Dancing David
Penultimate Amazing
Ah Pondhopper, there is nothing we know that is not observation.
JEROME - Black holes do not exist
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Ah Pondhopper, there is nothing we know that is not observation.
JEROME DA GNOME
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What force causes the acceleration to decrease?
KingMerv00
Penultimate Amazing
Inertia.
Dancing David
Penultimate Amazing
To be annoying.
Dancing David
Penultimate Amazing
Because it doesn't.
It is it's wont?
Why ask why? Some answers have no questions.
He (or she) was answering your question about why more massive objects don't accelerate more than less massive objects. If you don't want people to answer your questions, don't ask them in the first place.
Dancing David
Penultimate Amazing
The Harmony of the Virtual Particles, the Vacum Energy Dust Bunnies and of course Death and Taxes.
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Dancing David
Penultimate Amazing
The vacum Energy Dust Bunnies, the Harmony of the Virtual Particles, they defend the frivolous mass and are the Keepers of Inertia.
Now inertia is something that doesn't really have a good explanation for it at all. I think it is those darn Nutrinos.
See we don't really know why, all we can do itry to approximate the behaviors, as I said before. It could be warped space time it could be the action of angels in angel space.
Hold a known test-mass up with a spring. Observe the extension of the spring, and use Hooke's law to calculate the necessary force to produce that extension. Voila, that's the gravitational force acting on your test mass. Some people know this sophisticated device as a "spring balance".
Jerome,
I’m going to assume that you agree F = ma.
We have two objects with different masses, m(big) and m(small).
F(big) = m(big)a(big)
F(small) = m(small)a(small)
So, the force applied to m(big) would have to be larger than the force applied to m(small) for the two objects to have the same acceleration.
The force of gravity between two object is described by:
F(g) = G(mM)/r^2
So assuming the same mass of the second object M(in this case the earth) we have:
The force of gravity between M and m(big)
F(M-m(big)) = G(m(big)M)/r^2
and
the force of gravity between M and m(small)
F(M-m(small)) = G(m(small)M)/r^2
As you can see, the size of each force is different because the mass of the two non-earth masses are different.
So,
F(big) = m(big)a(big) = G(m(big)M)/r^2
And
F(small) = m(small)a(small) = G(m(small)M)/r^2
And after algebra:
a(big) = GM/r^2 = a(small)
The accelerations are the same because the force due to gravity between each object and the earth is different because the objects have different masses.
If you disagree with the above then your complaint is not with physics, but with Mother Nature. I hear she is a bitch when dealing with disputes about her behavior. Good luck.
I’m going to assume that you agree F = ma.
We have two objects with different masses, m(big) and m(small).
F(big) = m(big)a(big)
F(small) = m(small)a(small)
So, the force applied to m(big) would have to be larger than the force applied to m(small) for the two objects to have the same acceleration.
The force of gravity between two object is described by:
F(g) = G(mM)/r^2
So assuming the same mass of the second object M(in this case the earth) we have:
The force of gravity between M and m(big)
F(M-m(big)) = G(m(big)M)/r^2
and
the force of gravity between M and m(small)
F(M-m(small)) = G(m(small)M)/r^2
As you can see, the size of each force is different because the mass of the two non-earth masses are different.
So,
F(big) = m(big)a(big) = G(m(big)M)/r^2
And
F(small) = m(small)a(small) = G(m(small)M)/r^2
And after algebra:
a(big) = GM/r^2 = a(small)
The accelerations are the same because the force due to gravity between each object and the earth is different because the objects have different masses.
If you disagree with the above then your complaint is not with physics, but with Mother Nature. I hear she is a bitch when dealing with disputes about her behavior. Good luck.
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MattusMaximus
Intellectual Gladiator
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Okay, settle down everyone! I'm seeing entirely too many misconceptions in basic mechanics being slung around here! And, as a physics teacher, it's pissing me off 
Listen up (you especially Jerome) and gather 'round - it's time for another physics lesson!
First off, we need to make sure everyone is clear on their definitions. I've seen Jerome use the term "force" to describe (at least) three different phenomena, and I've seen some people reply to him using other physics terms out of context or improperly. So let's begin by clearing up these definitions and getting on the same page...
I am going to apply the following commonly-accepted (in physics) terms with their accompanying definitions:
1. Force - this is some quantity (call it a gnome if you wish) that, if unbalanced, causes an acceleration of an object. Key point: forces are not directly observed; their existence is inferred from our observations of motion, but we have a way to quantify them reliably and predictably. So because that works we say that forces exist. In addition, forces exist as an interaction between two objects; they cannot exist in isolation.
2. Acceleration - this is some change in the motion of an object, whether it be speeding up, slowing down, or changing direction. Accelerations are caused by unbalanced forces acting upon an object. Key Point: accelerations are directly observed! For example, you can see a car speeding up as it moves down the road.
3. Inertia - this is typically measured as the mass of an object (in kilograms). It is a property which displays an object's resistance to changes in motion; that is, the inertia of an object resists acceleration. The greater the inertia or mass of an object, the more "sluggish" it is. Key Point: inertia is independent of gravity; mass and weight are not the same thing; you can determine the mass of an object independently of weight by simply attempting to shake it back and forth; the more "sluggish" the object, the more mass it has.
4. Force Field - this is a distortion of space which creates a situation whereby forces can exist between objects. Call this a gnome if you wish, because fields are not directly observed (they are inferred like forces), but we have methods of reliably quantifying and predicting fields. So, again, we say that in this context they are "real". Key Point: force fields do exist independently of objects located within the field.
Now that I've outlined all these definitions, I'm going to put them into the context of gravity...
The first three quantities (force, acceleration, and mass (inertia)) are all related in classical physics by Newton's Second Law:
F = ma or a = F/m
F and a are bolded because they represent vector quantities (i.e., they have a direction - "down" in the case of gravity - associated with them). This law has been tested to very high precision and I have my students perform lab work using it all the time. What it basically says is that if you exert an unbalanced force (F) on an object with a certain mass (m), then it will experience a certain acceleration (a).
Bottom line: the harder you push on the object, the more it will accelerate; and the more massive the object, the more it will resist the acceleration. If you don't believe me, crunch some numbers using the formula. If you still don't believe me, try this: kick two objects really hard - a golf ball and a bowling ball; my guess is the one with less mass changed its motion much more, right? (And I hope you didn't hurt your foot
)
So how does this apply to gravity? Simple... in physics we call "the force of gravity" by a one-word moniker: weight. So replace F with W...
W = mg or g = W/m
What this says is that if the weight on an object is unopposed (i.e., there are no other forces involved, such as air resistance), then that object will undergo an acceleration of g (we call this the "acceleration due to gravity"). g plays the role that a did in the more general equation above.
So let's think about this in terms of freely-falling bodies. Aside: an object is in "free-fall" if the only force it experiences is weight; so technically speaking, objects falling through the air on Earth are not in free-fall, but objects (such as a hammer and feather) falling on the Moon are in free-fall (no air drag on the Moon).
It ends up that all objects in free-fall in the same gravitational force field will fall with the same acceleration. On Earth, we call this g. If you take the weight (in Newtons) of any object and divide it by its mass (in kilograms), then you should come up with the same number every time for every object: 9.8 m/sec2 - which is in units of acceleration.
Thus: g = W/m = 9.8 m/sec2 (on Earth in a vacuum)
So one way to look at the constant acceleration of all objects on Earth due to gravity is that the ratio of their weight to their mass is always the same. But there is a slightly deeper way to look at it: in the context of the gravitational force field.
Very roughly speaking, the gravity field of the Earth distorts space around the planet in such a manner that any object with mass placed into this field will experience a force of interaction (weight, in this case). To quantify the gravity field of the Earth, we need to look at Newton's Universal Law of Gravitation, which generalized gravity forces as follows:
F = -GMm/r2
Where F is the force of gravity (weight), G is the universal gravitational constant (as determined by the Cavendish experiment to be 6.67x10-11 Nm2/kg2), M is the mass of the object creating the field (for Earth M = 5.98x1024 kg), m is the mass of the object (doesn't matter - you'll see why not), r is the distance from the center of the object to the point in the field (for Earth's surface r = 6.37x106 m), and the minus sign (-) simply indicates the direction of the force (down).
If you want to calculate the gravitational field at the surface of the Earth, you must note that this quantity is independent of the mass (m) of the object on the surface (as per our definitions above). Thus, we divide out m...
F/m = -GM/r2
Now, if you grab a calculator and crunch the numbers outlined in the previous paragraph, you will get a very interesting result for the strength of the gravitational field on the Earth's surface.
F/m = -9.8 m/sec2
Which is what we called the "acceleration due to gravity" earlier. It ends up that in the case of gravity, as viewed through classical Newtonian mechanics, the terms "acceleration" and "field" are synonymous. I did the calculation assuming we're on the Earth's surface, but you could apply the equations anywhere.
So, to conclude, if we observe (as seen in many experiments and the video footage from the Moon) that objects in free-fall accelerate at the same rate, regardless of their weights or masses, then we can also conclude that the gravitational field in which these objects are located is also the same for all objects within that field.
To sum up:
1. Weights (forces of gravity) can vary from object to object.
2. Masses (measures of inertia) can also vary from object to object.
3. g (acceleration due to gravity) for all objects is the same, because the ratio W/m is constant for all objects.
4. g can also be expressed as the "gravitational field" and is synonymous with acceleration due to gravity. Thus, it is also independent of the mass of the objects.
If you've read this far, kudos to you.
If you actually worked out the calculations for yourself, you get a gold star!
Now... any questions?
ETA: I'm going to go have a drink and read up on the Eotvos experiment, as I have to prep for an introductory lecture on general relativity tomorrow. Phew!
PS: My apologies to Scott1972 - I was typing all this out (it took me 30 minutes) after you'd posted and I didn't see your post.
Listen up (you especially Jerome) and gather 'round - it's time for another physics lesson!
First off, we need to make sure everyone is clear on their definitions. I've seen Jerome use the term "force" to describe (at least) three different phenomena, and I've seen some people reply to him using other physics terms out of context or improperly. So let's begin by clearing up these definitions and getting on the same page...
I am going to apply the following commonly-accepted (in physics) terms with their accompanying definitions:
1. Force - this is some quantity (call it a gnome if you wish) that, if unbalanced, causes an acceleration of an object. Key point: forces are not directly observed; their existence is inferred from our observations of motion, but we have a way to quantify them reliably and predictably. So because that works we say that forces exist. In addition, forces exist as an interaction between two objects; they cannot exist in isolation.
2. Acceleration - this is some change in the motion of an object, whether it be speeding up, slowing down, or changing direction. Accelerations are caused by unbalanced forces acting upon an object. Key Point: accelerations are directly observed! For example, you can see a car speeding up as it moves down the road.
3. Inertia - this is typically measured as the mass of an object (in kilograms). It is a property which displays an object's resistance to changes in motion; that is, the inertia of an object resists acceleration. The greater the inertia or mass of an object, the more "sluggish" it is. Key Point: inertia is independent of gravity; mass and weight are not the same thing; you can determine the mass of an object independently of weight by simply attempting to shake it back and forth; the more "sluggish" the object, the more mass it has.
4. Force Field - this is a distortion of space which creates a situation whereby forces can exist between objects. Call this a gnome if you wish, because fields are not directly observed (they are inferred like forces), but we have methods of reliably quantifying and predicting fields. So, again, we say that in this context they are "real". Key Point: force fields do exist independently of objects located within the field.
Now that I've outlined all these definitions, I'm going to put them into the context of gravity...
The first three quantities (force, acceleration, and mass (inertia)) are all related in classical physics by Newton's Second Law:
F = ma or a = F/m
F and a are bolded because they represent vector quantities (i.e., they have a direction - "down" in the case of gravity - associated with them). This law has been tested to very high precision and I have my students perform lab work using it all the time. What it basically says is that if you exert an unbalanced force (F) on an object with a certain mass (m), then it will experience a certain acceleration (a).
Bottom line: the harder you push on the object, the more it will accelerate; and the more massive the object, the more it will resist the acceleration. If you don't believe me, crunch some numbers using the formula. If you still don't believe me, try this: kick two objects really hard - a golf ball and a bowling ball; my guess is the one with less mass changed its motion much more, right? (And I hope you didn't hurt your foot
)So how does this apply to gravity? Simple... in physics we call "the force of gravity" by a one-word moniker: weight. So replace F with W...
W = mg or g = W/m
What this says is that if the weight on an object is unopposed (i.e., there are no other forces involved, such as air resistance), then that object will undergo an acceleration of g (we call this the "acceleration due to gravity"). g plays the role that a did in the more general equation above.
So let's think about this in terms of freely-falling bodies. Aside: an object is in "free-fall" if the only force it experiences is weight; so technically speaking, objects falling through the air on Earth are not in free-fall, but objects (such as a hammer and feather) falling on the Moon are in free-fall (no air drag on the Moon).
It ends up that all objects in free-fall in the same gravitational force field will fall with the same acceleration. On Earth, we call this g. If you take the weight (in Newtons) of any object and divide it by its mass (in kilograms), then you should come up with the same number every time for every object: 9.8 m/sec2 - which is in units of acceleration.
Thus: g = W/m = 9.8 m/sec2 (on Earth in a vacuum)
So one way to look at the constant acceleration of all objects on Earth due to gravity is that the ratio of their weight to their mass is always the same. But there is a slightly deeper way to look at it: in the context of the gravitational force field.
Very roughly speaking, the gravity field of the Earth distorts space around the planet in such a manner that any object with mass placed into this field will experience a force of interaction (weight, in this case). To quantify the gravity field of the Earth, we need to look at Newton's Universal Law of Gravitation, which generalized gravity forces as follows:
F = -GMm/r2
Where F is the force of gravity (weight), G is the universal gravitational constant (as determined by the Cavendish experiment to be 6.67x10-11 Nm2/kg2), M is the mass of the object creating the field (for Earth M = 5.98x1024 kg), m is the mass of the object (doesn't matter - you'll see why not), r is the distance from the center of the object to the point in the field (for Earth's surface r = 6.37x106 m), and the minus sign (-) simply indicates the direction of the force (down).
If you want to calculate the gravitational field at the surface of the Earth, you must note that this quantity is independent of the mass (m) of the object on the surface (as per our definitions above). Thus, we divide out m...
F/m = -GM/r2
Now, if you grab a calculator and crunch the numbers outlined in the previous paragraph, you will get a very interesting result for the strength of the gravitational field on the Earth's surface.
F/m = -9.8 m/sec2
Which is what we called the "acceleration due to gravity" earlier. It ends up that in the case of gravity, as viewed through classical Newtonian mechanics, the terms "acceleration" and "field" are synonymous. I did the calculation assuming we're on the Earth's surface, but you could apply the equations anywhere.
So, to conclude, if we observe (as seen in many experiments and the video footage from the Moon) that objects in free-fall accelerate at the same rate, regardless of their weights or masses, then we can also conclude that the gravitational field in which these objects are located is also the same for all objects within that field.
To sum up:
1. Weights (forces of gravity) can vary from object to object.
2. Masses (measures of inertia) can also vary from object to object.
3. g (acceleration due to gravity) for all objects is the same, because the ratio W/m is constant for all objects.
4. g can also be expressed as the "gravitational field" and is synonymous with acceleration due to gravity. Thus, it is also independent of the mass of the objects.
If you've read this far, kudos to you.
If you actually worked out the calculations for yourself, you get a gold star!
Now... any questions?
ETA: I'm going to go have a drink and read up on the Eotvos experiment, as I have to prep for an introductory lecture on general relativity tomorrow. Phew!
PS: My apologies to Scott1972 - I was typing all this out (it took me 30 minutes) after you'd posted and I didn't see your post.
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Reality Check
Penultimate Amazing
What is strange about how they form?
MattusMaximus,
Thanks for the post. You added a lot of details that are helpful that I left out.
It really seems to me that Jerome's complaint is that nature isn't acting the way that he or she believes it should. If that is not the case I can only scratch my head.
Thanks for the post. You added a lot of details that are helpful that I left out.
It really seems to me that Jerome's complaint is that nature isn't acting the way that he or she believes it should. If that is not the case I can only scratch my head.
MattusMaximus
Intellectual Gladiator
- Joined
- Jan 26, 2006
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You're welcome
Well, to be fair to him, once I got past his belligerent attitude, I could see part of the trouble. He's basically got the same misconceptions about mechanics that almost all of my students have walking into my classroom (and I mean both high school and college). He's essentially mixing up his definitions, using them completely out of context, and I'm not sure he even knows it - hence my long post in outlining everything in detail.
But, if he does know what he's doing, and he still insists upon doing it, then...
KingMerv00
Penultimate Amazing
Okay, settle down everyone! I'm seeing entirely too many misconceptions in basic mechanics being slung around here! And, as a physics teacher, it's pissing me off
I knew it was only a matter of time until someone snapped and opened a can of physics on this thread. Glad to see it done.
Well, before we get to that, we need a clear understanding, that we can agree on, of exactly how our current theory describes the process.
We could use Wikipedia, or we could have one of our esteemed members explain it. What we need, and this would be both scientific and educational, is a description of how a star turns into a black hole. It might be best to ignore the supermassive black holes that are thought to be at the center of most Galaxies.
Lets look at an ordinary black hole.
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The problem with the Wikipedia article, is that it doesn't have a simple description of how they form. I did some searching, and there doesn't seem to be a good description of the process. Considering the topic, that might be a good starting point, especially if you are trying to convince somebody they exist.
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MattusMaximus
Intellectual Gladiator
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KingMerv00
Penultimate Amazing
Well I'm no expert but it seems simple enough that one doesn't have to be an expert to understand the formation of a black hole.
Two primary forces exist in a star. The inward force of gravity and the outward force of the continuous explosion. While the star is stable, these forces are balanced. After enough time passes, the fuel runs out and the outward force of the star decreases but the gravitational force stays more or less constant. The star self compresses.
If the radius is small enough and the mass is great enough, the escape velocity becomes greater than the speed of light.