Simon Bridge
Critical Thinker
- Joined
- Dec 27, 2005
- Messages
- 331
I've been away, excuse if this is late...
However - this is philosophically correct of forces in general. A force on an object is equal to the rate of change of it's momentum. Philosophically, the force dosn't arise from the acceleration or the other way around, it is the same thing!
When we observe acceleration, we compute the force from this. Where we wish to predict an acceleration, we compute the force first.
What a lot of people fail to realise is that the force law is a definition. You cannot, for instance, prove that F=ma.
However: gravity is a phenominon. Masses attract each other.
Gravity can be described in terms of a force-feild, and energy feild, or by assigning instantanious accelerations to points in space. It can also be described by geometric transformations on 4-space. However, it is not any of these things.
High School students of physics are taught to think of gravity in terms of a force feild. University physics students are taught to think of it in terms of an energy feild. (Engineers in terms of accelerations - while weight is in terms of masses and circular motion in terms of pseudovectors...)
The acceleration of gravitation is 9.8m/s/s at the mean radius from Earth's center of mass. However, this varies inversly as the square of the distance, where the distance is above-ground and inversly with distance as the distance is below ground. It is not a constant - make no mistake.
One can store energy in a gravitational field by doing work moving masses apart.
[derail]I have a big box and a little box. I weigh them at sea level on the Earth (using sensitive electronic balances) and discover they weigh the same. I repeat the entire experiment on the surface of the Moon. The weights are not the same - which is "heavier"?[/derail]
when the scale reads 1kg, the force is 9.8N, push a 1kg mass (weighing 9.8kg) horizontally will net you an acceleration of 9.8m/s (SI units are neet). try to push a 10kg mass with 9.8N and I get 0.1m/s/s
Weight is a force
If gravity were a force, weight would be constant
Weight is not a constant
Thus: gravity is not a force
The trouble is...
Weight = force of gravitation (being careful with my language - the force experienced by gravitating bodies)
You are saying that: if gravity were a force, then the force of gravitation would be a constant.
There are other phenomina (repulsion of like charges for eg) where the associated force is not a constant. Why should gravitation be any different?
Perhaps you feel that, as the acceleration of gravity is a constant, then the force of gravity must also be a constant? This would be consistent with the example you gave. So lets examine this:
Force of gravity: near-Earth approximation (Newton):
[latex]$F=GmM/{R^{2}}$[/latex] ...(1)
... this force is directly proportional to mass.
(Here R=Earth radius, M=Earth mass, m=mass of body under acceleration, and G=gravitational constant.)
Relationship, force and acceleration:
[latex]$F=ma$[/latex] ...(2)
... i.e. force is proportional to inertia, as well as acceleration.
If the m (gravitational mass) in (1) is the same as the m (inertial mass) in (2), as Newton asserts but Einstein says "nearly but not always", then the acceleration will be given by:
[latex]$a=GM/{R^{2}}$[/latex] ...(3)
Giving a constant acceleration from a varying force-feild. It works out this way because of the special relationship between gravitation and mass.
Under general relativity, this unusual relationship is understood in terms of geometry. Perhaps gravity is really a space-time curvature?
But really - where does this get is, vis a vis PMM?
While Newton would disagree with you there (for reference, I refer you to his Principia in the first case)...
However - this is philosophically correct of forces in general. A force on an object is equal to the rate of change of it's momentum. Philosophically, the force dosn't arise from the acceleration or the other way around, it is the same thing!
When we observe acceleration, we compute the force from this. Where we wish to predict an acceleration, we compute the force first.
What a lot of people fail to realise is that the force law is a definition. You cannot, for instance, prove that F=ma.
However: gravity is a phenominon. Masses attract each other.
Gravity can be described in terms of a force-feild, and energy feild, or by assigning instantanious accelerations to points in space. It can also be described by geometric transformations on 4-space. However, it is not any of these things.
High School students of physics are taught to think of gravity in terms of a force feild. University physics students are taught to think of it in terms of an energy feild. (Engineers in terms of accelerations - while weight is in terms of masses and circular motion in terms of pseudovectors...)
The acceleration of gravitation is 9.8m/s/s at the mean radius from Earth's center of mass. However, this varies inversly as the square of the distance, where the distance is above-ground and inversly with distance as the distance is below ground. It is not a constant - make no mistake.
One can store energy in a gravitational field by doing work moving masses apart.
Actually the "purpose" of physics is to try to figure out what is going on, and describe it in terms of physical processes... we do this by proposing models which we hope will predict the results of our experiments. We do not require the model to be "accurate", or even "true", only "useful". Though you will be aware that words like "accurate" have a specific meaning in physics.
Well - Newton treated it as a force and managed to get the orbits of comets... did he go "astray"?
Note - lbs is not a unit of force. You are an engineer I take it? Here's a puzzle:
[derail]I have a big box and a little box. I weigh them at sea level on the Earth (using sensitive electronic balances) and discover they weigh the same. I repeat the entire experiment on the surface of the Moon. The weights are not the same - which is "heavier"?[/derail]
when the scale reads 1kg, the force is 9.8N, push a 1kg mass (weighing 9.8kg) horizontally will net you an acceleration of 9.8m/s (SI units are neet). try to push a 10kg mass with 9.8N and I get 0.1m/s/s
This part bears further examination...
Weight is a force
If gravity were a force, weight would be constant
Weight is not a constant
Thus: gravity is not a force
The trouble is...
Weight = force of gravitation (being careful with my language - the force experienced by gravitating bodies)
You are saying that: if gravity were a force, then the force of gravitation would be a constant.
There are other phenomina (repulsion of like charges for eg) where the associated force is not a constant. Why should gravitation be any different?
Perhaps you feel that, as the acceleration of gravity is a constant, then the force of gravity must also be a constant? This would be consistent with the example you gave. So lets examine this:
Force of gravity: near-Earth approximation (Newton):
[latex]$F=GmM/{R^{2}}$[/latex] ...(1)
... this force is directly proportional to mass.
(Here R=Earth radius, M=Earth mass, m=mass of body under acceleration, and G=gravitational constant.)
Relationship, force and acceleration:
[latex]$F=ma$[/latex] ...(2)
... i.e. force is proportional to inertia, as well as acceleration.
If the m (gravitational mass) in (1) is the same as the m (inertial mass) in (2), as Newton asserts but Einstein says "nearly but not always", then the acceleration will be given by:
[latex]$a=GM/{R^{2}}$[/latex] ...(3)
Giving a constant acceleration from a varying force-feild. It works out this way because of the special relationship between gravitation and mass.
Under general relativity, this unusual relationship is understood in terms of geometry. Perhaps gravity is really a space-time curvature?
But really - where does this get is, vis a vis PMM?
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