UA and Inclined Planes
« on: October 11, 2019, 09:06:47 PM »
How would one calculate the rate of acceleration of an object on an inclined plane in a UA scenario?

With gravity (assuming no friction or applied force for simplicity), you begin by finding the perpendicular and parallel components of gravity acting on the object.  Since the normal and perpendicular forces will cancel each other out, we are left with only the parallel component of gravity acting as the net force accelerating the object.

My assumption would be that one would use the same process for UA. The directions of the UA force and normal force would be reversed from the directions of gravity and the normal force, but since they would still cancel each other out, it wouldn’t affect the calculations.  However, using the same process would mean that instead of gravity acting as the only force accelerating the object, UA is only force accelerating the object.
 
Objects require force to accelerate and they will always accelerate in the direction of net force…so how would anything slide down an incline in a UA environment?

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Re: UA and Inclined Planes
« Reply #1 on: October 13, 2019, 04:22:41 PM »
How would one calculate the rate of acceleration of an object on an inclined plane in a UA scenario?
The same way you would in RET, as per the Equivalence Principle.
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Re: UA and Inclined Planes
« Reply #2 on: October 13, 2019, 07:21:14 PM »
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The same way you would in RET, as per the Equivalence Principle.

I agree the numbers would look the same. The difference would be the net force you end up with would be UA instead of gravity.  How does the equivalence principle explain how UA…an upward force…can be responsible for accelerating something downhill?

This is what the calculations with gravity would look like.

Net Gravitational force 10kg @ 20 ⁰
 Fnorm = 10.000 * 9.810 * cos(20) = 92.184N
 F⊥= 10.000 * 9.810 * cos(20) = 92.184N
F// = 0.000 * 9.810 * sin(20) = 33.552N
The normal and perpendicular forces cancel each other out, so the net gravitational force is 33.552N.  The net UA force would be the same, but in the opposite direction.  How does that account for being accelerated downhill?

Net Gravitational force 10kg @ 30 ⁰
Fnorm = 10.000 * 9.810 * cos(30) = 84.957N
F⊥= 10.000 * 9.810 * cos(30) = 84.957N
F// =   10.000 * 9.810 * sin(30) = 49.050N
The normal and perpendicular forces cancel each other out, so the net gravitational force is 49.050N...same question as above.

Interesting observation…the net gravitational force increases as the angle increases.  It’s almost as if the magnitude of the net gravitational forces on something change in response to how level it is.  I wonder if there is some device that could demonstrate that? 


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Re: UA and Inclined Planes
« Reply #3 on: October 13, 2019, 07:25:13 PM »
How does the equivalence principle explain how UA…an upward force…can be responsible for accelerating something downhill?
This is the same argument as your spirit level fiasco. You do not seem to understand that acceleration is relative to a frame of reference. There will be no helping that until you brush up on high school physics.

Your question boils down to "What is the equivalence principle?" You're well capable of Googling that.
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Re: UA and Inclined Planes
« Reply #4 on: October 13, 2019, 09:37:47 PM »
Quote
Your question boils down to "What is the equivalence principle?" You're well capable of Googling that.

I understand EP enough to know that in order for it to apply, in one reference the object is at rest and in the other, the object is being accelerated.  However, the example I have given, the object is being accelerated in both references. 

UA explains why, if I released a box from a height, the box would appear to fall to the ground, when in reality, the ground is rising up to meet the box.
It would not explain why a box would accelerate down an inclined plane if placed on an inclined plane that was already sitting on the ground.

Those are two different things.  The ground is not rising up to meet the box

Let S1 be accelerated in the direction of its X axis, and let g be the (temporally constant) magnitude of that acceleration. S2 shall be at rest, but it shall be located in a homogeneous gravitational field that imparts to all objects an acceleration –g in the direction of the X axis. As far as we know, the physical laws with respect to S1 do not differ from those with respect to S2; this is based on the fact that all bodies are equally accelerated in a gravitational field. At our present state of experience we have thus no reason to assume that the systems S1 and S2 differ from each other in any respect, and in the discussion that follows we shall therefore assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system.

The fact that an object at rest in a UA reference will appear to behave the same way as an accelerated object in a gravity reference does not mean an object being accelerated in an UA reference would appear to behave the same as an object being accelerated in a gravity reference
« Last Edit: October 14, 2019, 12:54:26 AM by pricelesspearl »

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Re: UA and Inclined Planes
« Reply #5 on: October 14, 2019, 06:54:30 AM »
I understand EP enough to know that in order for it to apply, in one reference the object is at rest and in the other, the object is being accelerated.
Yes, that's the problem. You "understand" it so well that the very first part of your attempt at describing it is wrong.

There's no way around this. You need to learn physics before you can meaningfully argue it. Again, nothing to do with FE vs RE, and everything to do with understanding of the fundamentals.
« Last Edit: October 14, 2019, 07:40:40 AM by Pete Svarrior »
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Re: UA and Inclined Planes
« Reply #6 on: October 14, 2019, 09:13:30 PM »
Quote
You "understand" it so well that the very first part of your attempt at describing it is wrong.

You mean this part?

Quote
Let S1 be accelerated in the direction of its X axis, and let g be the (temporally constant) magnitude of that acceleration.

I guess you understand EP better than Einstein, since that is a direct quote from him.

https://www.mathpages.com/home/kmath622/kmath622.htm


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Re: UA and Inclined Planes
« Reply #7 on: October 16, 2019, 09:07:15 AM »
You mean this part?
Yes, obviously I meant something I didn't quote, and not what I explicitly quoted prior to replying. Sigh.
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Re: UA and Inclined Planes
« Reply #8 on: October 17, 2019, 12:25:20 AM »
You mean this part?
Yes, obviously I meant something I didn't quote, and not what I explicitly quoted prior to replying. Sigh.

The two statements were substantively the same. And they are both correct.

This is the so called Equivalence hypothesis, which in other words states that it’s impossible to tell the difference between an object at rest in a gravitational field or an accelerating object in free space, where the acceleration is generated by a force equal to the gravitational field.

https://esc.fnwi.uva.nl/thesis/centraal/files/f31871018.pdf

A state of rest in a homogeneous gravitational field is physically indistinguishable from a state of uniform acceleration in a gravity-free space. However, in the Universal Relativity, only the change in the geometry has to be taken into account. An object moving in space at an acceleration g, and an object at rest under gravitation g are not equivalent; the principle of equivalence does not hold.
 
(Note here that the author is arguing that under Universal Relativity, EP would not hold.  The point of the quote is how the author defines EP)

https://www.researchgate.net/publication/276105151_Universal_Relativity_Absolute_Time_and_Mass

A charged particle at rest in a gravitational field, such as on the surface of the Earth, must be supported by a force to prevent it from falling. According to the equivalence principle, it should be indistinguishable from a particle in flat space being accelerated by a force
https://en.wikipedia.org/wiki/Paradox_of_radiation_of_charged_particles_in_a_gravitational_field

Mid-slide UA could account for the object appearing to accelerate downwards, when in reality the inclined plane was rising...not really sure about that but will accept it for the sake of argument...but it would not account for what caused the object to begin accelerating downwards to begin with.

If I release an object in a UA environment, it will not accelerate it downwards. It will remain stationary until the floor makes contact with it, but for some reason UA will accelerate an object downwards when it is on an inclined plane.  Not sure how EP turns UA into a force that accelerates objects down in one case and not the other.

What you are not getting is that EP only applies to free falling bodies…bodies not subject to any forces, and an object on an inclined plane, is by definition is not a free falling body.

« Last Edit: October 17, 2019, 12:28:09 AM by pricelesspearl »

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Re: UA and Inclined Planes
« Reply #9 on: October 17, 2019, 08:20:43 AM »
Well, sorry. Until you learn the basics, I won't be able to help you, no matter how much you protest. If your misunderstandings of simple physics applied in reality, it would break RET.

As always, you can easily test your hypothesis to see just how blatantly confused you are. You can place an item on an inclined plane, and accelerate the system upwards by hand. You can try this with different objects and inclines to see how the resultant forces interact with friction. You could make a fun-filled day out of it.

You should also have a read on how to represent problems in inertial and non-inertial frames of reference. Your confusion between the two is the source of your "why are things not accelerated downwards?" conundrum.
« Last Edit: October 17, 2019, 08:23:36 AM by Pete Svarrior »
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Re: UA and Inclined Planes
« Reply #10 on: October 17, 2019, 07:59:16 PM »
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You should also have a read on how to represent problems in inertial and non-inertial frames of reference

Thanks, but I am satisfied with my understanding. The preferred refence frame in GR is the Lorentz frame, which by definition is a free falling (inertial) frame of reference.

EP simply does not apply in the situation I have described. A supported object is not by definition in free fall and EP does not apply.

Quote
Lorentz Frames

The conclusion is that we need to abandon the entire distinction between Newton-style inertial and noninertial frames of reference. The best that we can do is to single out certain frames of reference defined by the motion of objects that are not subject to any nongravitational forces. A falling rock defines such a frame of reference. In this frame, the rock is at rest, and the ground is accelerating. The rock’s world-line is a straight line of constant x = 0 and varying t. Such a free-falling frame of reference is called a Lorentz frame. The frame of reference defined by a rock sitting on a table is an inertial frame of reference according to the Newtonian view, but it is not a Lorentz frame

EP is much more nuanced than your wiki suggests or that you want to pretend it is so that you can use it as your response to any difficult question. There are multiple versions with multiple interpretations that even leading academics can’t seem to agree on.  Whether or not it applies only infinitesimally is hotly debated as well as what defines “locally”, but all agree that to the extent tidal effects are measurable it doesn’t apply and that it only applies to an isolated observer.

What they all agree on is that it does not apply all the time, in every situation, to everything.

If you can’t or won’t address why you believe your interpretation is correct or why it should apply, don’t be surprised when you get push back.  “Because EP” is a pretty low effort response.




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Re: UA and Inclined Planes
« Reply #11 on: October 19, 2019, 06:18:25 PM »
Dude, you are just wrong, whether the incline is pushing up or the ball is rotating down the result looks the same. I’m a REer and I know this to be true. Once you complete high school physics you should be able to visualize it too.
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Re: UA and Inclined Planes
« Reply #12 on: October 19, 2019, 10:37:14 PM »
Dude, you are just wrong, whether the incline is pushing up or the ball is rotating down the result looks the same. I’m a REer and I know this to be true. Once you complete high school physics you should be able to visualize it too.

Like a said a few post above, if just seeing it mid-slide, you are right. But UA doesn't explain why it would begin to slide in the first place  I know enough about physics to know that an object at rest will not move unless a force is applied to it. 

If I simply released an object in a UA environment, there is no force to move it. It will just remained suspended until the floor made contact.   If I place it on an inclined plane instead of releasing it, there is still no force to move it.  No force means no movement. That is high school physics.

And I am not a dude.
« Last Edit: October 19, 2019, 10:42:22 PM by pricelesspearl »

Re: UA and Inclined Planes
« Reply #13 on: October 20, 2019, 07:16:39 AM »
And I am not a dude.
In that case, madam, I think the point you are failing to understand about the UA theory is that the earth itself shields us from the force which powers it.
So the earth is accelerated upwards but if you jump then you are not affected by the force of UA - if you were then you wouldn't fall.
So if something is on an inclined plane then it's the acceleration of the earth caused by UA which imparts the force which causes the ball to move.
If you are making your claim without evidence then we can discard it without evidence.

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Re: UA and Inclined Planes
« Reply #14 on: October 20, 2019, 03:52:50 PM »
Dude, you are just wrong, whether the incline is pushing up or the ball is rotating down the result looks the same. I’m a REer and I know this to be true. Once you complete high school physics you should be able to visualize it too.

Like a said a few post above, if just seeing it mid-slide, you are right. But UA doesn't explain why it would begin to slide in the first place  I know enough about physics to know that an object at rest will not move unless a force is applied to it. 

If I simply released an object in a UA environment, there is no force to move it. It will just remained suspended until the floor made contact.   If I place it on an inclined plane instead of releasing it, there is still no force to move it.  No force means no movement. That is high school physics.

And I am not a dude.

Dude, tidal forces are pretty much the death of UA and there is no even remotely Ad Hoc explanation for them, except perhaps some weird Sandokhan voodoo. But your inclined plane thought experiment shows a lack of understanding of the discussions on this site.
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Re: UA and Inclined Planes
« Reply #15 on: October 20, 2019, 04:35:18 PM »
Quote
So the earth is accelerated upwards but if you jump then you are not affected by the force of UA - if you were then you wouldn't fall.

That’s not what the wiki says. It says that when you jump…you don’t fall…the earth catches up. Things don’t” fall” in UA, that is the point. I don't see why an object being released would be affected any differently by UA than someone who is jumping.  Both should just remain suspended, with no force acting upon it until the earth "catches up".

Quote
When you jump, your upward velocity is for a moment, greater than the Earth's so you rise above it. But after a few moments, the Earth's increasing velocity due to its acceleration eventually catches up

In addition, nobody has really addressed the initial question I asked is how you would calculate the rate of acceleration.  As I pointed out in a previous post

Quote
The calculations should be the same except the direction of the UA force and normal force would be opposite of gravity and normal force.
So let’s compare the calculations for both, using negative to indicate the gravity/normal direction and positive to indicate the UA/normal direction.


Using negative for gravity to calculate the net force on a 10k object at a 20 ⁰ angle
 Fnorm = 10.000 * -9.810 * cos(20) = -92.184N
 F⊥= 10.000 * -9.810 * cos(20) =-92.184N
F// = 0.000 -.810 * sin(20) = -33.552N
So in gravity the net force on the object would be -33.552N…IOW, down, in the negative direction

Using the same process using positive for UA to calculate the net force on a 10k object at a 20 ⁰ angle
Net UA force 10kg @ 20 ⁰
 Fnorm = 10.000 * +9.810 * cos(20) = +92.184N
 F⊥= 10.000 * +9.810 * cos(20) =+92.184N
F// = 0.000 -.810 * sin(20) = +33.552N
So with UA, the net force on the object would be +33.552N…IOW, up in the positive direction.

So using the same calculation formula, with UA the object is actually being pushed up.  So if UA is actually responsible for accelerating it down, how would you calculate it? 

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Re: UA and Inclined Planes
« Reply #16 on: October 20, 2019, 05:08:24 PM »
But calculating the excess force is not the end of the problem, you have to assess what happens with that excess force. Once you figure that out you should understand that both situations result in what looks like a ball rotating in the direction of the declining slope.
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Re: UA and Inclined Planes
« Reply #17 on: October 20, 2019, 06:09:50 PM »
But calculating the excess force is not the end of the problem, you have to assess what happens with that excess force. Once you figure that out you should understand that both situations result in what looks like a ball rotating in the direction of the declining slope.

The excess force is what accelerates the object and it will always accelerate it in the direction of the force.  If the excess force is in the negative direction, it will accelerate it in proportion to the mass in the negative direction.  If the excess force is in the positive direction, it will accelerate the object in the positive direction.

Quote
Acceleration is produced by a net force on an object and is directly proportional to the magnitude of the force, in the same direction as the force, and is inversely proportional to the mass of the object.
Acceleration = Force/mass (a = F/m)
http://www.csun.edu/~psk17793/S9CP/S9%20Acceleration.htm

Using the same figures as above :

Gravity a=-33.552/10.00
a= -3.3552 in negative or downward direction for gravity

UA a = 33.552/10.0
a=3.3552 in the positive or upward direction for UA

If there is another way to calculate it so that UA actually accelerates something down, perhaps you can provide it.

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Re: UA and Inclined Planes
« Reply #18 on: October 20, 2019, 07:22:50 PM »
So you think you can’t spin a wheel in same direction by spinning upwards on the left side or downwards on the right side?
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Re: UA and Inclined Planes
« Reply #19 on: October 20, 2019, 07:49:30 PM »
Quote
That’s not what the wiki says. It says that when you jump…you don’t fall…the earth catches up. Things don’t” fall” in UA, that is the point.

Ok, fine. It was a mistake to use the word “fall”. I used it because that’s how we think of it. But ok, try this. Let’s say you put a ball on an inclined plane in a weightless environment, so no gravity is acting. The ball stays where it is, yes?
Now imagine you accelerate the inclines plane upwards. The plane now exerts a force upwards on the ball. So the ball is pushing down on the plane. But because the plane is inclined a part of that force acts down the slope, so it moves (assuming that force is greater than the friction force). No?
If that upward acceleration produces the same force as gravity does in conventional physics you’d get the same result.
« Last Edit: October 20, 2019, 08:36:01 PM by AllAroundTheWorld »
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