Airplane on a treadmill

[A.B.Normal]

I'm not saying the plane stops moving - I'm saying it reaches a stationary state cos of newton's first law - ie velocity = zero.

states that if the forces acting upon an object are balanced, then the acceleration of that object will be 0 m/s/s."

what forces? speed is not a force its a measure of distance vs time,which I interpret as it(PLANE) is moving at the same rate from point a (center of belt ) as the belt is moving away from the center point of the belt (only in the opposite direction)As posed if the plane stops moving foward I.e. 0 MPH then the belt must also be not moving.

 

[Inkara1]

I think the treadmill thing would actually be a physical impossibility. That's because planes' wheels have no apparatus to drive them. In order for the plane to start moving, the treadmill would have to stay stopped for a second until the plane gets rolling. But the question, as I understood it, says the treadmill going backwards always matches the speed of the plane going forward. But there's no way that could happen. Even if it only takes a split second of stationary ground to get the plane going, it would not ALWAYS be at the same speed as the plane. The simulation also doesn't take into account that moving the wheels at that many RPM would make just about any bearing burn up. If we assume the wheels are 16 feet around, meaning if there were a nail in the tire tread, it would touch the ground every 16 feet, then the wheels would make 330 revolutions per mile. Those planes typically cruise at 500 mph or so... even if we assume we only need 350 miles an hour to produce enough lift to take off, the wheels are doing 1,925 RPM... which isn't much for an engine with a foot-wide flywheel, and isn't much for a hard drive with a couple ounces of platter weight, but is really fast for something that would weigh several hundred pounds. The amount of centrifugal force (centripetal?) force from spinning the tires at twice that speed, or 3,850 RPM, would make something go boom.

 

[A.B.Normal]

Okay now... huh?

Plane ---> 5km .... 5km <--- Treadmill

Zero velocity.

Of what? the belt or the Plane .Because the plane is still moving forward at 5km/h and in an hour will be 5km farther down the belt.

 

[BeardofPants]

Ink? We know that - the whole thing is an impossibility. That aside, factoring all other things out like friction, etc, we are still left with the HYPOTHETICAL problem of the equal velocities. If both velocities equal the sum of zero, and there is no acceleration, the plane enters a state of stationarity. This does not mean that the force acting on the plane (ie thrust), or the force of the treadmill stops. It just means that the plane is stationary.

 

[BeardofPants]

+5 - 5 = 0.
Basic maths.

 

[BeardofPants]

Of what? the belt or the Plane .Because the plane is still moving forward at 5km/h and in an hour will be 5km farther down the belt.

Nuh uh. The movements are equal. The plane will never leave its initial position on the belt.

 

[Scn64]

Here's a few links to answers for this question. It's a lot of reading so enter at your own risk, but hopefully someone from one of these links can explain it better than me.

http://www.straightdope.com/columns/060203.html

http://answers.google.com/answers/threadview?id=428718

http://digg.com/videos_comedy/Plane_and_a_Treadmill_Problem_Explained_by_a_Canadian

 

[A.B.Normal]

P=plane
A=spot on belt

After an hr at 5kph the plane is five km down the belt and the (a) is where the plane was .

 

[BeardofPants]

Um. But the plane never leaves the initial position on the treadmill. If a person is jogging on the treadmill, they stay in the same place unless they accelerate or decelerate. They are stationary - otherwise a person will leave the treadmill!

|__plane__
|__plane__ (time = 1 hr)
|__plane__ (time = 2 hr)
|__plane__ (time = 3 hr)
|__plane__ (time = 4 hr)

Thus, the plane is stationary.

 

[BeardofPants]

A better way to state this would be that the plane would be stationary relative to the ground/earth.

 

[Scn64]

Um. But the plane never leaves the initial position in its position on the treadmill. If a person is jogging on the treadmill, they stay in the same place unless they accelerate or decelerate. They are stationary - otherwise a person will leave the treadmill!

|__plane__
|__plane__ (time = 1 hr)
|__plane__ (time = 2 hr)
|__plane__ (time = 3 hr)
|__plane__ (time = 4 hr)

Thus, the plane is stationary.

A person running relies on their feet to propel them forward. Feet act on the ground. A plane relies on its jet engines or propellers. Jet engines and propellers act on air.

 

[BeardofPants]

Not that it matters, but that is irrelevant; the question assumes that the total momentum generated by the plane will be matched by the treadmill. The wheels can be going at its own momentum relative to the engine thrust, and the treadmill will compensate. And as we all know, jogging requires not only your feet, but also the pumping action of your arms as well. You are arguing that the treadmill will not compensate for the differences in velocity between the engines and the wheels. I am arguing that the question states that the treadmill will match the total momentum generated, thus there being no extra force to accelerate the plane.

 

[A.B.Normal]

Um. But the plane never leaves the initial position in its position on the treadmill. If a person is jogging on the treadmill, they stay in the same place unless they accelerate or decelerate. They are stationary - otherwise a person will leave the treadmill!

.

Right because of Newtons third law(assuming its not a powered one) "for every action there is an opposite and equal reaction" the plane and the belt are not reacting with one another except for the qualifier that the belt must match the planes speed.The speed of the plane is not impeded by the belt .

 

[A.B.Normal]

Not that it matters, but that is irrelevant; the question assumes that the total momentum generated by the plane will be matched by the treadmill. The wheels can be going at it's own momentum relative to the engine thrust, and the treadmill will compensate. And as we all know, jogging requires not only your feet, but also the pumping action of your arms as well.

Once again "speed" not momentum.

 

[BeardofPants]

Upon reading through the google answers, I've got to reiterate my earlier point. The question as stated in this thread says that no matter what the plane is doing, the treadmill will compensate (no matter how infeasible), but apparently the question is supposed to be about the velocity of the plane WHEELS vs the theadmill, n which case the thrust comes into the equation, which would cause acceleration, as I alluded to earlier. It all depends on which version of the question you're going with.

 

[Scn64]

Upon reading through the google answers, I've got to reiterate my earlier point. The question as stated in this thread says that no matter what the plane is doing, the treadmill will compensate (no matter how infeasible), but apparently the question is supposed to be about the velocity of the plane WHEELS vs the theadmill, n which case the thrust comes into the equation, which would cause acceleration, as I alluded to earlier. It all depends on which version of the question you're going with.

The question simply says that the treadmill will match the speed of the plane. That doesn't mean it will create an impossible force to hold it back. It simply spins backwards at 100mph if the plane is moving forward at 100mph.

The reason I keep bringing up the wheels is because the treadmill can only push against the wheels, not the rest of the plane. As the treadmill pushes against the wheels, all it does is make them spin faster. The treadmill has no effect on the rest of the plane because the engines are pushing it forward, not the wheels. The plane could be moving forward at 50mph and the treadmill could be moving backward at 500mph but the plane would still move forward. If the wheels were locked in place and not allowed to spin the outcome would be different, but they're not locked. They are free spinning so, in the example I just gave, the wheels would be spinning at 550 mph (500 + 50). This means the plane would still be moving forward at 50mph.

 

[chcr]

The Airplane on a Treadmill is a type of physics riddle that usually results in two groups of people taking different sides and calling each other idiots for hours at a time. None the less it’s a fun thought puzzle and worth taking a look at.

The Set Up:

Let’s say that we have a jet airplane (like a 747 for example) trying to take off on a giant runway sized treadmill. The treadmill, which turns in the opposite direction that the plane is facing, is capable of precisely matching the speed of the airplane. Here’s a visual to bring it all together (not drawn to scale obviously )

The Question: Can the airplane take off under these conditions?

Answer: No

If you want to keep redefining the problem you can make it so the plane takes off but as originally stated the answer is still no.

capable of precisely matching the speed of the airplane.

That the treadmill keeps the plane from moving forward is implicit in that statement.

Also the wheels do have friction, they will keep a plane from moving against the thrust of the engines (as in a takeoff from an aircraft carrier again). If you want to make it a semantics problem that's your business, but as a physics problem and as originally stated, the plane won't fly.

Now, given that the treadmill only matches the speed of the wheels, I still say no (but in this case I am uncertain). In the case of our imaginary 747 it needs 360 kph through the air to take off. this can be any combination of ground speed and air speed but it takes that much, no less. In other words, given this redefinition of the thought experiment, you'd have to thrust the plane up to 360 kph faster than the wheel speed. Possible? I have no idea. Thrust is not unlimited though, so I still doubt that it would. If you'd like to add unlimited thrust to the equation then yes, you'll be able to take off.

By the way Scn64, go back to physics class. Jet engines don't push against the air. Propellers do but jets don't. If they did, then rockets wouldn't work in space. They don't push against anything, they just create thrust (every action has an equal and opposite reaction).

 

[rrfield]

Right. Bernoulli's principle. The delta of fluid flows, above and below the wings, = 0, no takeoff.

 

[unclehobart]

It just clicked. I now understand. The plane will move forward. The plane will lift off.

Damn.

I, being of the power, have changed the poll to reflect my changed answer.

 

[tonksy]

Ha-ha!