Free Body Diagram / Normal Force

There may be a trivial answer that eludes me, but this question popped up after thinking on the Flat Earth Hypothesis.

Under conventional physics, the force due to gravity is balanced by the vertical component of the normal force. This explains why objects do not accelerate vertically under this model while on the ground. I attempted to remove the gravitational force but was unable to figure out what could balance the normal force. Again, it may be trivial, but can such a force be pointed to under FEH?

There may be a trivial answer that eludes me, but this question popped up after thinking on the Flat Earth Hypothesis.

Under conventional physics, the force due to gravity is balanced by the vertical component of the normal force. This explains why objects do not accelerate vertically under this model while on the ground. I attempted to remove the gravitational force but was unable to figure out what could balance the normal force. Again, it may be trivial, but can such a force be pointed to under FEH?

They would be exactly the same, but the notation would be inverted. In the gravity situation, the object exerts a force due to gravity (F_g) on the surface, which reacts with a reactive force (F_r) upward.

In the flat earth model, the earth exerts a an impact force due to universal acceleration (F_ua) on the object (upwards), which in turn reacts with a downward force (F_r).

Quote from: Galactian on April 20, 2013, 11:40:43 PM

There may be a trivial answer that eludes me, but this question popped up after thinking on the Flat Earth Hypothesis.

Under conventional physics, the force due to gravity is balanced by the vertical component of the normal force. This explains why objects do not accelerate vertically under this model while on the ground. I attempted to remove the gravitational force but was unable to figure out what could balance the normal force. Again, it may be trivial, but can such a force be pointed to under FEH?

They would be exactly the same, but the notation would be inverted. In the gravity situation, the object exerts a force due to gravity (F_g) on the surface, which reacts with a reactive force (F_r) upward.

In the flat earth model, the earth exerts a an impact force due to universal acceleration (F_ua) on the object (upwards), which in turn reacts with a downward force (F_r).

That makes sense, though would the forces still balance on an angled surface? In order to get the same results, wouldn't the force due to the UA need to be perpendicular to the surface? It would need to if it is the force pointing upwards, right? I wonder if there is a site that allows you to create FBDs. That would help illustrate the situation better.

That makes sense, though would the forces still balance on an angled surface? In order to get the same results, wouldn't the force due to the UA need to be perpendicular to the surface? It would need to if it is the force pointing upwards, right? I wonder if there is a site that allows you to create FBDs. That would help illustrate the situation better.

Yes, they'd still be balanced. Just imagine you're standing in an elevator with a slanted floor that's accelerating upwards, you'll still be able to stand just fine. Of course this analogy includes gravity in it, but you'll essentially get the same result if you remove gravity.

Quote from: jason_85 on April 21, 2013, 03:22:16 AM

Quote from: Galactian on April 20, 2013, 11:40:43 PM

There may be a trivial answer that eludes me, but this question popped up after thinking on the Flat Earth Hypothesis.

Under conventional physics, the force due to gravity is balanced by the vertical component of the normal force. This explains why objects do not accelerate vertically under this model while on the ground. I attempted to remove the gravitational force but was unable to figure out what could balance the normal force. Again, it may be trivial, but can such a force be pointed to under FEH?

They would be exactly the same, but the notation would be inverted. In the gravity situation, the object exerts a force due to gravity (F_g) on the surface, which reacts with a reactive force (F_r) upward.

In the flat earth model, the earth exerts a an impact force due to universal acceleration (F_ua) on the object (upwards), which in turn reacts with a downward force (F_r).

That makes sense, though would the forces still balance on an angled surface? In order to get the same results, wouldn't the force due to the UA need to be perpendicular to the surface? It would need to if it is the force pointing upwards, right? I wonder if there is a site that allows you to create FBDs. That would help illustrate the situation better.

The forces balance. I can just direct you to Einstein's Equivalence Principle, but I rather enjoy physics so I'm gonna try to tackle this one head on.

I don't know of any sites that allow you to make FBDs, but I do know of Google Docs, which allow you to draw things, which is close enough

https://docs.google.com/drawings/d/19iK8JqR90IvvCEoxnOMnufIi1tTyN9khzvlo8he2J1Q/edit?usp=sharing

Here's a terrible drawing of a box on an inclined plane in RET.

Let's call the angle of inclination 30 degrees. The box will weigh 10 kg, because ten is an easy number. Coefficient of friction is .1, because why not?

Give me moment to calculate all of the forces.

Fw= 98.1 N
Fw||= 49.05 N
Fw⊥= 84.96 N
Fn= 84.95 N
Ff=8.59 N

Now let's look at it from a Flat Earth perspective, shall we?

https://docs.google.com/drawings/d/1KoabP6y_TRBwguyqlbFcDFX2dOMgOV9VAHzbtZSgguQ/edit?usp=sharing

Now, I'm going to have to explain all of the forces, I'd imagine.

The UA force is pushing up on the inclined plane, not the box. It would be difficult to actually give it a value in newtons, because f=ma and we have the a but not the m. So let's just call it a 9.81 m/s² acceleration and leave it at that.

So let's calculate some vectors. For the purposes of this thought experiment, let's pretend that the incline is a flat plane and the UA force is what is rotated 30 degrees.

The vertical acceleration vector that is acting on the box is 4.905. Adding in the box's mass to get a force, we get 49.05 N. Does that number sound familiar?

The horizontal acceleration vector is 8.495, or 84.95 N. Which, as you'll remember, is equivalent to the RET scenario as well. Putting the scenario back into the context of an inclined plane, we get this to be the FW⊥ value, which, being equivalent to the normal force value, means that normal force is equal for both theories.

Any questions?

No, your explanation is sufficient enough to resolve the question. The gravity model is still more intuitive to me, however.  I'm just about to finish my first class in mechanics, so I don't have much physics background to refute many arguments for the FEH, except those that involve forces and circular rotation. I appreciate your thorough response!

No, your explanation is sufficient enough to resolve the question. The gravity model is still more intuitive to me, however.  I'm just about to finish my first class in mechanics, so I don't have much physics background to refute many arguments for the FEH, except those that involve forces and circular rotation. I appreciate your thorough response!

Proofs for why the FE model is false tend to be more based on astronomical observations and philosophy; as tausami mentioned the equivalence principle basically ensures that there is no observable difference between the accelerating and gravitational models.

Quote from: Galactian on April 21, 2013, 10:27:30 AM

No, your explanation is sufficient enough to resolve the question. The gravity model is still more intuitive to me, however.  I'm just about to finish my first class in mechanics, so I don't have much physics background to refute many arguments for the FEH, except those that involve forces and circular rotation. I appreciate your thorough response!

Proofs for why the FE model is false tend to be more based on astronomical observations and philosophy; as tausami mentioned the equivalence principle basically ensures that there is no observable difference between the accelerating and gravitational models.

I'm aware of the equivalence principle, however I was unsure if within the principle all the forces would balance out just as well. I learned something new today -- thanks!

From what I've seen so far on the site there have been no real falsifiable ways to check whether or not the FE model is accurate, since most, if not all, of the ways that the RE model is determined are apparently not correct or misguided (in FE eyes).

At my campus there is an impressive Foucault Pendulum setup, with a placard next to it explaining in simple terms how the experiment proved the shape and rotational speed of the Earth. I asked my physics professor about any magnets present, and he said something along the lines of "the pendulum is slightly altered to take into effect friction, else it would eventually stop all together", which doesn't bother me at all. This apparently does so for many on this website.

My main issue with the Flat Earth Hypothesis is that you would have to discard a whole lot of observational data and well-known physics in order to achieve such a conclusion. On a more philosophical note, if the greatest minds of the last 3000 years were mistaken by the shape of the Earth, then I doubt anyone on this forum will have the knowledge or aptitude to conclusively decide what the shape is either.

My main issue with the Flat Earth Hypothesis is that you would have to discard a whole lot of observational data and well-known physics in order to achieve such a conclusion. On a more philosophical note, if the greatest minds of the last 3000 years were mistaken by the shape of the Earth, then I doubt anyone on this forum will have the knowledge or aptitude to conclusively decide what the shape is either.

I don't know about that number, but the flat earth theories are fallible. The problem is that they require an agreed methodology (the scientific method) which is not supported here. There are some more basic proofs for why the flat earth model is false, but those are usually ignored.

It was just an estimation. I know the Babylonians were aware that the Earth was spherical and they were around over 2500 years ago.

You've hit the head on another one of my gripes regarding FET. It should be called the Flat Earth Hypothesis, not theory, since it has not met the criteria for being one. I might as well say I am the founder of the Cheesy Moon Theory since I don't need it to be accepted, right?

You've hit the head on another one of my gripes regarding FET. It should be called the Flat Earth Hypothesis, not theory, since it has not met the criteria for being one. I might as well say I am the founder of the Cheesy Moon Theory since I don't need it to be accepted, right?

Yup.

By the way Tausami that second link seems to be locked, I can't access it without asking for permission.

By the way Tausami that second link seems to be locked, I can't access it without asking for permission.

Sorry about that. Fixed.

Galatian, have you read the free internet book" Earth Not a Globe". I did not because on my phone. There a lot of proof of the earth's flatness.

Galatian, have you read the free internet book" Earth Not a Globe". I did not because on my phone. There a lot of proof of the earth's flatness.

Here's a link to the book: http://www.sacred-texts.com/earth/za/

Has the book been through peer review and the proofs accepted by scientists? If not, then I cannot accept the text as a proof of anything and reading the book will not at all effect my acceptance of the Earth's shape. A few topics have been created that place doubt on some of the book's key points (perspective, height of sun/moon, etc) which would therefore place the entire text in jeopardy of being wrong. Then again, because I don't believe in a global space conspiracy, the book still would be meaningless to myself. 

Has the book been through peer review and the proofs accepted by scientists?

Yes. Earth not a globe (or ENaG, as it's known in academic circles) is the de facto standard for introductory astronomy and is still used today as an informal set of guidelines for Engineering students in field of aerospace engineering and orbital mechanics.

Has the book been through peer review and the proofs accepted by scientists? If not, then I cannot accept the text as a proof of anything and reading the book will not at all effect my acceptance of the Earth's shape. A few topics have been created that place doubt on some of the book's key points (perspective, height of sun/moon, etc) which would therefore place the entire text in jeopardy of being wrong. Then again, because I don't believe in a global space conspiracy, the book still would be meaningless to myself.

Well, we have to define 'scientist'. RE'ers wouldn't debase themselves enough to actually test whether or not the Earth is flat. Several people have tested the experiments, notably Bedford Level, and the vast majority have found it to be accurate. Lady Blount even took a picture, which is floating around somewhere on the forum. The only two who did not are A.R. Wallace, who was found by a court of law to have cheated (it was a bet between him and an FE'er) and Henry Oldham, who pretty much just showed up one day and said "Yeah, I totally just proved the Earth is round, guys! Nobody saw me do it and I can't prove it, but I totally did!"

Quote from: Galactian on April 21, 2013, 06:57:24 PM

Has the book been through peer review and the proofs accepted by scientists? If not, then I cannot accept the text as a proof of anything and reading the book will not at all effect my acceptance of the Earth's shape. A few topics have been created that place doubt on some of the book's key points (perspective, height of sun/moon, etc) which would therefore place the entire text in jeopardy of being wrong. Then again, because I don't believe in a global space conspiracy, the book still would be meaningless to myself.

Well, we have to define 'scientist'. RE'ers wouldn't debase themselves enough to actually test whether or not the Earth is flat. Several people have tested the experiments, notably Bedford Level, and the vast majority have found it to be accurate. Lady Blount even took a picture, which is floating around somewhere on the forum. The only two who did not are A.R. Wallace, who was found by a court of law to have cheated (it was a bet between him and an FE'er) and Henry Oldham, who pretty much just showed up one day and said "Yeah, I totally just proved the Earth is round, guys! Nobody saw me do it and I can't prove it, but I totally did!"

Why do you keep on saying A.R. Wallace was found by a court of law to have cheated?  It is patently untrue, in fact the opposite is what happened.  Wallace was found to have been the vicitim of libel and was awarded the prize for winning the challenge.  If you have a citation that disagrees, and shows that Wallace's results were fraudulent please enlighten us.

Well, we have to define 'scientist'. RE'ers wouldn't debase themselves enough to actually test whether or not the Earth is flat. Several people have tested the experiments, notably Bedford Level, and the vast majority have found it to be accurate. Lady Blount even took a picture, which is floating around somewhere on the forum. The only two who did not are A.R. Wallace, who was found by a court of law to have cheated (it was a bet between him and an FE'er) and Henry Oldham, who pretty much just showed up one day and said "Yeah, I totally just proved the Earth is round, guys! Nobody saw me do it and I can't prove it, but I totally did!"

You make it sound as though the only experiments done to determine whether the Earth is round or flat was conducted once or twice a few hundred years ago.

Several people have tested the experiments, notably Bedford Level, and the vast majority have found it to be accurate.

You just took the truth and then said the opposite... Several people have used the Bedford experiment to prove that the world was round, and not a single peer reviewed or otherwise reliable study has ever suggested otherwise. It's not reasonable for you to continually cite a few isolated incidences where one experiment, which has otherwise consistently shown the world to be round, was used incorrectly.

Quote from: Galactian on April 21, 2013, 06:57:24 PM

Has the book been through peer review and the proofs accepted by scientists?

Yes. Earth not a globe (or ENaG, as it's known in academic circles) is the de facto standard for introductory astronomy and is still used today as an informal set of guidelines for Engineering students in field of aerospace engineering and orbital mechanics.

While it may have academic use in certain areas, I was referencing whether or not scientists have accepted the proofs for a flat earth.

While it may have academic use in certain areas, I was referencing whether or not scientists have accepted the proofs for a flat earth.

I was just taking the piss earlier, the book is not peer reviewed, and not really taken seriously by any sane person with a high school education.

Quote from: Galactian on April 21, 2013, 09:03:15 PM

While it may have academic use in certain areas, I was referencing whether or not scientists have accepted the proofs for a flat earth.

I was just taking the piss earlier, the book is not peer reviewed, and not really taken seriously by any sane person with a high school education.

As you can see sarcasm just flies over my head! : D

Why do you keep on saying A.R. Wallace was found by a court of law to have cheated?  It is patently untrue, in fact the opposite is what happened.  Wallace was found to have been the vicitim of libel and was awarded the prize for winning the challenge.

Although Wallace did win the libel cases, Hampden gave all of his assets to his son-in-law so that he could declare bankruptcy and not have to pay damages.  Later, a judge declared the initial wager to be an illegal bet and Wallace was ordered to return the winnings.
http://drvitelli.typepad.com/providentia/2010/08/the-flat-earth-fiasco.html

Quote from: Rama Set on April 21, 2013, 08:46:15 PM

Why do you keep on saying A.R. Wallace was found by a court of law to have cheated?  It is patently untrue, in fact the opposite is what happened.  Wallace was found to have been the vicitim of libel and was awarded the prize for winning the challenge.

Although Wallace did win the libel cases, Hampden gave all of his assets to his son-in-law so that he could declare bankruptcy and not have to pay damages.  Later, a judge declared the initial wager to be an illegal bet and Wallace was ordered to return the winnings.
http://drvitelli.typepad.com/providentia/2010/08/the-flat-earth-fiasco.html

Who cares, the Bedford level experiment still repeatedly proved the radius of the earth.

Quote from: Rama Set on April 21, 2013, 08:46:15 PM

Why do you keep on saying A.R. Wallace was found by a court of law to have cheated?  It is patently untrue, in fact the opposite is what happened.  Wallace was found to have been the vicitim of libel and was awarded the prize for winning the challenge.

Although Wallace did win the libel cases, Hampden gave all of his assets to his son-in-law so that he could declare bankruptcy and not have to pay damages.  Later, a judge declared the initial wager to be an illegal bet and Wallace was ordered to return the winnings.
http://drvitelli.typepad.com/providentia/2010/08/the-flat-earth-fiasco.html

That does not mean that Wallace was fraudulent. Indeed the win for Hambden was because of "an obscure legal technicality", which proving fraud most definitely is not.

Quote from: markjo on April 21, 2013, 10:13:23 PM

Quote from: Rama Set on April 21, 2013, 08:46:15 PM

Why do you keep on saying A.R. Wallace was found by a court of law to have cheated?  It is patently untrue, in fact the opposite is what happened.  Wallace was found to have been the vicitim of libel and was awarded the prize for winning the challenge.

Although Wallace did win the libel cases, Hampden gave all of his assets to his son-in-law so that he could declare bankruptcy and not have to pay damages.  Later, a judge declared the initial wager to be an illegal bet and Wallace was ordered to return the winnings.
http://drvitelli.typepad.com/providentia/2010/08/the-flat-earth-fiasco.html

Who cares, the Bedford level experiment still repeatedly proved the radius of the earth.

Please provide evidence for your outrageous claims

Quote from: jason_85 on April 21, 2013, 10:54:48 PM

Quote from: markjo on April 21, 2013, 10:13:23 PM

Quote from: Rama Set on April 21, 2013, 08:46:15 PM

Why do you keep on saying A.R. Wallace was found by a court of law to have cheated?  It is patently untrue, in fact the opposite is what happened.  Wallace was found to have been the vicitim of libel and was awarded the prize for winning the challenge.

Although Wallace did win the libel cases, Hampden gave all of his assets to his son-in-law so that he could declare bankruptcy and not have to pay damages.  Later, a judge declared the initial wager to be an illegal bet and Wallace was ordered to return the winnings.
http://drvitelli.typepad.com/providentia/2010/08/the-flat-earth-fiasco.html

Who cares, the Bedford level experiment still repeatedly proved the radius of the earth.

Please provide evidence for your outrageous claims

While we wait for Jason, could you do the same with your seemingly fatuous claim about the fraudulence of A.R. Wallace's experiment?

Quote from: jason_85 on April 21, 2013, 10:54:48 PM

Quote from: markjo on April 21, 2013, 10:13:23 PM

Quote from: Rama Set on April 21, 2013, 08:46:15 PM

Why do you keep on saying A.R. Wallace was found by a court of law to have cheated?  It is patently untrue, in fact the opposite is what happened.  Wallace was found to have been the vicitim of libel and was awarded the prize for winning the challenge.

Although Wallace did win the libel cases, Hampden gave all of his assets to his son-in-law so that he could declare bankruptcy and not have to pay damages.  Later, a judge declared the initial wager to be an illegal bet and Wallace was ordered to return the winnings.
http://drvitelli.typepad.com/providentia/2010/08/the-flat-earth-fiasco.html

Who cares, the Bedford level experiment still repeatedly proved the radius of the earth.

Please provide evidence for your outrageous claims

It's not outrageous at all, and we've had this discussion already:

Quote from: Arctangent on April 07, 2013, 01:28:02 PM

I'm a Christian, but I don't base my belief in the Flat Earth solely on Scripture. The evidence (simple observation, Bedford Level, model utility, ice wall historicity) pretty clearly points to a planar rather than globular model.

The Bedford Level experiment confirmed the radius of the earth, and there is no photographic evidence of the ice wall. I don't know what you mean by "historicity" though.

In 1870 Dr. A. R. Wallace performed his well-known Bedford Level experiment. In the summers of 1900 and 1901 a series of similar experiments was made with the special object of obtaining photographic records of the same... The height of the parapet of Welney bridge above the water level was measured, a mark was set up on Denver bridge at the same height above the water-level, and midway — three miles from each end — a mark was set up on a pole at the same height above the water-level. A telescope was then directed from the parapet of Welney bridge to the mark on Denver bridge, and the middle mark was seen to stand up about six feet above the line of sight, agreeing with the effect calculated to be produced by the curvature of the earth's surface.

Source: Oldham, H Yule (1901) - "The experimental demonstration of the curvature of the Earth's surface" British Association for the Advancement of Science (Annual Report) p725–6

There are others, and you won't be able to find a single, reliable study that shows evidence to the contrary. The only reason the Bedford experiment ended was because it has already proved that the earth was round and gave its radius with startling accuracy. The only time it showed otherwise was in the early 19th century when it was either performed dishonestly or with inaccurate equipment/methods.

EDIT: As a point of interest, the original Wallace experiment (which is referred to in the Yule study abstract) estimated the diameter of the earth to be 7920 miles, which is only 6 miles, or 0.1% off the actual diameter at the equator. I am not aware of Yule citing an actual estimation for the circumference, although he did demonstrate that the curvature is in line with the expected rate for the understood diameter of the earth at the time.