Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: thedoc on 15/11/2016 11:39:35
-
Wayne Coetzer asked the Naked Scientists:
If I could hover in the air totally unattached to the earth, and I am hovering let's say 2m from a building on its Eastern side, would the building crash into me as the earth rotates?
Thanking you in advance.
Wayne
What do you think?
-
No; you would be quite safe from attack by buildings because you would be hovering in the Earth's atmosphere which is travelling with the Earth, and therefore with the buildings.
-
It depends what you mean by "hover".
Normally it's taken to mean" to stay still in the air" but you have to say what you are "still" compared to.
If you are stationary with respect to the building, you are going to be fine.
-
If you are able to hover in a train or an airplane moving at a constant rate, will you hit the back wall?
-
If you are able to hover in a train or an airplane moving at a constant rate, will you hit the back wall?
That's a good point.
Wayne should think about hovering in a moving train. If he jumps in the air he temporarily hovers, he does not move towards the back of the train because he was moving with at at the same speed as the train.
Same is true if hovers relative to the earth.
Wind would have an effect however.
Question: if he hovered for a long time and say he had an inertial guidance system to keep him stationary, would he drift as the earth 'turned a corner' and he carried straight on?
-
Wayne Coetzer asked the Naked Scientists:
If I could hover in the air totally unattached to the earth, and I am hovering let's say 2m from a building on its Eastern side, would the building crash into me as the earth rotates?
Thanking you in advance.
Wayne
What do you think?
No, and for the same reasons why when you drop something off of a tall building it falls down in a straight line and isn't swept to one side. In the frame of reference in which the Earth is rotating, the falling object's velocity has transverse component to the vertical. Since there is no transverse force there is no transverse acceleration so the transverse component of velocity remains unchanged and thus it falls in a straight line as observed in the rest frame of the Earth.
It's for such reasons that helicopters, which do hover, aren't accelerating in a direction parallel to the Earth's surface so if it starts out at rest relative to the Earth's surface then it will remain at rest.
-
Wayne Coetzer asked the Naked Scientists:
If I could hover in the air totally unattached to the earth, and I am hovering let's say 2m from a building on its Eastern side, would the building crash into me as the earth rotates?
Thanking you in advance.
Wayne
What do you think?
No, and for the same reasons why when you drop something off of a tall building it falls down in a straight line and isn't swept to one side.
Nearly.
Imagine a really tall building (of negligible mass just to make it easier) on a planet with no air. The planet is the same size as the earth and the building is on the equator.
The important thing is that it's a really tall building, in fact the top is twice as far from the centre of the Earth as the ground floor is.
Because the planet is spinning, the foot of the building is doing roughly 1000 miles an hour. (Expressed as a tangential speed)
But the top of the building is doing twice that (tangential) speed.
If you drop a coin from the top how fast (tangentially) is it travelling when it hits the floor?
Well, there's no force acting on it except gravity- and that pulls straight down.
So there's no sideways acceleration.
So the tangential velocity when it reaches the floor is still about 2000 miles an hour.
But the speed of the foot of the building is about 1000 miles an hour.
That's a problem.
"Straight up and down" is not well defined on a rotating body.
-
If the planet were rotating at relativistic speed then there would be a motion perpendicular to the field that moves opposite to the rotation of the planet. In which case the descent would not be a straight line geodesic path. It all depends upon how near to the speed of light the angular velocity is. In this case hovering would tend to crash you into objects.
-
So the tangential velocity when it reaches the floor is still about 2000 miles an hour.
But the speed of the foot of the building is about 1000 miles an hour.
That's a problem.
"Straight up and down" is not well defined on a rotating body.
But not in this case. What you did was to change the model by changing the problem. The original problem was well modeled as a small region on a flat plane moving in a straight line with a small "building" (i.e. recall the OP was thinking of dropping something from 2 meters). Then you came along and used a building the a height the diameter of the Earth making it a very different problem.
-
So the tangential velocity when it reaches the floor is still about 2000 miles an hour.
But the speed of the foot of the building is about 1000 miles an hour.
That's a problem.
"Straight up and down" is not well defined on a rotating body.
But not in this case. What you did was to change the model by changing the problem. The original problem was well modeled as a small region on a flat plane moving in a straight line with a small "building" (i.e. recall the OP was thinking of dropping something from 2 meters). Then you came along and used a building the a height the diameter of the Earth making it a very different problem.
Nope, the OP said
"I am hovering let's say 2m from a building on its Eastern side"
there's no mention of the height of the building, just that you start off 2 feet from it.
-
oops 2 metres.
-
there's no mention of the height of the building
I'm not sure he envisaged the ht you suggested [;)]
-
Nope, the OP said
"I am hovering let's say 2m from a building on its Eastern side"
there's no mention of the height of the building, just that you start off 2 feet from it.
He most certainly did imply such a height since the height is irrelevant. It's assumed that he's referring to real building and not the fantasy one you concocted. Since the object is hovering it means that nothing above or below the height of the hovering object comes into play. Since a real building and not a fantasy one less than hundred or so stories the change in gravity is irrelevant. And that model what I was talking about when I was talking about a straight line. But you have a propensity of trying to make the valid seem invalid. In fact you're famous for it.
-
only during a big earth quake, a building could possibly hit a floating man/stuff near by.
-
Nope, the OP said
"I am hovering let's say 2m from a building on its Eastern side"
there's no mention of the height of the building, just that you start off 2 feet from it.
He most certainly did imply such a height since the height is irrelevant. It's assumed that he's referring to real building and not the fantasy one you concocted. Since the object is hovering it means that nothing above or below the height of the hovering object comes into play. Since a real building and not a fantasy one less than hundred or so stories the change in gravity is irrelevant. And that model what I was talking about when I was talking about a straight line. But you have a propensity of trying to make the valid seem invalid. In fact you're famous for it.
LOL
I see, your fantasy- that it's a straight line is OK, but my fantasy, that you might consider a really tall building isn't OK.
In a thread about being able to hover- which is, of course, a fantasy.
Then there's a side order of "He most certainly did imply such a height since the height is irrelevant. ".
Well, nothing he said implied that (feel free to show where he did so)
and, of course I have shown that the height of the building does matter, even if, in doing so, I showed that you were wrong to make a blanket statement that it fell in a straight line.
And this
"Since there is no transverse force there is no transverse acceleration so the transverse component of velocity remains unchanged and thus it falls in a straight line as observed in the rest frame of the Earth."
Is flat-out wrong too, the path is viewed as curved from, for example someone at either the top or bottom of the tower.
Of course, my point- that "stationary" is a matter of viewpoint- still stands.
And, because of that, the OP is not fully specified.
"you have a propensity of trying to make the valid seem invalid. In fact you're famous for it."
It was, at best, "valid" for a give set of assumptions (specifically a building of precisely zero height) which you didn't explain.
So, unless you think that the OP meant a building of zero height (and that's an odd definition of a building- especially if you plan to drop something from it) then there's no way that your statement was correct.
The thing that I made look invalid was your statement.
I did that because it wasn't valid.
So, no I didn't try to" to make the valid seem invalid. "
I made explained why it was not actually valid.
And, for the record, I'm not famous for anything.
-
If we launch an object off the top of a building its velocity perpendicular to the gravitational field remains constant as it follows its parabolic path to the ground. Since the velocity of an object dropped vertically downwards has no velocity perpendicular to the field this should remain constant.
-
I see, your fantasy- that it's a straight line is OK,
What I referred to as a straight line is not by any means a fantasy. Especially since I said it was a straight line as observed in the rest frame of the Earth. A real building is one of the buildings that has already been built and we assume such unless stated otherwise. Your nonsense about a building twice has high as the diameter of the earth has nothing to do with the question asked. When someone asks a question here and posted by doc it's assumed that we're dealing with real life objects.
-
It's far from clear that the Earth has a "rest" frame- it's always accelerating You and i are both currently accelerating towards the centre of the Earth. My head is doing so slightly faster than my feet.
In reality the statement you made is only true for a building of zero height- which is a bit silly.
Calling me "childish" for pointing it out doesn't seem helpful.
In the mean time, I have a suspicion; you didn't read the OP properly.
There's grounds for me to think that- you said "(i.e. recall the OP was thinking of dropping something from 2 meters). "
Now, had the OP talked of such a small building you would have had a point, but it didn't.
And I think you got "caught out" about your mistake when I pointed out that, when you said "He most certainly did imply such a height since the height is irrelevant."
you were wrong twice.
There was nothing there to imply any height and
The height is very clearly relevant (though you keep getting the arithmetic wrong about the building I suggested).
And I think you are now annoyed and starting to act like a shouty five year old who doesn't want to admit he made a mistake.
One of the most inciteful posts in this thread is from Colin 2B who said "I'm not sure he envisaged the ht you suggested ;)"
Well, I'm not sure either- the OP never said how high the building was.
But my points remain valid for any size of building- albeit that for sensible sized buildings the effects are small.
I think the tallest building is about 800 metres or so.
The radius of the earth is about 6000 km.
If that tower were on the equator its footings would be doing something like 1000 miles an hour, but the top is going faster by about 130 parts per million.
So a dropped penny (ignoring lots of other effects- mainly air resistance) would land travelling sideways at about 0.14 miles an hour.
That's about 6 cm per second.
Now, if this is righthttp://keisan.casio.com/exec/system/1231475371 (http://keisan.casio.com/exec/system/1231475371)
then falling 800 metres will take about 13 seconds (A bit longer if you take air resistance into account).
At an average of about 3 cm/sec the coin would drift about 0.4 metres.
Not far- not the 2 metres that the OP talked about. But still definitely real.So, even with a real building there's a perfectly measurable predicted departure from the straight line.
Do you accept that you were wrong when you said "for the same reasons why when you drop something off of a tall building it falls down in a straight line and isn't swept to one side. "?
-
Fellas, let's try to stay on subject and not quibble about some old beef that one or both of you have with the other. (if you must discuss such issues, PMs are fine, but keep it private). Give the attacks a rest.
-
Fellas, let's try to stay on subject and not quibble about some old beef that one or both of you have with the other. (if you must discuss such issues, PMs are fine, but keep it private). Give the attacks a rest.
He's been doing this to everyone for years and we've gotten very sick of him. He never gives it a rest. He just keeps in saying stupid stuff and posting insults to push people into submission. So its not him and I but him and most members. If you'd been here longer you'd know more about it.
-
Fellas, let's try to stay on subject and not quibble about some old beef that one or both of you have with the other. (if you must discuss such issues, PMs are fine, but keep it private). Give the attacks a rest.
He's been doing this to everyone for years and we've gotten very sick of him. He never gives it a rest. He just keeps in saying stupid stuff and posting insults to push people into submission. So its not him and I but him and most members. If you'd been here longer you'd know more about it.
I look forward to the poll.
Meanwhile back at the topic (nearly)
Do you accept that, for a real building, the predicted effect is perfectly measurable in principle (the wind would screw it up in practice)?