Gravity as Tension

[Sovereign]

Since force is dynamic I've been wondering why gravity is called a force.

 

Something like:

F = ma <---dynamic since it involves acceleration

F = GMm/R² <---static since no motion is involved

 

Shouldn't it be:

Tension = GMm/R²

[ydoaPs]

But there is acceleration with gravity. [math]a=G\frac{m}{r^2}[/math]

 

There is no motion(assuming you're talking about objects resting on the Earth's surface) because of the normal force that is exerted on the object by the Earth.

[Sovereign]

But there is acceleration with gravity. [math]a=G\frac{m}{r^2}[/math]

 

There is no motion(assuming you're talking about objects resting on the Earth's surface) because of the normal force that is exerted on the object by the Earth.

 

So a(acceleration?) = G(universal gravitational constant?) times m(mass?) divided by r^2(radius?)

 

None of those terms involve motion.

[ydoaPs]

So a(acceleration?) = G(universal gravitational constant?) times m(mass?) divided by r^2(radius?)

 

None of those terms involve motion.

 

You do know that [math]a=\frac{d}{dt}v[/math], right? How does that not involve motion?

[Sovereign]

You do know that [math]a=\frac{d}{dt}v[/math], right? How does that not involve motion?

 

Is acceleration not the change in velocity over time? If nothing is moving then there is no acceleration.

[Cap'n Refsmmat]

[math]a=G\frac{m}{r^2}[/math] is the equation for free-fall acceleration due to gravity. It tells you what the acceleration would be given nothing in the way.

 

If there is something in the way, it exerts a force on you to stop you.

[ydoaPs]

Is acceleration not the change in velocity over time? If nothing is moving then there is no acceleration.

 

If nothing is moving, the acceleration due to gravity is canceled by another acceleration. [math]\sum{F}=m\sum{a}[/math]

 

Zero net force means zero acceleration.

[mooeypoo]

Since force is dynamic I've been wondering why gravity is called a force.

 

Something like:

F = ma <---dynamic since it involves acceleration

F = GMm/R² <---static since no motion is involved

 

Shouldn't it be:

Tension = GMm/R²

[math]\frac{GMm}{r^2}[/math] is not static at all... why do you define it as static?

 

In fact, this is the gravitational force between two bodies. If two bodies are otherwise-unaffected in space (rare situation, if any), they will attract one another with a force that is explained through the above equation.

 

If they are, indeed, unaffected by any other force that might negate this (above) force, they *will* move.

 

For example, this is the basis for the plan on diverting asteroids that may result in potentially disastrous impacts. The plan states that all we need to do is send a relatively heavy object *NEAR* the asteroid, and if it is there long enough, then the mere effect of gravity alone (that equation above) will divert it enough to miss the earth.

 

http://calitreview.com/1714

 

Check out the part about "Gravity Tug", it's really cool. BTW, that book is *awesome*.

 

~moo

[Sovereign]

[math]\frac{GMm}{r^2}[/math] is not static at all... why do you define it as static?

 

In fact, this is the gravitational force between two bodies. If two bodies are otherwise-unaffected in space (rare situation, if any), they will attract one another with a force that is explained through the above equation.

 

If they are, indeed, unaffected by any other force that might negate this (above) force, they *will* move.

 

For example, this is the basis for the plan on diverting asteroids that may result in potentially disastrous impacts. The plan states that all we need to do is send a relatively heavy object *NEAR* the asteroid, and if it is there long enough, then the mere effect of gravity alone (that equation above) will divert it enough to miss the earth.

 

http://calitreview.com/1714

 

Check out the part about "Gravity Tug", it's really cool. BTW, that book is *awesome*.

 

~moo

 

I define it as static since there is no motion involved.

[D H]

What ever gives you the idea motion is not involved? Hint: Step off of the roof of a six story building.

 

You are forgetting a basic mathematical precept here: if a=b and b=c then a=c. Newton's second law defines a force in terms of what a force does: F=ma. It does not say a thing about what a force is. Newton's third law doesn't even do that: It just says forces come in equal-but-opposite pairs, each operating on a different body. Newton's law of gravity defines one kind of force, the gravitational force. There are other forces, including some that are functions of position only (e.g., the electrostatic force).

[Sovereign]

What ever gives you the idea motion is not involved? Hint: Step off of the roof of a six story building.

 

You are forgetting a basic mathematical precept here: if a=b and b=c then a=c. Newton's second law defines a force in terms of what a force does: F=ma. It does not say a thing about what a force is. Newton's third law doesn't even do that: It just says forces come in equal-but-opposite pairs, each operating on a different body. Newton's law of gravity defines one kind of force, the gravitational force. There are other forces, including some that are functions of position only (e.g., the electrostatic force).

 

Maybe I'm missing something here but I don't see how mass is motion, or how distance is motion, or how the gravitational constant is motion.

[D H]

What you are missing is transitivity. I'll spell it out for you.

1. 
    
   
2. [math]F=ma[/math] Newton's second law.
    
    
   
3. [math]F=\frac{GMm}{r^2}[/math] Newton's law of gravitation.
    
    
   
4. [math]ma=\frac{GMm}{r^2}[/math] Transitivity.
    
    
   
5. [math]a=\frac{GM}{r^2}[/math] Divide both sides by m.
    
    
   
6. [math]a=\frac{d^{\,2}r}{dt^2}[/math] Definition of acceleration.
    
    
   
7. [math]\frac{d^{\,2}r}{dt^2} = \frac{GM}{r^2}[/math] Transitivity again.

 

Step 6 is a second order differential equation relating how distance changes over time: Motion.

[Sovereign]

Scratch that it just dawned on me.

Edited December 31, 2008 by Sovereign

[mooeypoo]

Please explain how [math]\frac{GM}{r^2}[/math] involves motion.

AGAIN

 

[math]a=\frac{d^{\,2}r}{dt^2}= \frac{GM}{r^2}[/math]

 

a is acceleration. Acceleration is the change of velocity per unit time -- obviously related to movement, since velocity is movement and acceleration is movement.

 

Maybe it will be easier if you think of it this way:

 

The acceleration close to the Earth's surface is g. Approximately 9.8 m/s^2 . F=ma will be F=mg

 

In *LARGER* scales, it isn't g anymore, it is [math]\frac{GM}{r^2}[/math]-- still involves movement. It's a value of the rate of change.

 

The *DEFINITION* of this equation is movement.

 

Rate of change of speed == acceleration == a == [math]\frac{GM}{r^2}[/math]

Edited December 31, 2008 by Cap'n Refsmmat

[Sovereign]

What you are missing is transitivity. I'll spell it out for you.

1. 
    
   
2. [math]F=ma[/math] Newton's second law.
    
    
   
3. [math]F=\frac{GMm}{r^2}[/math] Newton's law of gravitation.
    
    
   
4. [math]ma=\frac{GMm}{r^2}[/math] Transitivity.
    
    
   
5. [math]a=\frac{GM}{r^2}[/math] Divide both sides by m.
    
    
   
6. [math]a=\frac{d^{\,2}r}{dt^2}[/math] Definition of acceleration.
    
    
   
7. [math]\frac{d^{\,2}r}{dt^2} = \frac{GM}{r^2}[/math] Transitivity again.

 

Step 6 is a second order differential equation relating how distance changes over time: Motion.

 

I think I see now, the distance in Newton's Second Law is the distance-traveled by one object(dynamic, like a movie), while the distance in Newton's Gravitational Equation is the distance between two objects(static like a photo).

[mooeypoo]

Sovereign, the equation signifies the VALUE OF THE FORCE APPLIED.

 

Here's the application of it. Assume you have two objects, one of mass 2kg and another of mass 10kg (for the sake of simplicity, we are ignoring ANY other forces, and assume we're in "the middle of space" -- so there's no gravity from the surface of the earth).

 

The equation above states that the force that attracts both masses is proportional to the distance between them.

 

When they are 10,000 meters apart, the attractive force between them is:

[math]F=\frac{GMm}{r^2}=F=\frac{G*2*10}{(10,000)^2}[/math]

 

But that means that there's a POSITIVE *attractive* force between the two objects. So, they will *move* (because of the existence of the force), and the distance will become smaller.

As the distance becomes smaller, the force changes too. If we look at the force when the two objects are 500m away, then the force between them will be:

[math]F=\frac{GMm}{r^2}=F=\frac{G*2*10}{(500)^2}[/math]

Smaller force, but the force is still existing, so thre will be acceleration.

 

 

Even though the force equation itself has no "intuitive" indication of movement, it REPRESENTS movement. It is *not* static.

 

** G=6.67*10^-11 http://en.wikipedia.org/wiki/Gravitational_constant

 

And it might help you to read some basics about what a force *is* and *isn't*: http://en.wikipedia.org/wiki/Force#Newtonian_mechanics

[Klaynos]

Mod note: absolute1's posts and replies have been moved here

[Sovereign]

Sovereign, the equation signifies the VALUE OF THE FORCE APPLIED.

 

Here's the application of it. Assume you have two objects, one of mass 2kg and another of mass 10kg (for the sake of simplicity, we are ignoring ANY other forces, and assume we're in "the middle of space" -- so there's no gravity from the surface of the earth).

 

The equation above states that the force that attracts both masses is proportional to the distance between them.

 

When they are 10,000 meters apart, the attractive force between them is:

[math]F=\frac{GMm}{r^2}=F=\frac{G*2*10}{(10,000)^2}[/math]

 

But that means that there's a POSITIVE *attractive* force between the two objects. So, they will *move* (because of the existence of the force), and the distance will become smaller.

As the distance becomes smaller, the force changes too. If we look at the force when the two objects are 500m away, then the force between them will be:

[math]F=\frac{GMm}{r^2}=F=\frac{G*2*10}{(500)^2}[/math]

Smaller force, but the force is still existing, so thre will be acceleration.

 

 

Even though the force equation itself has no "intuitive" indication of movement, it REPRESENTS movement. It is *not* static.

 

** G=6.67*10^-11 http://en.wikipedia.org/wiki/Gravitational_constant

 

And it might help you to read some basics about what a force *is* and *isn't*: http://en.wikipedia.org/wiki/Force#Newtonian_mechanics

 

How does the equation represent movement if non of it's terms involve movement?

[Cap'n Refsmmat]

It represents force. And force, unless opposed, can create movement. It is not movement by itself.

[mooeypoo]

Because it represents a snapshot of the situation. What is the MOMENTARY distance (as the distance changes).

 

The term is *defined* as a momentary "snapshot", by the double-derivative (see D H's post about it). It's as if you are taking a pictures in rapid-succession of something moving, then you look at each one - you can *predict* the distance between those two bodies using this equation.

 

For that matter, if you integrate this equation in terms of t (hence, you are now moving from a "double derivative" to a "single derivative") it will represent *VELOCITY* (as opposed to momentary distance), and will have both distance *and* time.

[Cap'n Refsmmat]

You are making this far more complicated than it is, I think.

 

Force isn't motion. It's something that can cause motion, but it isn't motion.

[mooeypoo]

Also, tension, too, is only static when the net force is zero.

Otherwise, there's acceleration (like in any other force), and therefore movement.

 

So even the definition of tension as static is not very accurate and might add to your confusion.

[Cap'n Refsmmat]

But force doesn't represent movement -- it merely can cause it. Much in the same way that acceleration isn't velocity -- it merely implies a change in velocity.

[mooeypoo]

Indeed, you're right, point taken.

 

When I said "represent", I meant what the formula represents, not the force. You're absolutely right.

[czimborbryan]

I think gravity is the result of a variation of time. The variation of time creates movement which causes movement toward a mass and is perceived as a seperate force from time. This is why I say it's time/gravity.