the key is the wheels having no resistance (i.e. to rotate both clockwise and counterclockwise). i think alot of us who are having trouble with this example assume that the plane's wheels cannot spin backwards....
waggy
No Lifer
- Dec 14, 2000
- 68,143
- 10
- 81
for some damn reason i been thinking about this.
say you have a model car on a tredmill. you are a super genius and are able to configure the treadmill to match the speed of the wheels on the car perfectly. Then say you threw on some bottle rockets. would the car move? Since the thrust is now from the rockets what happens?
If you throw a bottle rocket on the ground it travels. Short of holding on the little red stick (that hurts by the way..) its going to take off in some direction. nothing besides air resistance slows it down. so question is would that make the car move?
unless im mistaken on how rockets work. they are going to move NO matter what the wheels are doing. So please correct me if wrong. heh wouldnt be the first time.
say you have a model car on a tredmill. you are a super genius and are able to configure the treadmill to match the speed of the wheels on the car perfectly. Then say you threw on some bottle rockets. would the car move? Since the thrust is now from the rockets what happens?
If you throw a bottle rocket on the ground it travels. Short of holding on the little red stick (that hurts by the way..) its going to take off in some direction. nothing besides air resistance slows it down. so question is would that make the car move?
unless im mistaken on how rockets work. they are going to move NO matter what the wheels are doing. So please correct me if wrong. heh wouldnt be the first time.
Originally posted by: waggy
sorry. that was a poor excuse of something... hahaha
maybe this is what's confusing me?
and inveterate, stop being a fvcking DOUCHE
If the conveyor belt always moves at the same speed that the wheels rotate, in the opposite direction, then the plane never moves relative to anything except the conveyor belt, so it doesn't move through the air.
Adding thrust will only increase the speed of the wheels and the conveyor belt, which will always cancel each other out.
It isn't the same as taking off on water or ice, in those cases the airplane does move relative to it's surroundings and the ground.
It also isn't the same as the rope attached to a wall, in this scenario there is no wall, and no rope, all there is increased thrust, which is exaclty the same as a man running on a treadmill. The man can run faster, but he won't move forward if the treadmill matches his speed in the opposite direction.
Adding thrust will only increase the speed of the wheels and the conveyor belt, which will always cancel each other out.
It isn't the same as taking off on water or ice, in those cases the airplane does move relative to it's surroundings and the ground.
It also isn't the same as the rope attached to a wall, in this scenario there is no wall, and no rope, all there is increased thrust, which is exaclty the same as a man running on a treadmill. The man can run faster, but he won't move forward if the treadmill matches his speed in the opposite direction.
What do you mean the conveyor belt can't keep up ? One of the premises of the original question is that the conveyor belt DOES keep up.
Given the wording of the question, there is no way for the wheels to move relative to anything but the conveyor belt. All forward movement of the wheels is completely balanced by backwards movement of the belt. It doesn't matter where the force that is making the wheels turn is coming from, increasing the force just makes the wheels and the belt turn faster, in opposite directions.
And if the wheels can't move, neither can the plane.
KK
Lifer
- Jan 2, 2001
- 15,903
- 4
- 81
But thats the thing, its impossible for the conveyor belt to keep up. The treadmill scenerio is along the same lines, if you are on a treadmill with roller blades on, and you have that rope attached to the wall in front, if you pull on the rope you will move forward. The treadmill will not be able to counteract the force you are pulling. Does that make any sense the way I'm trying to explain it?
But there is no rope or wall in the airplane scenario. Those are external forces not present. In the airplane scenario, there is no force that can act on the airplane that does not also act on the wheels and conveyor belt, simultaneously. The engines acting on the air, are going to apply a forward force to the plane, and necessarily the wheels, but all of that work will only make the conveyor go faster in the opposite direction.
And besides, the question isn't whether or not the conveyor belt CAN keep up, it is a given fact as part of the problem that it WILL keep up. Whether it makes sense in the real world or even in physics, is irrelevant.
It doesn't matter if the conveyor belt can "keep up" or not, the plane takes off. Even if you set it up to move at twice the speed of the airplane in the opposite direction, the plane takes off.
Another example. The plane starts in the air, on a landing approach with the gear down. The conveyor is moving backwards at, oh, 300 MPH. The plane touches down, holding a constant throttle position, rolls to the end of the runway, and lifts off again. As it circles around to make the approach again, we switch the conveyor so it moves FORWARDS at 300mph. Once again our plane touches down, rolls to the end of the runway under constant throttle, and takes off. As long as the pilot didn't do anything silly like touch the brakes, the two approaches would appear identical to an observer on the ground. Maybe a few feet plus or minus, because of rolling resistance, but certainly nothing drastic.
If THAT doesn't demonstrate that groundspeed isn't airspeed, nothing will. Groundspeed (at least in the direction the plane's pointing) only affects airspeed when the brakes are applied!
KK
Lifer
- Jan 2, 2001
- 15,903
- 4
- 81
The engine is the external force, whereas the rope & wall would be the external force in the treadmill scenerio. When you say that the engines are going to apply a forward force to the plane, it doesn't matter what the wheels are going to do as the engine pushes just the body of the plane. The wheels just spin freely in relationship to how fast the plane in going thru the air to whatever is happening on the ground.
It's funny, because in your attempt to give an example that proves your point, you actually prove mine !
In your example the conveyor belt has no effect on the speed of the moving plane. That is because the conveyor belt cannot transfer any force to the plane. The plane is moving because it has momentum, the conveyor belt prevents any force in the opposite direction from affecting this momentum.
In the same way, the plane at rest cannot move, because the special condition that it is resting on a device that will prevent any force from having an effect on it's present state at rest.
Observe this diagram. There are four forces involved. Gravity and the normal force counteract each other perfectly. The force of the conveyor is unconnected to the force on the plane. However, each force IS connected to the wheel, and the diagram clearly shows that both these forces serve to spin the wheel faster, in the same direction. The only "forces" which oppose this (and therefore the only forces capable of preventing the plane from rolling down the runway and taking off) are the friction in the bearing, and the angular momentum of the wheel. The momentum is obviously not a big deal. And assuming they lubricate their bearings every so often, and don't have the brakes applied, neither is the force of friction.
Show me how exactly Fc affects Fa, and I might recant.
edit: note that this diagram is valid, whether the aircraft is initially at rest, or whether it just landed on the conveyor per the first half of my earlier scenario.
The engine is not external, it is part of the plane. Your description of the wheels sounds crazy, how are the engines going to push the "body" without moving the wheels ?? And we already know as a condition that the wheels cannot move, any movement forward by the wheels is countered by the same movement in the opposite direction by the belt.
The problem with your diagram is that the plane moves relative to the ground, but the ground is moving relative to everything else, in the opposite direction. So the airplane is not moving relative to anything else but the moveable ground.
I beg your pardon? I agree the conveyor cannot transfer any force to the plane, but how is the conveyor able to "prevent any forces from acting in the opposite direction"? The WHEELS (more specifically, the wheel bearings) are what's preventing the force of the conveyor from acting on the plane.
Besides, the engines still affect the plane's momentum in my example, and they do so independently of the conveyor. If he lands, and cuts the throttle, the plane will slow down. If he lands, and hits full throttle, the plane will speed up, regardless of the direction or speed at which the conveyor is moving.
Again I will refer those that don't understand to my example(as I think it is the easiest to picture).
A toy car on a downhill treadmill. The force of gravity represents the force applied by the engines. Spin that treadmill as damn fast in reverse you want...but that car is still going to accelerate.
Notice that using gravity as the force is fair because the thrust of the engine(force) is not affected by treadmill speed, and neither is gravity. The "system" that the engines force is in is completely seperate from the "system" that the wheels forces are in(yes there are forces but they only cause the wheels to spin because the wheels CANNOT push back. This causes an unopposed force that results in the moment that spins the wheels)
Hope that helps you guys picture it.
Abraxas
Golden Member
- Oct 26, 2004
- 1,056
- 0
- 0
It depends entirely on the level of friction generated between the two. Theoretically, if the belt is moving fast enough, the belt can prevent the plane from taking off by providing enough frictional force to directly halt the engines of the plane, or at least reduce it to speeds that would not allow it to take off. If we assume zero friction, as many of you want to, yeah, the plane will take off as with zero friction it won't even act on the plane. However, do NOT assume this means that a ten mile an hour plane will be prevented from taking off if you apply a ten mph belt in the other direction unless you likewise assume that 100% of that becomes frictional drag on the plane. This could go both ways depending on how much friction play into it. The motion of the belt, outside of friction, won't matter.
All you will succeed in doing in that case is make the plane move forward at mostly normal speed, once again, substracting friction. The wheels will spin at double speed keeping place with the plane on top of it and connected to it. This would be no different than the plane taking off from a high friction surface while the wheels spin uselessly below it. To illustrate, take up a pop bottle or a pop can and wrap your hand around it as far as you can without using your thumb. Take note of how far around it goes. Then put it at the base of one hand and the tip of the other and move the hands past each other until the position of each hand is reversed. Do this slowly and observe how far the pop-can moves. It will move at twice the distance of the ability of your fingers to wrap around it. For example, if you can get one hand halfway around it, when you roll it between two, it should make a full rotation. Now, take out the pop can/bottle and press your hands together hard and try moving them in opposite directions. Harder, isn't it? This is because the wheel, or pop can, serves to seperate the two objects from each other and almost entirely reduce the friction that would move the plane backwards. It allows the full force of the planes engines to move it forward by applying all the force of the belt to the wheels which will spin independantly of the plane.
All this talk about wings, air velocity, ground velocity, etc. detract from the point. Even if you cut the wings off the plane and mounted the engines directly to the body, the plane would move forward. The plane itself will move forward along the belt in these conditions. Some seem to have been suggesting that this would allow the plane to take off from a smaller space, only a conveyor belt the length of the plane. However, this is not the case. Once again, the plane will have to take off normally, however, the conveyor belt, seperated from the plane by the wheels, will not serve to slow the plane down very much.
All you will succeed in doing in that case is make the plane move forward at mostly normal speed, once again, substracting friction. The wheels will spin at double speed keeping place with the plane on top of it and connected to it. This would be no different than the plane taking off from a high friction surface while the wheels spin uselessly below it. To illustrate, take up a pop bottle or a pop can and wrap your hand around it as far as you can without using your thumb. Take note of how far around it goes. Then put it at the base of one hand and the tip of the other and move the hands past each other until the position of each hand is reversed. Do this slowly and observe how far the pop-can moves. It will move at twice the distance of the ability of your fingers to wrap around it. For example, if you can get one hand halfway around it, when you roll it between two, it should make a full rotation. Now, take out the pop can/bottle and press your hands together hard and try moving them in opposite directions. Harder, isn't it? This is because the wheel, or pop can, serves to seperate the two objects from each other and almost entirely reduce the friction that would move the plane backwards. It allows the full force of the planes engines to move it forward by applying all the force of the belt to the wheels which will spin independantly of the plane.
All this talk about wings, air velocity, ground velocity, etc. detract from the point. Even if you cut the wings off the plane and mounted the engines directly to the body, the plane would move forward. The plane itself will move forward along the belt in these conditions. Some seem to have been suggesting that this would allow the plane to take off from a smaller space, only a conveyor belt the length of the plane. However, this is not the case. Once again, the plane will have to take off normally, however, the conveyor belt, seperated from the plane by the wheels, will not serve to slow the plane down very much.
No, my diagram is drawn relative to a stationary point not on the conveyor. Perhaps I shouldn't have used "Fg" and "Vg", switch those for "Fc" and "Vc" for the force and velocity of the conveyor, which is what I had intended to indicate. I updated the diagram to reflect this. My apologies. Now both Va and Vc are relative to a stationary point not connected to the plane or conveyor.
Good diagram...it might make it easier to see if you point out Fc only causes a rotation in the wheels and cannot counteract the thrust of the engines...but you have been saying this in your arguments so hopefully this is clear to those trying to figure it out.
You keep trying to introduce external forces that don't exist in the original scenario. An inclined plane is an external force of gravity.
As I stated before, the plane engines are not an external force. They are part of the plane .
If this was a car and not a plane, I bet you would readily concede that it wouldn't matter how powerful the car was, that as long as the conveyor matched the speed of the wheels in the opposite direction, that the car would not move relative to anything but the belt.
The airplane behaves exactly the same way. It doesn't matter that the wheels are not "driven" by the powerplant, the fact is the wheels have to move for the plane to move, and they can't move relative to anything but the conveyor belt, just like in the car scenario.
I find it funny how a lot of you just talk out of your ass without giving any fundamental physics proof...
Everyone knows F=MA right? Well, maybe not everyone so here's a quick physics lesson.
F = sum of all forces acting on the mass
M = mass of airplane = FIXED CONSTANT.
A = acceleration of mass.
Now that the basics are out of the way for those folks who decided not to pay attention in their high school physics class,
In this simplified problem,
F = engine thrust - friction (air, wheel bearing, wheel to surface, and any other losses).
A = F / M.
Obviously, for the plane to accelerate, the force of the engine has to overcome all frictional losses. If the plane accelerates, then it will have velocity over time. Once it has velocity, then the physics of aerodynamics come into play and the plane will take off.
The only reason why the plane WOULDN'T take off is if the frictional losses is more than engine thrust can produce.
This problem is poorly worded, just like the $30 bell boy problem that pops up every week on ATOT.
Here's some more questions for you PHYSICally challenged people:
1) If the earth was all land and everyone ran (in synch) to the east, would the earth spin faster and cause the days to be less than 24 hours?
2) Which will hit the ground first? A bullet fired from 2 feet high, or a bullet dropped from 2 feet high?
3) If you can travel faster than the speed of light, can you go around the world and come back to the same spot to see yourself start on the journey around the world?
Everyone knows F=MA right? Well, maybe not everyone so here's a quick physics lesson.
F = sum of all forces acting on the mass
M = mass of airplane = FIXED CONSTANT.
A = acceleration of mass.
Now that the basics are out of the way for those folks who decided not to pay attention in their high school physics class,
In this simplified problem,
F = engine thrust - friction (air, wheel bearing, wheel to surface, and any other losses).
A = F / M.
Obviously, for the plane to accelerate, the force of the engine has to overcome all frictional losses. If the plane accelerates, then it will have velocity over time. Once it has velocity, then the physics of aerodynamics come into play and the plane will take off.
The only reason why the plane WOULDN'T take off is if the frictional losses is more than engine thrust can produce.
This problem is poorly worded, just like the $30 bell boy problem that pops up every week on ATOT.
Here's some more questions for you PHYSICally challenged people:
1) If the earth was all land and everyone ran (in synch) to the east, would the earth spin faster and cause the days to be less than 24 hours?
2) Which will hit the ground first? A bullet fired from 2 feet high, or a bullet dropped from 2 feet high?
3) If you can travel faster than the speed of light, can you go around the world and come back to the same spot to see yourself start on the journey around the world?
Tell me how the force of gravity acts different on the place than its own engines do. Draw the FBD and you will see they act in the same way(neglecting stresses put on the wings by the engines). The wheels on a car are much different than the wheels on a plane. If you stop a car on a treadmill and turn the treadmill on...the car will be pulled backwards. A plane, assuming negligeable friction, would not move when the treadmill began.
Part of the plane or not, the engines don't affect the wheels of a plane directly. Instead, they make the plane move forward, and friction with the ground makes the wheels turn. The gravity example is valid, since gravity makes his example car's wheels turn in exactly the same fashion.
The wheels DON'T have to move for the plane to move. And the wheels can move without the plane moving. My example of the plane landing on the conveyor should show that...if you match the speed of the conveyor to the plane, the plane can land and then take off, without the wheels moving one bit. Yet the plane's travelling at 300MPH relative to a stationary object. If you put the plane on the conveyor, and hold it steady, you can get the wheels to move without the plane moving.
Wheel motion isn't directly tied to plane motion! In real life situations, we often find the two linked, but that doesn't make it a scientific law!
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