I have generated a web page with the above at
http://www.ozziesnaps.com/force_paradox.htm if that is convenient
http://www.ozziesnaps.com/force_paradox.htm if that is convenient
Force paradox - a test of reasoning
- Thread starter Quantum Quack
- Start date
In your rocket ship example, there are only two forces at work: the attraction of gravity and the repulsion of the rocket engines. The net force is:
F(net) = F(engines) - F(gravity) = ma.
If the force of the engines is greater than the force of gravity at the particular location, the acceleration of the rocket is positive and it accelerates away from the sun/planet generating the gravity.
If the force of the engines is less than gravity, the acceleration is negative and the rocket accelerates towards the sun.
If the two forces are exactly equal, the acceleration is zero, which means that if the rocket is initially stationary it remains stationary.
You seem to be talking about a situation where you ramp up the engines to move the rocket to a greater distance. The force of gravity decreases with distance, so after the initial acceleration the rocket will keep accelerating away at a greater and greater rate unless the engines are continuously throttled back. If you want the rocket to slow to a stop at a greater distance than it was originally at, then you need to throttle the engines back until the force of gravity is larger than the engine force, which gradually slows the rocket to rest.
I don't see any problem with this.
F(net) = F(engines) - F(gravity) = ma.
If the force of the engines is greater than the force of gravity at the particular location, the acceleration of the rocket is positive and it accelerates away from the sun/planet generating the gravity.
If the force of the engines is less than gravity, the acceleration is negative and the rocket accelerates towards the sun.
If the two forces are exactly equal, the acceleration is zero, which means that if the rocket is initially stationary it remains stationary.
You seem to be talking about a situation where you ramp up the engines to move the rocket to a greater distance. The force of gravity decreases with distance, so after the initial acceleration the rocket will keep accelerating away at a greater and greater rate unless the engines are continuously throttled back. If you want the rocket to slow to a stop at a greater distance than it was originally at, then you need to throttle the engines back until the force of gravity is larger than the engine force, which gradually slows the rocket to rest.
I don't see any problem with this.
JamesR, thanks for taking the time to post a response however I wonder if you saw both posts of just the first one?
Would you care to comment on the second part of the explanation? [ the one with the animations]
thinking:
Infinitely smooth gradient of force over and infinitely small distance. Or even using a Planck length would show the same result
Would you care to comment on the second part of the explanation? [ the one with the animations]
thinking:
Infinitely smooth gradient of force over and infinitely small distance. Or even using a Planck length would show the same result
Quantum Quack:
A flaw in your presentation:
The force exerted on the ship would not be in its mid point, but at its point closest to the sun. That is to say, the force would be at 81, not at 80. Going at 80 would not be sufficient to break free, and in fact, one would actually be pulled back, to higher and higher degrees of force. A gravitational quick sand only to be overcome by massive force.
Now, the other problem here is that you are also not realizing that any movement requires energy. That in order to overcome hte greater force behind you to achieve a lower-exertion of that force, that you must first match that force, and then if you wish to slow down again so that you do not exceed the force all together, you have to slow down to that force's power to hold you in place. This is not saying that a "lower energy level" requires more energy to reach than a higher energy level, but rather, that to move positions requires an exertion of energy, that there is not "higher pressure" or "lower pressure", and that the source of this attraction, one must also realize, is always pulling from behind, rather than being pushed from before. In essence, there is no paradox.
Let me also ask you this: Suppose we make the gravitational source so that landing on it would not destroy one. Now, what would happen if the gravitational force overcame the rocket ship and the rocket ship landed on the surface? Would not the "infinitely small exactitude" of zero be reached? For if it has stopped on the surface - and relative to the surface, and regardless of whether the planet is moving itself, it is indeed stopped - be reached? And therefore demonstrates that an infinitely small point would not prohibit exact rest?
Also, to clarify my entire objection: Take a rubber band. Affix it to a nail or something else that will be stable. Now, pull that rubber band away from the nail, keeping one end looped on the nail. Notice that you are exerting more and more force as you pull it? Now, stop at one point. Notice that you now have to keep that force consistant, or your finger will be pulled back. Now, pull it until the band breaks (let's hope the nail holds!) and you have reached a point where your force so exceeds the pull of the rubber band, that the band can no longer hold, and you are free. Note that what you just did was tantamount to escape velocity, where the gravity of an object has (virtually) no hold anymore and what you have actually done was not "reach a lower level of energy", but broke free from a force by matching and execeding that force.
A flaw in your presentation:
The force exerted on the ship would not be in its mid point, but at its point closest to the sun. That is to say, the force would be at 81, not at 80. Going at 80 would not be sufficient to break free, and in fact, one would actually be pulled back, to higher and higher degrees of force. A gravitational quick sand only to be overcome by massive force.
Now, the other problem here is that you are also not realizing that any movement requires energy. That in order to overcome hte greater force behind you to achieve a lower-exertion of that force, that you must first match that force, and then if you wish to slow down again so that you do not exceed the force all together, you have to slow down to that force's power to hold you in place. This is not saying that a "lower energy level" requires more energy to reach than a higher energy level, but rather, that to move positions requires an exertion of energy, that there is not "higher pressure" or "lower pressure", and that the source of this attraction, one must also realize, is always pulling from behind, rather than being pushed from before. In essence, there is no paradox.
Let me also ask you this: Suppose we make the gravitational source so that landing on it would not destroy one. Now, what would happen if the gravitational force overcame the rocket ship and the rocket ship landed on the surface? Would not the "infinitely small exactitude" of zero be reached? For if it has stopped on the surface - and relative to the surface, and regardless of whether the planet is moving itself, it is indeed stopped - be reached? And therefore demonstrates that an infinitely small point would not prohibit exact rest?
Also, to clarify my entire objection: Take a rubber band. Affix it to a nail or something else that will be stable. Now, pull that rubber band away from the nail, keeping one end looped on the nail. Notice that you are exerting more and more force as you pull it? Now, stop at one point. Notice that you now have to keep that force consistant, or your finger will be pulled back. Now, pull it until the band breaks (let's hope the nail holds!) and you have reached a point where your force so exceeds the pull of the rubber band, that the band can no longer hold, and you are free. Note that what you just did was tantamount to escape velocity, where the gravity of an object has (virtually) no hold anymore and what you have actually done was not "reach a lower level of energy", but broke free from a force by matching and execeding that force.
Accepted and will be considered in future diagrams...thanks.
This is so close to showing my point that I will let it stand with out criticism and instead ask you some questions that will, if answered, show the actual point I am trying to make ok? [ and then allow discussion upon that point directly - hopefully]
1] A ship is maintaining it's position at 80 units of attraction by applying a counter force of 80 units. The ship can be considered as being extremely small [ infinitely small if you like]
What has to happen to the forces exerted by the ship to move a millimetre away from the source of attraction and then maintain that new distance?
How would you graph that force?
2] What would have to happen to the forces exerted by the ship to move an infinitely small distance and then maintain that new distance?
Would graphing that force be any different to your answer to question 1?
3] Consider the nature of the infinitely small and ask how can movement be achieved with out an infinitely small "scallopping effect" in those forces?
An infinitely small increase followed by a very small reduction over and infinitely small distance?
Actually this is a good question and intuitively one would say that the ship is not longer metastable and in fact has reached an equalibrium of forces and counter forces. However I wonder at a quantum level if equalibrium can actually be confirmed. My guess would be that even though it woud appear to be at rest that it is still in a metastable condition as the ship is never actually touching anything and that simply the forces involved are considerably more intense.
ever tried to control what happens after the rubber band breaks?
Say at 10 inches the band is stretched to it's absolute maximum and you wish to move your restrained hand only a another 1/8th of an inch immediately after the band breakes [ in the one action]. Is this possible? If not ----why not? This is the issue I am attempting to address.
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Quantum Quack:
"1] A ship is maintaining it's position at 80 units of attraction by applying a counter force of 80 units. The ship can be considered as being extremely small [ infinitely small if you like]"
Okay.
"What has to happen to the forces exerted by the ship to move a millimetre away from the source of attraction and then maintain that new distance?
How would you graph that force?"
Accelerate by one unit, then decelerate by 2.
"2] What would have to happen to the forces exerted by the ship to move an infinitely small distance and then maintain that new distance?
Would graphing that force be any different to your answer to question 1?"
No. Only the units, not the degree of force, would change. I.E. I'd still be going forward 1, then decelerating 2.
"3] Consider the nature of the infinitely small and ask how can movement be achieved with out an infinitely small "scallopping effect" in those forces?
An infinitely small increase followed by a very small reduction over and infinitely small distance?"
Well presumably, no. For it is the stopping at each point that necessitates the extra energy, not the acceleration. But the end result would be similar, just magnified.
"Actually this is a good question and intuitively one would say that the ship is not longer metastable and in fact has reached an equalibrium of forces and counter forces. However I wonder at a quantum level if equalibrium can actually be confirmed. My guess would be that even though it woud appear to be at rest that it is still in a metastable condition as the ship is never actually touching anything and that simply the forces involved are considerably more intense."
Even if on the quantum level we'd have to deal with the Heisenberg Uncertainty Principle, it seems evident that Quantum MEchanics does not hold true in the same sense on the macroscopic, otherwise the principles in QM would extend to everything, which clearly they do not. In fact, it is the synthesis of QM and Einstein-Newtonian theories of space that has occupied science for the last one hundred years, no?
"ever tried to control what happens after the rubber band breaks?
Say at 10 inches the band is stretched to it's absolute maximum and you wish to move your restrained hand only a another 1/8th of an inch immediately after the band breakes [ in the one action]. Is this possible? If not ----why not? This is the issue I am attempting to address. "
It is possible, but very difficult, and requires further exertion of force. But this is also because we are dealing with a release of potential energy when that energy becomes kinetic upon the breaking of the bond. Take a yoyo or just a ball attached to a string, weaken the string near the end, and whip it around (outside!) as hard as you can. What happens when the string breaks? All the potential energy becomes kinetic and sends the ball rocketting outwards.
Now here is an interesting gravitic question: If gravity is a force, why does not the exertion of that force diminish the power of the source? For instance, why does not the sun shrink from exerting its gravitational pull on things? Perhaps it is not a force in sense the others are and this accounts for its intense weakness as "something else"?
"1] A ship is maintaining it's position at 80 units of attraction by applying a counter force of 80 units. The ship can be considered as being extremely small [ infinitely small if you like]"
Okay.
"What has to happen to the forces exerted by the ship to move a millimetre away from the source of attraction and then maintain that new distance?
How would you graph that force?"
Accelerate by one unit, then decelerate by 2.
"2] What would have to happen to the forces exerted by the ship to move an infinitely small distance and then maintain that new distance?
Would graphing that force be any different to your answer to question 1?"
No. Only the units, not the degree of force, would change. I.E. I'd still be going forward 1, then decelerating 2.
"3] Consider the nature of the infinitely small and ask how can movement be achieved with out an infinitely small "scallopping effect" in those forces?
An infinitely small increase followed by a very small reduction over and infinitely small distance?"
Well presumably, no. For it is the stopping at each point that necessitates the extra energy, not the acceleration. But the end result would be similar, just magnified.
"Actually this is a good question and intuitively one would say that the ship is not longer metastable and in fact has reached an equalibrium of forces and counter forces. However I wonder at a quantum level if equalibrium can actually be confirmed. My guess would be that even though it woud appear to be at rest that it is still in a metastable condition as the ship is never actually touching anything and that simply the forces involved are considerably more intense."
Even if on the quantum level we'd have to deal with the Heisenberg Uncertainty Principle, it seems evident that Quantum MEchanics does not hold true in the same sense on the macroscopic, otherwise the principles in QM would extend to everything, which clearly they do not. In fact, it is the synthesis of QM and Einstein-Newtonian theories of space that has occupied science for the last one hundred years, no?
"ever tried to control what happens after the rubber band breaks?
Say at 10 inches the band is stretched to it's absolute maximum and you wish to move your restrained hand only a another 1/8th of an inch immediately after the band breakes [ in the one action]. Is this possible? If not ----why not? This is the issue I am attempting to address. "
It is possible, but very difficult, and requires further exertion of force. But this is also because we are dealing with a release of potential energy when that energy becomes kinetic upon the breaking of the bond. Take a yoyo or just a ball attached to a string, weaken the string near the end, and whip it around (outside!) as hard as you can. What happens when the string breaks? All the potential energy becomes kinetic and sends the ball rocketting outwards.
Now here is an interesting gravitic question: If gravity is a force, why does not the exertion of that force diminish the power of the source? For instance, why does not the sun shrink from exerting its gravitational pull on things? Perhaps it is not a force in sense the others are and this accounts for its intense weakness as "something else"?
Quantum Quack:
This just came to mind. Consider also that if you were to move backwards instead, we'd simply see a reverse of the process described above. Decelerate by 1, accelerate by 2.
But what are we here saying? That the two pressures are equal? No. Because you are also adding into the context -stability-. You are not accounting that at each point, the pressures are different, only that you are returning to stability each time.
Let's name three positions:
B. Beginning position. Force exerted 80.
A. One point back. Force exerted 81.
C. One point forward. Force exerted 79.
Now right off the bat, we see clearly that point A and C differ by two force from eachother. Right off the bat, this shows that relative to point B, that A is high pressure, and C is low pressure. But what you are introducing here is a return to stability, which necessitates that any movement be cancelled out in relation to the force exerted by the gravitational point. So you do get an "equal amount" by returning to that stability, because you have added that to the equation, not found it in the forces exerted by the gravitational source.
This just came to mind. Consider also that if you were to move backwards instead, we'd simply see a reverse of the process described above. Decelerate by 1, accelerate by 2.
But what are we here saying? That the two pressures are equal? No. Because you are also adding into the context -stability-. You are not accounting that at each point, the pressures are different, only that you are returning to stability each time.
Let's name three positions:
B. Beginning position. Force exerted 80.
A. One point back. Force exerted 81.
C. One point forward. Force exerted 79.
Now right off the bat, we see clearly that point A and C differ by two force from eachother. Right off the bat, this shows that relative to point B, that A is high pressure, and C is low pressure. But what you are introducing here is a return to stability, which necessitates that any movement be cancelled out in relation to the force exerted by the gravitational point. So you do get an "equal amount" by returning to that stability, because you have added that to the equation, not found it in the forces exerted by the gravitational source.
And how is this de-accelleration achieved?
and then apply this to an infinitely small distance.....
Thinking:
Within that infinitely small point of space there is a need for a pseudo paradox of forces to maintain any degree of stability and that a state of absolute equalibrium is impossible due to this need. There fore the gravitational or attractive force naturally generates this need simply due to it's reduction as one travels further away from it's source.
so that dissecting line [ say center of gravity] whilst being infinitely thin has within it's infinite thinness a contradiction of forces.
Therefore gravity it self is a contradictory force, being both a push and a pull simultaneously but qualified as being more pull than push.
Which can then be extended to providing reason why a free-fall in gravity is at the speed it is and not faster or slower. That fall being governed by the degree of differential within that infinitely thin dissection [ Center of gravity] This answer deals with the questions:
"What governs the speed of something in freefall?"
"Why is it the speed it is and not faster or slower?"
And insight into:
"What I mean by suggesting that matter can be described as a governed singularity?"
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Interestingly enough it also goes a long way to help describe why an object in orbit is considerably more stable if not in a state of equalibrium when compared to a non-orbiting object. The perpedicular [angular] momentum providing the object with the stabilizing orbital accelleration that affords our orbiting object greater stability when compared. [ they do say that an orbiting object is under continuous acceleration even though it's velocity appears to remain uniform. yes?]
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I would be extremely interested how mathematically this could be shown to prove "speed of free-fall" relative to distance relative to the mass of the attractor.
I am condfident that an appropriate formula could be generated that would eventually tie in with other proven formulas.
I am condfident that an appropriate formula could be generated that would eventually tie in with other proven formulas.
Quantum Quack:
"And how is this de-accelleration achieved?
and then apply this to an infinitely small distance....."
By exerting a countering force.
"Within that infinitely small point of space there is a need for a pseudo paradox of forces to maintain any degree of stability and that a state of absolute equalibrium is impossible due to this need. There fore the gravitational or attractive force naturally generates this need simply due to it's reduction as one travels further away from it's source."
By virtue that nothing in this universe is ever truly alone to find stability?
"so that dissecting line [ say center of gravity] whilst being infinitely thin has within it's infinite thinness a contradiction of forces.
Therefore gravity it self is a contradictory force, being both a push and a pull simultaneously but qualified as being more pull than push."
I do not follow you.
Where is this "pushing force" to be found in gravity? Perhaps we can simply speak of gravity as being unable to move certain masses at certain distances and at certain strengths? That the mass itself overcomes gravity passively, that is, by being immovable to it until it reaches a certain strength.
"Which can then be extended to providing reason why a free-fall in gravity is at the speed it is and not faster or slower. That fall being governed by the degree of differential within that infinitely thin dissection [ Center of gravity] This answer deals with the questions:
"What governs the speed of something in freefall?"
"Why is it the speed it is and not faster or slower?"
Interestingly enough it also goes a long way to help describe why an object in orbit is considerably more stable if not in a state of equalibrium when compared to a non-orbiting object. The perpedicular [angular] momentum providing the object with the stabilizing orbital accelleration that affords our orbiting object greater stability when compared. [ they do say that an orbiting object is under continuous acceleration even though it's velocity appears to remain uniform. yes?]"
How does this lead to any insight into that? I am afraid I do not follow?
"I would be extremely interested how mathematically this could be shown to prove "speed of free-fall" relative to distance relative to the mass of the attractor.
I am condfident that an appropriate formula could be generated that would eventually tie in with other proven formulas. "
Current scientific knowledge on terminal velocity might all ready explain this.
"And how is this de-accelleration achieved?
and then apply this to an infinitely small distance....."
By exerting a countering force.
"Within that infinitely small point of space there is a need for a pseudo paradox of forces to maintain any degree of stability and that a state of absolute equalibrium is impossible due to this need. There fore the gravitational or attractive force naturally generates this need simply due to it's reduction as one travels further away from it's source."
By virtue that nothing in this universe is ever truly alone to find stability?
"so that dissecting line [ say center of gravity] whilst being infinitely thin has within it's infinite thinness a contradiction of forces.
Therefore gravity it self is a contradictory force, being both a push and a pull simultaneously but qualified as being more pull than push."
I do not follow you.
Where is this "pushing force" to be found in gravity? Perhaps we can simply speak of gravity as being unable to move certain masses at certain distances and at certain strengths? That the mass itself overcomes gravity passively, that is, by being immovable to it until it reaches a certain strength.
"Which can then be extended to providing reason why a free-fall in gravity is at the speed it is and not faster or slower. That fall being governed by the degree of differential within that infinitely thin dissection [ Center of gravity] This answer deals with the questions:
"What governs the speed of something in freefall?"
"Why is it the speed it is and not faster or slower?"
Interestingly enough it also goes a long way to help describe why an object in orbit is considerably more stable if not in a state of equalibrium when compared to a non-orbiting object. The perpedicular [angular] momentum providing the object with the stabilizing orbital accelleration that affords our orbiting object greater stability when compared. [ they do say that an orbiting object is under continuous acceleration even though it's velocity appears to remain uniform. yes?]"
How does this lead to any insight into that? I am afraid I do not follow?
"I would be extremely interested how mathematically this could be shown to prove "speed of free-fall" relative to distance relative to the mass of the attractor.
I am condfident that an appropriate formula could be generated that would eventually tie in with other proven formulas. "
Current scientific knowledge on terminal velocity might all ready explain this.
sorry to be a bit persistant here but:
At what point in an infinitely small distance does one apply this countering force?
At what point in an infinitely small distance does one apply this countering force?
Quantum Quack:
Ha. Got me there. As both accelerating and deacellerating cannot occur at the same time, and we can assume tha tonly one could occur in an infinitely distance's crossing, then you must by necessity miss your mark. However, if you move back an infinitely a certain space, and exert enough force to accelerate that space's distance to the infinitely small point you initially wanted to reach at the start and then immediatly counteract it as soon as one reaches the appropriate cut off point, one would stop at one's destination.
Here it is explained more easily.
Take the starting position to be B.
One back to be A.
One forward to be C.
In order to get from A-C, B must be reached. And at each point, one can only do one action.
In order to go from B to C one must necessarily overshoot one's bounds, because one can only accelerate in the time frame.
But if one starts from A, accelerates at A enough to reach C (say it goes "2 infinitely small miles an hour") and then counteracts that force when it reaches B, then it could stop at C and be at rest.
Ha. Got me there. As both accelerating and deacellerating cannot occur at the same time, and we can assume tha tonly one could occur in an infinitely distance's crossing, then you must by necessity miss your mark. However, if you move back an infinitely a certain space, and exert enough force to accelerate that space's distance to the infinitely small point you initially wanted to reach at the start and then immediatly counteract it as soon as one reaches the appropriate cut off point, one would stop at one's destination.
Here it is explained more easily.
Take the starting position to be B.
One back to be A.
One forward to be C.
In order to get from A-C, B must be reached. And at each point, one can only do one action.
In order to go from B to C one must necessarily overshoot one's bounds, because one can only accelerate in the time frame.
But if one starts from A, accelerates at A enough to reach C (say it goes "2 infinitely small miles an hour") and then counteracts that force when it reaches B, then it could stop at C and be at rest.
Quantum Quack:
What is the programme that you use for your animations? I'd like to use the same so I can occasionally respond with my own animations of my viewpoints.
What is the programme that you use for your animations? I'd like to use the same so I can occasionally respond with my own animations of my viewpoints.
and of course A,B and C are all a part of that infinitely thin dissection.
Can you see what I am driving at with regards to an infinitely thin line with two different forces when comparing the two sides and why the inverse can only be true of those forces to facilitate this metastability within that infinitely dissection [ center of gravity ]
imagine
A
B
C as a single infinitely thin line.
because in the end it is a single two sided infinitely thin line we are talking about. And if the forces appeared converse there would be no need to de-accellerate in an infinitely small distance.
Can you see what I am driving at with regards to an infinitely thin line with two different forces when comparing the two sides and why the inverse can only be true of those forces to facilitate this metastability within that infinitely dissection [ center of gravity ]
imagine
A
B
C as a single infinitely thin line.
because in the end it is a single two sided infinitely thin line we are talking about. And if the forces appeared converse there would be no need to de-accellerate in an infinitely small distance.
Prince_James said:
check out this web site:
http://www.freeserifsoftware.com/default.asp
and down load Serif Draw Plus
With A at one end, C at the other, and B in the middle? That is what I was essentially doing. Or do you mean that is the end and that is it? One could not go back two points, because there is not two points back?
given that we are dealing with infinitey A,B and C are on top of each other and simultaneous.Prince_James said:
or at least A and C is [ B being uneccesssary.]
So are you saying they are more like ___ (three _'s) rather than ...? No distinctness? Because I had assumed we are dealing with three infinitely small points lined up from A-C, with your question pertaining to movement from B-C and how to go one space forward only.
Quantum Quack said:
you could take this diagram and reduce it to the infinitely small and you can see that that thin line has a lot more too it than just being infinitely thin.
<img src=http://www.ozziesnaps.com/diagram%206.gif>
and the only way to describe this force contradiction within that infinitely thin line is with this diagram:
<img src=http://www.ozziesnaps.com/diagram%203.jpg>