust.
So we have a cart on a moving treadmill, just sitting there. Now take the rope and begin to pull on the cart, does the cart remain stationary? No, the wheels spin at an increased rate based on the speed you pull and the speed of the treadmill. Since the wheels do not factor into how fast a shopping cart moves, the cart moves forward with an increased wheel speed.
Now, double/triple/quadruple the speed of the shopping cart as you are still pulling on the rope. Does the increased speed stop you from being able to pull the shopping cart forward? No, once again, the wheels spin faster and faster, (I'm assuming for this that the wheels won't fall apart), but no matter how fast they spin the cart will only move forward equal to the amount of force you are pulling the rope.
Now, if we replace the shopping cart with a plane, the plane only needs to be able to move forward to make air pass over the wings and therefore create lift. Since the plane/shopping cart will move forward how ever fast you pull it/however fast the jets propel it, the plane will take off as normal. "
Which is why it all goes back to how you interpret the question.
At the same time, if the same amount force was applied to the wheels of the cart, it would accelerate at the same rate. This is the law of conservation of motion/momentum in action. Newton's Laws of Motion;
Newton's Laws of Motion
For a guaranteed headache, read this:
Conservation of Momentum
Is the treadmill allowed to speed up to prevent this movement through increased frictional forces of the wheels, so the plane never moves in terms of its position on the treadmill?
Or is it merely allowed to go to the speed the plane would be moving on normal ground?
There is the rub. It is a trick question of sorts.
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Herbicide, do you understand that there is a difference in how a plane is powered as opposed to how a person is powered? Or a car? When a person runs, the propulsion is from the feet pushing the ground, this is not so on a plane. The wheels do no transfer power to the ground, they are simply spinning.
And yes, of course it matters how much friction is present, thats just asinine. The amount of friction in a planes wheels is obviously small, because if it weren't planes would have very difficult times taking off even in normal conditions. We understand there would be backward forces acting on the plane, we know this since there are no frictionless wheels. HOWEVER, the amount of thrust produced by a plane would easily overcome a treadmill traveling at an equal speed, we know this because airplane wheels are engineered to provide a very small amount of friction.
And yes, of course it matters how much friction is present, thats just asinine. The amount of friction in a planes wheels is obviously small, because if it weren't planes would have very difficult times taking off even in normal conditions. We understand there would be backward forces acting on the plane, we know this since there are no frictionless wheels. HOWEVER, the amount of thrust produced by a plane would easily overcome a treadmill traveling at an equal speed, we know this because airplane wheels are engineered to provide a very small amount of friction.
NO, NO, NO, NO, NO, NO, NO, NO, NO, NO, NO, NO, NO
YES, YES, A MILLION TIMES YES.
Please re-read the problem on the first page again. The treadmill moves at a speed equal to the speed of the plane. How can that possibly be hard to understand? You can't possibly be serious.
They are just different methods of applying force. In the realm of physics all that matters is the amount and the direction of the force(s) Newton's Laws of Motion;
Newton's Laws of Motion
If the same force generated by the thrust of the planes engines were applied to the wheels, or pulled with a rope, pushed with a stick, etc, it would accelerate the same.
Physically speaking, the only things the wheels do is decrease the amount of friction, therefore (as you mention) making it easier (engines need to apply less thrust) for the plane to accelerate to take-off speeds.
This is not a matter of quantity of thrust. I agree that if in this scenario that the treadmill belt was traveling at the same speed as the planes normal take-off speed, that the plane would likely take off assuming the wheels/tires could withstand the additional speeds.
But, if the intention of the question is for the treadmill to hold the plane stationary, no way does the plane fly. I realize that this would take one heck of a treadmill moving at a very fast speed (we could calculate that speed with enough information on the plane)
I am starting to think that the question is worded as in your line of thinking (otherwise why would the treadmill have to be infinitely long) but I don't think we know for sure. At least I don't. None of that changes any laws of physics though.
That right there is the correct answer. Period. End of story.
If that was the intention, it would make this the stupidist question of all time. In that case, they could have asked: If a plane never moves forward, will it take off?
You are reading WAY too much into the question by not taking it at face value. As they say.... ATFQ.
Please read that sentence.....done?...now one more time....k
How can you possibly read "capable of accelerating to match the speed of the plane", and interpret it as "capable of reaching a speed so that the plane cannot move forward." Do you see the difference there?
The question is very easily laid out here, the plane is on a treadmill, the treadmill is going at a speed equal to the plane, will the plane take off? Nowhere does it, or anyone besides you, mention that it might be possible that the treadmill will stop moving at a speed equal to the plane and instead move at a much faster speed that would inhibit the plane from moving.
I agree, under your completely different scenario where the treadmill is moving much much much faster than the plane, it may be possible that it wouldn't take off. But that has nothing to do with this problem.
WHAT?
Original question: if a plane is on an infinitely long treadmill that is capable of accelerating to match the speed of the plane, will the plane take off?
Yet you say he is wrong, all the while arguing that the question might mean: if a plane is on an infinitely long treadmill that is capable of accelerating to stop all forward motion of the plane, will the plane take off?
It sure looks like he's a lot closer to the original question than you.
Originally thats how I interpreted the question. I have since stated many times that I am not sure if I originally interpreted the question correctly. I am now thinking I misunderstood or misinterpreted the question.
With that being said, along the way some have argued things that do not agree with the laws of physics, both in theoretical and real terms. There has also been disputes on how an airfoil works.
If I did misunderstand the question, that still does not change the laws of physics.
I agree it doesn't change physics, but it completely changes how the question works. If the treadmill is just spinning equal to the planes speed like the problem says, and not some theoretical speed to stop movement, then the forces of friction could not possibly outdo the forces of thrust.
Airfoils really have nothing to do here. All we really have to show is that the plane won't remain stationary but will instead move forward. Then, since the treadmill is "infinitely long" it's only a matter of how quickly the plane can reach the required speed to take off.
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