Ascending Object and Earth Spin

[Fishbowl]

Hello good people!

If i liftoff from the Earth in a helicopter and continually ascend slowly, at that moment i have beat gravity(i realize it is still hanging on to me, however the rotorforce/upforce is greater than it), therefore gravity should no longer hold me to the ballearth(because it has no force over me, although it still hangs on). Now, this means that while gravity has no force over me, the Earth should eventually spin away from me. Thus if i ascend slowly for say 10 hours and then descend, i should land a different place. This does not happen and I am starting to become a flat earther lol. Do anyone have an explanation? I'm not too good at physics nor math so cartoons and stuff would be the preferred explanation :D If you too are stumped i want to know too. I like to be confused together with people

 

[Dale]

Hi Fishbowl, welcome to PF

The helicopter continues to interact with the atmosphere and and atmosphere continues to interact with the earth. The helicopter is not isolated at all. Gravity continues to act on it, as does air pressure.

 

[A.T.]

Thus if i ascend slowly for say 10 hours and then descend, i should land a different place. This does not happen

It does happen, but it's a small effect compared to effects of wind and other noise:

https://en.wikipedia.org/wiki/Coriolis_force

 

[Nugatory]

Thus if i ascend slowly for say 10 hours and then descend...

If you were to throw a ball straight up (and I mean absolutely perfectly exactly vertical to surface of the earth, and if the Earth were an absolutely perfect sphere) so high that it took fully ten hours for the ball to come back down, and if the Earth had no atmosphere so we didn't have to consider wind and air resistance... Then yes, the ball would land at a different place on earth. It would come back to the exact same point in space that it had been thrown from, but in the meantime the Earth's surface will would have moved so a different point on the Earth's surface (10/24 of the way around, if you are standing on the equator) will be at that point in space. It's easiest to see how this works if you imagine yourself watching it from a spaceship hovering high above the north pole.

However, as @Dale points out, this is a completely different situation than taking a helicopter flight. A hovering helicopter is moving along with the Earth's atmosphere, and the Earth's atmosphere is (mostly - when it isn't we call it "wind") moving along with the surface of the earth.

 

[A.T.]

If you were to throw a ball straight up (and I mean absolutely perfectly exactly vertical to surface of the earth,...It would come back to the exact same point in space that it had been thrown from...

Only if "perfectly vertical to surface" refers to the inertial frame of the Earth's center, not the frame of the surface itself.

 

[Fishbowl]

The helicopter continues to interact with the atmosphere and and atmosphere continues to interact with the earth. The helicopter is not isolated at all. Gravity continues to act on it, as does air pressure.

I know that gravity does not effect it at all -- even though you could make an argument that it still "held on" to the chopper -- it does not effect it. If you want to claim that gravity effects it you must explain how the chopper was able to lift off in the first place then! Either it effects the chopper or it doesn't. We cannot have it both ways. Remember the chopper is continually ascending, have thus won over gravity, and is not held in place whatsoever. Even though gravity works as a counterforce it is not strong enough to hold the chopper in place.Now, the atmosphere is air molecules, correct? Are you saying that air molecules are "pushing" the chopper in the velocity/spindirection of the earth? Because i would think that very unlikely considering the fact that gravity isn't too strong and wouldn't be able to effect a force on the side of the chopper "pushing" the chopper in the direction of the spin.

Just to make things clearer: we are presupposing no wind. so the only thing that holds the airmolecules perpendicular to the Earth is gravity. What i am claiming is that when these airmolecules hit the side of the chopper because of the spin of the Earth they will not move it and rather move around the chopper.

 

[A.T.]

... it does not effect it...Even though gravity works as a counterforce...

If gravity acts on the chopper then it does affect it, according to the common usage of that word.

when these airmolecules hit the side of the chopper because of the spin of the Earth they will not move it

If they hit the chopper, the exert a force on it.

 

[Fishbowl]

I don't know how to explain it more clearly A.T. Try reading it again

I have not said that the airmolecules doesn't exert a force on the chopper, only that the force is too weak to move the chopper to the side.

 

[Dale]

I know that gravity does not effect it at all

Gravity certainly does affect the helicopter in flight. If it did not affect it then the downwash from the rotor would cause the helicopter to accelerate upwards at about 10 m/s^2 instead of hovering at about 0 m/s^2. The force of gravity on a hovering helicopter is essentially identical to the force of gravity on a helicopter in the ground. What has changed is the downwash force, not the force of gravity.

Are you saying that air molecules are "pushing" the chopper in the velocity/spindirection of the earth?

Yes.

Just to make things clearer: we are presupposing no wind. so the only thing that holds the airmolecules perpendicular to the Earth is gravity.

Air molecules also interact rather strongly with other air molecules, the ground, and (in this example) the chopper. You are neglecting a bunch of important interactions and reaching incorrect conclusions as a result.

What i am claiming is that when these airmolecules hit the side of the chopper because of the spin of the Earth they will not move it and rather move around the chopper.

That isn't how it works.

 

[A.T.]

...the force is too weak ...

Prove it.

 

[Nugatory]

Only if "perfectly vertical to surface" refers to the inertial frame of the Earth's center, not the frame of the surface itself.

Yes, although for this particular problem that's the easiest way of visualizing what's going on - the rotating frame that we instintctively start with just complicates things.

(And because we are standing on the moving surface of the earth, we're moving eastwards at the moment that we throw the ball, and throwing the ball straight up requires aiming very slightly to the west to cancel that sideways motion).

 

[Fishbowl]

I got the personal message Dave. I must admit i am a bit disappointed, as i am only trying to understand how this works and will shut up the moment i understand that i am wrong. Believe me when i say that my only motivation is understanding and the truth. I hope people can talk so that they can understand even if they have a wrong view of things.

Gravity certainly does affect the helicopter in flight. If it did not affect it then the downwash from the rotor would cause the helicopter to accelerate upwards at about 10 m/s^2 instead of hovering at about 0 m/s^2. The force of gravity on a hovering helicopter is essentially identical to the force of gravity on a helicopter in the ground. What has changed is the downwash force, not the force of gravity.

This will be the third time i have to say this but the helicopter is continually ascending. If the helicopter manages to ascend then that means that gravity is not holding it. So the only force that supposedly makes it so that the helicopter stays in place relative to the spin are the air molecules(and in this example there is no wind). At this point in our thoughtexperiment the molecules being dragged in the direction of the Earth's spin are supposed to crash into the side of the helicopter and push it to the side. If the Earth rotates 1000 mph then winds of 1000 mph should hit us the moment we are free of gravity... Not while we are standing on the ground however because then the force of gravity is apparently enough to be able to hold us down even from a centrifugal force on an object with a velocity of 1000 mph...

However! A windforce of 1000 mph are obviously not hitting us in reality as anyone can attest to who have ever jumped upwards. For anyone who has hovered above the Earth in a chopper knows, the Earth just stands still(even while ascending! i know it is weird) and you are not being hit with windspeeds up to 1000 mph. So in the real world if we are to assume both that the Earth spins and that what we see with our eyes at the same time is true, let's assume that it does spin, however so friggin' slow that we can't see it. If so there is no chance than any wind can move the chopper one millimeter(not any of those "locked"-to-the-ground-wind forces anyway).

If no one gives me a good argument and being that Nugatory has agreed with my point(but only in no atmosphere) i might have to put on my tinfoil hat

 

[Dale]

i am only trying to understand how this works

The problem is that you have been told how it works and, instead of listening to the answers, you continue to assert your incorrect understanding. Repeating a wrong position is not a way to gain understanding. If you really want to understand then you need to ask questions of the people who do understand and learn from their responses.

This will be the third time i have to say this but the helicopter is continually ascending.

I understand that. If it is ascending at a constant rate then its acceleration is 0 m/s^2, indicating that gravity is affecting it and preventing the upwards acceleration of ~10 m/s^2 that would otherwise occur.

If the helicopter manages to ascend then that means that gravity is not holding it.

This claim does not match with the observed fact that it is accelerating at approximately 0 m/s^2. Gravity is holding it the same in the air as on the ground, the difference is not that the force of gravity is less, it is that the force from the air on the rotor is greater. You are completely incorrect in this assertion and repeating it multiple times does not help you to understand the correct physics.

If the Earth rotates 1000 mph then winds of 1000 mph should hit us the moment we are free of gravity...

Again, we are not "free of gravity" while we are in the air. However, you are neglecting the fact that we start off with the same initial velocity as the ground (as does the air). By Newton's first law, it does not require any force to continue moving at that same velocity. The air, the chopper, and the ground all start off with the same initial velocity. Because anemometers (the devices used to measure windspeed) measure the difference in the velocity between the air and the ground, they measure 0 in this problem.

However! A windforce of 1000 mph are obviously not hitting us in reality as anyone can attest to who have ever jumped upwards.

Agreed. This fact does not support your analysis. See above.

 

[Buckleymanor]

If the Earth rotates 1000 mph then winds of 1000 mph should hit us the moment we are free of gravity...

That is the nub of your misunderstanding The winds don't hit you once the helicopter takes off because the wind is held by gravity and moving at the same speed as the helicopter or all most. Just like the oceans are held by gravity they still move at the same speed as the Earth's rotation you don't suddenly feel a force of 1000mph if you swim in them you are surrounded by the water and travel with it at around the same speed.

 

[Cutter Ketch]

Sometimes it helps to invoke a spherical cow. Let's try some simpler non physical examples.

Example one: the Earth has no atmosphere and it is a rocket not a helicopter. The rocket works directly against gravity providing no tangential forces. I.e. All forces are radial. As the rocket launches from the spinning Earth it too is traveling tangentially with the angular velocity of the earth. So there is no sudden slipping away of the launch pad when the rocket leaves the ground.

Now suppose the rocket hovers an inch above the ground. With no tangential force it's tangential velocity does not change. To a very high precision it is at the same radial distance from the axis of rotation as when it was on the pad, so it's angular velocity does not change. The rocket stays directly above the pad.

Now suppose the rocket goes up a small but significant fraction of the radius of the earth. with no tangential force it's tangential velocity does not change. However, at a significantly larger radius it's angular velocity is slower and the Earth does indeed slip away under the rocket. This, I think is the situation you envision.

Second non physical example: the sun heats the Earth which in combination to the Earth's rotation causes wind which seems to have confused the question. Let's take a case where the Earth has atmosphere but there is no sun. What is the state of the atmosphere in this case? The lowest energy condition is if the atmosphere spins right along with the Earth which avoids all shear and mixing. So in this example the atmosphere spins right along with the earth. Note that that means the angular velocity is constant at all altitudes and therefore the tangential speed is not! Now we have a helicopter rather than a rocket. Despite what so many people on this thread have been saying, you get the exact same effect. If it were only gravity and radial lift at play you would indeed have the tendency for the Earth to slip away under the helicopter. However, since the atmosphere is stationary relative to the spinning Earth as you got higher and higher you would experience a larger and larger tangential wind. If you insisted on only applying lift to oppose the force of gravity, the side wind of the atmosphere will apply a tangential force and drag you along. This tangential drag of the atmosphere is very compelling on a helicopter and you wind up tied to the constant angular velocity of the atmosphere. However, to a small degree the tendency to drag behind as you increase altitude will show up hidden under the relentless drag of the atmosphere.

BTW, I should mention that real rockets never go straight up, and instead do the opposite. They go up only enough to get out of the drag of the atmosphere, and mostly apply tangential force accelerating the tangential speed to achieve orbit. If there were no atmosphere they wouldn't have to go up at all. (Well, enough to clear the mountains, I suppose). Not that that matters. I just thought I'd mention it.