• fluidistic
In summary, mathematics is necessary in physics as it helps explain counterintuitive phenomena such as the behavior of a helium balloon in a moving car. Questions that may seem impossible to answer with intuition can be solved using mathematical models. Physicists use math not for fun, but because it is necessary.
fluidistic
Gold Member
micromass said:
You absolutely need mathematics in physics. It may seem unnecessary at first, but after a while you'll see many counterintuitive things that can only be worked out with mathematics.

For example, consider these questions:
1) A helium balloon flies in a car, the car stops, does the balloon go backwards or forwards?
2) You are with a ship in a lake and you have a heavy rock in your ship. You drop the rock in the water, does the water level go up or down?
3) There an airplane on a threadmill. The threadmill goes as fast as the plane. Can the plane fly?

These three question are impossible (for me) to answer with intuition. You must use mathematical models here and you must calculate things. Physicists don't use math for fun, but because it's necessary!
1)When the car goes forward we tend to go backward and our back is pressed into the sit, so I'd say the balloon does the same, i.e. goes backward. It would be counter intuitive if it went the other way.
2)I have to use common sense here, pure intuition would leave me clueless. Say you have a very, very, very heavy little ball inside a boat, making water level up. Clearly, this ball makes the boat almost go under water (I don't know the name in English). If you remove it from the boat and throw it in water, a big part of the boat will emerge and the water level will go down. So common sense says water goes down.
3)I don't know what a treadmill is. Google translation and good picture seems to show a gym apparatus. Well, if the effect is to make the wind speed 0 with respect to the wings of the plane, we must imagine a bird that doesn't move his wings under no wind. Can it fly? As far as I know, no. So intuition says no, if I'm understand well the action of a treadmill. I will add one that I found much harder to answer without a basic physics knowledge that you don't find with intuition only. If you throw up a rigid body into the air, does it take more time to goes up or fall down?
My answer with common sense: Say you throw it with a huge speed upward, exceeding the terminal velocity of the object, it will reach its maximum height faster than falling down since when it will fall down it will reach the terminal velocity. Now if you throw it upward with a velocity lesser than the terminal velocity, I don't think common sense can answer the question.

I didn't use any math to answer these questions, so yes my intuition might be all wrong. What says yours?

fluidistic said:

1)When the car goes forward we tend to go backward and our back is pressed into the sit, so I'd say the balloon does the same, i.e. goes backward. It would be counter intuitive if it went the other way.

It may be counter intuitive, but TRY IT. You'll see that your intuition is wrong.

The difference between you in an accelerating car, and a helium balloon in the same situation is that you are denser than the surrounding air, while the helium balloon is not. We know this because the helium balloon is floating, you are not. When the vehicle accelerates, the surrounding, air are pushed back MORE than the less dense helium balloon. The air then displaces the balloon, and the balloon will move forward!

This is no different than the balloon being released in air and floating upwards. Standing on the ground, we can also view ourselves as accelerating upwards equivalent to g. We feel ourselves being pushed "downwards" due to such acceleration. Yet, the balloon is moving upwards, along the same direction as the direction of acceleration!

Zz.

ZapperZ said:
It may be counter intuitive, but TRY IT. You'll see that your intuition is wrong.

The difference between you in an accelerating car, and a helium balloon in the same situation is that you are denser than the surrounding air, while the helium balloon is not. We know this because the helium balloon is floating, you are not. When the vehicle accelerates, the surrounding, air are pushed back MORE than the less dense helium balloon. The air then displaces the balloon, and the balloon will move forward!

This is no different than the balloon being released in air and floating upwards. Standing on the ground, we can also view ourselves as accelerating upwards equivalent to g. We feel ourselves being pushed "downwards" due to such acceleration. Yet, the balloon is moving upwards, along the same direction as the direction of acceleration!

Zz.
Wow you're right. I can't test it (lack both car and helium) but your explanation makes sense :D
So if I'm in an elevator that has a huge acceleration (and I go upstairs), the balloon will tend to be pressed into the ceiling? Very weird...

ZapperZ said:
It may be counter intuitive, but TRY IT. You'll see that your intuition is wrong.

The difference between you in an accelerating car, and a helium balloon in the same situation is that you are denser than the surrounding air, while the helium balloon is not. We know this because the helium balloon is floating, you are not. When the vehicle accelerates, the surrounding, air are pushed back MORE than the less dense helium balloon. The air then displaces the balloon, and the balloon will move forward!

This is no different than the balloon being released in air and floating upwards. Standing on the ground, we can also view ourselves as accelerating upwards equivalent to g. We feel ourselves being pushed "downwards" due to such acceleration. Yet, the balloon is moving upwards, along the same direction as the direction of acceleration!

Zz.

So to be clear, if the balloon moves forward when the car accelerates, it will move backwards when the car stops? So the answer to the original question is it moves backwards?

And what is the answer to the 3rd question?

Kaldanis said:
So to be clear, if the balloon moves forward when the car accelerates, it will move backwards when the car stops? So the answer to the original question is it moves backwards?
Yes.

I believe the answer to 3 is the plane will take off, assuming the wheels aren't braked of course. Imagine the plane was held in place, the wheels will spin along treadmill, this shows the planes movement is independent of the wheels (apart from the friction between the wheels to the plane). If the propeller starts up and a force is applied, it should accelerate forwards and take off.

Waterfox said:
I believe the answer to 3 is the plane will take off, assuming the wheels aren't braked of course. Imagine the plane was held in place, the wheels will spin along treadmill, this shows the planes movement is independent of the wheels (apart from the friction between the wheels to the plane). If the propeller starts up and a force is applied, it should accelerate forwards and take off.

We're debating this one in work right now. I would think the plane isn't actually moving, it's only wheels that are moving. So how can the plane take off if the air isn't rushing over the wings etc - due to it not moving? I could be wrong though!

Since these are my questions, I feel obliged to answer

Mind, I know very little about physics...

1) If the car accelarates, then all the air in the car is pushed backwards. The balloon with helium is lighter than air and is pushed forwards by all the air going backwards.

2) I already said it in a previous thread. Consider a heavy mass with a negligable volume. When it is dropped into the water, the water gets displaced very little. However, the boat loses a lot of mass and gets to get out of the water. Thus there is less displacement of water, thus the water level goes down. (Note: even Oppenheimer reportedly got this question wrong )

3) This is the hardest to see, but in fact the airplane will fly. I only believed it once I saw the mythbusters episode:
But you can argue: if the conveyor belt goes as fast as the airplane, then the airplane stays still and cannot fly. This is a good argument, but it is wrong because the airplane will not stay still.
With a car, the wheels provide the accelaration, but with the airplane, it are the turbines/rotors providing the acceleration. Thus it is the air that pushes the airplane forwards. A very analogous situation is when you're on a threadmill with roller skates and you're holding a rope to pull yourself forwards. No matter how fast the threadmill goes backwards, you will always go forwards...

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micromass said:
Since these are my questions, I feel obliged to answer
:D Nice ones.
3) This is the hardest to see, but in fact the airplane will fly. I only believed it once I saw the mythbusters episode:
But you can argue: if the conveyor belt goes as fast as the airplane, then the airplane stays still and cannot fly. This is a good argument, but it is wrong because the airplane will not stay still.
With a car, the wheels provide the accelaration, but with the airplane, it are the turbines/rotors providing the acceleration. Thus it is the air that pushes the airplane forwards. A very analogous situation is when you're on a threadmill with roller skates and you're holding a rope to pull yourself forwards. No matter how fast the threadmill goes backwards, you will always go forwards...

Damn it seems I answered wrong, but... I still do not know what a threadmill is. I watched the video and didn't understand what was going on. I just saw a plane taking off and there was a car going in the other direction... so what?
What is the action of a treadmill? I thought it was setting no air flow over/under the wings. Seems like I'm wrong on this?

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fluidistic said:
:D Nice ones.

Damn it seems I answered wrong, but... I still do not know what a threadmill is. I watched the video and didn't understand what was going on. I just saw a plane taking off and there was a car going in the other direction... so what?

Here's the original question:

"A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?"​

I hope that clarifies thingies?

What is the action of a treadmill? I thought it was setting no air flow over/under the wings. Seems like I'm wrong on this?

The only thing the threadmill does is go as fast as the plane does, in the opposite direction. That doesn't mean that the plane can't move, though

A treadmill is just a piece of exercise equipment that let's you run without moving anywhere. It is basically just a conveyor belt that you run on with adjustable speed.

The plane will take off. It's thrust is independent of wheel speed since it comes from te propellor/jet engine rather than the wheels. The treadmill/conveyor has no effect on that so the plane will just accelerate like normal. The only difference would be the wheels would be spinning faster since the ground is moving.

fluidistic said:
1)When the car goes forward we tend to go backward and our back is pressed into the sit, so I'd say the balloon does the same, i.e. goes backward. It would be counter intuitive if it went the other way.

micromass said:
Here's the original question:

"A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?"​

I hope that clarifies thingies?

The only thing the threadmill does is go as fast as the plane does, in the opposite direction. That doesn't mean that the plane can't move, though

A treadmill is just a piece of exercise equipment that let's you run without moving anywhere. It is basically just a conveyor belt that you run on with adjustable speed.

The plane will take off. It's thrust is independent of wheel speed since it comes from te propellor/jet engine rather than the wheels. The treadmill/conveyor has no effect on that so the plane will just accelerate like normal. The only difference would be the wheels would be spinning faster since the ground is moving.

Borek said:
Thanks guys! Lol Borek very nice video :D

I mean, I believe in order for the plane to take off, there must be some wind "flowing" all over the wings, just like a bird would fly if it doesn't move his wings.
I understand that if the plane isn't moving with respect to the ground, having helices will make some wind around the wings, but I'd never guess that's enough to take off. But the fact that the motors are running very fast might play a role.
What if you use only helices to take off a plane? You can't use wheels. Can the plane take off? For my intuition it's an analogous situation and I'd answer no.

fluidistic said:
I understand that if the plane isn't moving with respect to the ground, having helices will make some wind around the wings, but I'd never guess that's enough to take off. But the fact that the motors are running very fast might play a role.

You are missing the point. The forward motion of a plain is not coupled to the motion of the wheels at all, so while a plane may be on a treadmill, that doesn't do anything to the motion of the plane. The motion of the plane is governed entirely by the thrust of the propeller or jet engine, which is unaffected by the treadmill, so the actual thrust vector is the same regardless of whether the plane is on a treadmill or an unmoving surface and the forward motion of the plane is the same regardless of the motion of the surface. It has nothing to do with the engines blowing over the wings.

fluidistic said:
What if you use only helices to take off a plane? You can't use wheels. Can the plane take off? For my intuition it's an analogous situation and I'd answer no.

You don't need wheels to take off. Think about a seaplane. It has no wheels and no way to get moving other than the engine. It is exactly the same as a normal plane except it lands on water. The wheels on a plane are there solely to provide the plane with something to sit on when it is on the ground. In theory, you could give a plane skids like on a helicopter and still take off, you would just need more thrust because the friction on the skids would be much greater than on wheels.

Think of the question as will the plane move forward?

You are missing the point. The forward motion of a plain is not coupled to the motion of the wheels at all, so while a plane may be on a treadmill, that doesn't do anything to the motion of the plane. The motion of the plane is governed entirely by the thrust of the propeller or jet engine, which is unaffected by the treadmill, so the actual thrust vector is the same regardless of whether the plane is on a treadmill or an unmoving surface and the forward motion of the plane is the same regardless of the motion of the surface. It has nothing to do with the engines blowing over the wings.

You don't need wheels to take off. Think about a seaplane. It has no wheels and no way to get moving other than the engine. It is exactly the same as a normal plane except it lands on water. The wheels on a plane are there solely to provide the plane with something to sit on when it is on the ground. In theory, you could give a plane skids like on a helicopter and still take off, you would just need more thrust because the friction on the skids would be much greater than on wheels.
I get it now and understand the analogy micromass pointed out about the roller-skate man.
What about a plane that has 1 helix as a propeller but has a frictionless, motor-less helix that would turn in the opposite direction than the one of the motor?

fluidistic said:
I get it now and understand the analogy micromass pointed out about the roller-skate man.
What about a plane that has 1 helix as a propeller but has a frictionless, motor-less helix that would turn in the opposite direction than the one of the motor?

I am not 100% sure what you mean by that. It would create a bit of drag but it wouldn't stop the plane entirely. That isn't a realistic situation, either.

1) A helium balloon flies in a car, the car stops, does the balloon go backwards or forwards?
2) You are with a ship in a lake and you have a heavy rock in your ship. You drop the rock in the water, does the water level go up or down?
3) There an airplane on a threadmill. The threadmill goes as fast as the plane. Can the plane fly?

Good brain teaser but poorly formulated questions.

1) The helium balloon will go forward if the car is sealed because it is lighter than the surrounding air in the car.

2) The water level in the lake or the water level relative to the boat? the question is poor. If the rock is considered heavy then it probably means its causes the boat to ride lower in the water causing more displacement to the lake water levels while in the boat. Once it is removed from the boat and placed into the lake. The volume displacement of the lake is less so the Lake's water level went down a negligible amount.

3) The question does not even make sense. All treadmills are stationary or it would not be called a treadmill. The fact that they can move a conveyor belt around themselves has no bearing on the question. The only time a treadmill can ever go as fast as a plane is if the treadmill is completely stationary. Therefore the plane is also stationary and can not fly. The question is trying to trick the responder into envisioning a treadmill which can magically propel itself forward! LOL

drmagtri said:
Good brain teaser but poorly formulated questions.

1) The helium balloon will go forward if the car is sealed because it is lighter than the surrounding air in the car.

If the car stops, the balloon will actually go backwards.

drmagtri said:
2) The water level in the lake or the water level relative to the boat? the question is poor. If the rock is considered heavy then it probably means its causes the boat to ride lower in the water causing more displacement to the lake water levels while in the boat. Once it is removed from the boat and placed into the lake. The volume displacement of the lake is less so the Lake's water level went down a negligible amount.
Correct.

drmagtri said:
3) The question does not even make sense. All treadmills are stationary or it would not be called a treadmill. The fact that they can move a conveyor belt around themselves has no bearing on the question. The only time a treadmill can ever go as fast as a plane is if the treadmill is completely stationary. Therefore the plane is also stationary and can not fly. The question is trying to trick the responder into envisioning a treadmill which can magically propel itself forward! LOL

I agree that this question is poorly worded (at best). I've always disliked this question, since it relies more on the reader's interpretation of the question than on any actual science.

drmagtri said:
3) The question does not even make sense. All treadmills are stationary or it would not be called a treadmill. The fact that they can move a conveyor belt around themselves has no bearing on the question. The only time a treadmill can ever go as fast as a plane is if the treadmill is completely stationary. Therefore the plane is also stationary and can not fly. The question is trying to trick the responder into envisioning a treadmill which can magically propel itself forward! LOL
The treadmill is stationary, the point is the that thrust is provided by the propeller, not the wheels unlike a car so it can still go forward and takeoff.

Here's another one I came across earlier this year, this is how it goes off by memory:
You are in orbit around the Earth piloting the space shuttle. You are preparing to rendezvous with the ISS. You are 20km away from the ISS and at the same altitude. You point the shuttle towards the ISS and fire you thrusters to get closer. Will this work?

That's an interesting one, and definitely nonintuitive to a lot of people.

(It brings back painful memories of my orbital mechanics and spacecraft dynamics class)

A better description of the plane thing is that there isn't enough friction between the plane's wheels and the conveyor belt to do anything.

## 1. Can intuition alone be used to unlock a thread?

No, intuition alone is not enough to unlock a thread. Unlocking a thread requires a combination of intuition and logical thinking.

## 2. How can I develop my intuition to unlock a locked thread?

Developing intuition takes time and practice. Some ways to improve your intuition include meditation, mindfulness, and paying attention to your gut feelings.

## 3. Is there a specific process to using intuition to unlock a locked thread?

There is no one-size-fits-all process for using intuition to unlock a locked thread. It is a highly individualized process and may vary depending on the person and the situation.

## 4. Are there any risks to using intuition to unlock a locked thread?

Using intuition to unlock a locked thread may come with some risks, such as making a wrong decision or missing important details. It is important to balance intuition with logical thinking and consider all factors before making a decision.

## 5. Can intuition be used in any field of science to unlock a locked thread?

Intuition can be used in various fields of science to unlock a locked thread, but it is not the only tool. It is important to also use evidence and data to support any intuitive insights.

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