G-Force: Understanding the Difference Between Force and Acceleration

[Archosaur]

What exactly is a "g"?

I've heard it used to describe the force of gravity, and the acceleration due to gravity. It surely can't be both.

Sitting here in my chair, I am not accelerating. Am I experiencing 1g (force) or 0g (acceleration)?

What about a spinning space station, far enough away that Earth's gravity is negligible, but spinning fast enough to simulate gravity (9.8 m/s^2 at the outer wall). Are the astronauts, standing on this wall, experiencing 1g (acceleration) or 0g (force)?

 

[Naty1]

I've heard it used to describe the force of gravity, and the acceleration due to gravity. It surely can't be both.

Sitting here in my chair, I am not accelerating. Am I experiencing 1g (force) or 0g (acceleration)?

get ready for a bevy of confusing answers...this takes a while to sort thru...if you search you'll find lots of similar posts and threads which might help...

Newton's approximate theory describes gravity as an instantaneous force...a very good approximation...Einstein's more sophisticated and more accurate general relativity describes it as a curvature of space and time...but neither is the final explanation...because even GR breaks down at the big bang and inside black holes...

You are 'attracted' to Earth via "g" forces...you might accelerate, as when you step off a high ladder...otherwise you stayed fixed because your feet are pressed against the floor and feel the 'force" of gravity...
Netwon would say you are accelerating when you free fall...say when you jump out of a plane without a parachuite...Einstein would say you feel no forces so you don't accelerate...it's all "relative"...

Einstein also pointed out there is a very close relationship between acceleration and gravity..his 'equivalence principle' says they are pretty much indistinguishable...try wikipedia

 

[D H]

I've heard it used to describe the force of gravity, and the acceleration due to gravity. It surely can't be both.

To answer the question raised by the title of this thread, g = 9.80665 m/s², exactly. This has units of acceleration, so it obviously is not a force.

Ignoring air resistance and local variations in gravity due to terrain, this is the acceleration that would be observed in a falling object by someone located at sea level at about 45.5 degrees latitude. Because the value is defined with respect to a rotating Earth, it includes both gravitational and centrifugal terms.

Sitting here in my chair, I am not accelerating. Am I experiencing 1g (force) or 0g (acceleration)?

Actually you are accelerating, both in Newtonian mechanics and general relativity. Newtonian mechanics point of view: You are undergoing accelerating toward the Sun and the Moon. These are fairly small, particularly so when you subtract the acceleration of the Earth as a whole toward the Sun and Moon. It's best to just ignore these for now. More importantly, from the perspective of an inertial frame, you are accelerating at R_e \cos (\text{lat})\,(2\pi/\text{sidereal day})^2 pointing toward the Earth's rotation axis (not the center of the Earth). The Earth is rotating on its axis. The upward force due to the ground does not quite cancel the downward force due to gravity. What's left is a residual force that results in this smallish acceleration.

In general relativity you are accelerating upwards at about 9.81 m/s². An accelerometer would confirm this: It would say you are accelerating upward. A falling apple is not accelerating, and an accelerometer attached to the falling apple would confirm this, too.

 

[Archosaur]

To answer the question raised by the title of this thread, g = 9.80665 m/s², exactly. This has units of acceleration, so it obviously is not a force.

This was my guess. Thank you.

Actually you are accelerating, both in Newtonian mechanics...

Right, I knew this one. I should have provided a frame of reference.

...and general relativity...
In general relativity you are accelerating upwards at about 9.81 m/s². An accelerometer would confirm this: It would say you are accelerating upward. A falling apple is not accelerating, and an accelerometer attached to the falling apple would confirm this, too.

This is bothering me. Could you point me to a thread/resource that could help me with this?
I don't want to waste time here on what has undoubtedly already been discussed.

 

[D H]

Could you point me to a thread/resource that could help me with this?
I don't want to waste time here on what has undoubtedly already been discussed.

You have asked similar questions before. https://www.physicsforums.com/showthread.php?t=292997

 

[Archosaur]

You have asked similar questions before. https://www.physicsforums.com/showthread.php?t=292997

That had to do with Newtonian physics; centrifugal forces of the revolution and rotation of the Earth around the Sun and its own axis amplifying or diminishing each other.

My question now is: how am I accelerating at 9.8 m/s^2 when I'm sitting in my chair?

 

[A.T.]

My question now is: how am I accelerating at 9.8 m/s^2 when I'm sitting in my chair?

This is the proper acceleration that you 'feel' and what an accelerometer you hold measures. It is the deviation from inertial movement (free fall) and frame invariant (absolute), unlike the relative coordinate acceleration, which is the change in velocity in some arbitrary frame of reference.

Why stationary objects in an gravitational field are accelerated is explained very well in chapter 2.6 of this:
http://www.relativitet.se/Webtheses/tes.pdf

 

[russ_watters]

My question now is: how am I accelerating at 9.8 m/s^2 when I'm sitting in my chair?

The way I like to think of it is that if g is the acceleration due to gravity, then for a stationary object on earth, f=ma (where a=g) is the force required to not accelerate due to gravity!

But it really doesn't matter either way. An object has the same gravitational force acting on it whether it is sitting still on a table or dropping from an airplane. The only difference is if there is a force opposing it to stop the acceleration.

 

[pixel01]

I've heard it used to describe the force of gravity, and the acceleration due to gravity. It surely can't be both.

Sitting here in my chair, I am not accelerating. Am I experiencing 1g (force) or 0g (acceleration)?

What about a spinning space station, far enough away that Earth's gravity is negligible, but spinning fast enough to simulate gravity (9.8 m/s^2 at the outer wall). Are the astronauts, standing on this wall, experiencing 1g (acceleration) or 0g (force)?

Gravitation exerts a force to every object in its field and if the object is free, the accelaration due to it is g.
If you sit in your chair, your acceleration is 0, but you tolerate a force and in free fall, you are under no force.
In spinning spacecraft , a man standing on the wall will experience a force, not acceleration. The only difference is the force is changing from the head to the foot if you are standing and the spacecraft is not too big.

 

[Archosaur]

Gravitation exerts a force to every object in its field and if the object is free, the accelaration due to it is g. ...in free fall, you are under no force.

Isn't this a contradiction?

In spinning spacecraft , a man standing on the wall will experience a force, not acceleration.

But he is accelerating. he is constantly changing direction, right?

 

[D H]

Isn't this a contradiction?

It's time to remind you of what Naty1 said in post #2:

get ready for a bevy of confusing answers...

In Newtonian mechanics, Newton's laws of motion are strictly valid in inertial frames only. From your perspective, at rest with respect to the surface of the Earth, the remote stars appear to be moving at much faster than the speed of light and appear to be accelerating Earthward at a fierce pace. For example, a star 100 light years distance appears to be accelerating Earthward at over 500 million g. This is because your perspective is a rotating reference frame. An alien on a planet orbiting that remote star of course feels none of this acceleration. This apparent force due to frame rotation is the centrifugal force. It is in a sense a fiction used to make Newton's second law appear to be valid in a rotating frame.

These apparent forces go by several names: Inertial forces, d'Alembert forces, pseudo forces, and fictional forces. Whatever name you want to use for them, they have two things in common:

1. The force acting on an object is proportional to the mass of the object.
2. An accelerometer cannot measure these forces.

Now look at gravity:

1. The gravitational force exerted by some massive body on an object is proportional to the mass of the object.
2. An accelerometer cannot measure the gravitational force.

In general relativity, gravitation is essentially an inertial force. Not quite real. The rationale for this view is Einstein's elevator experiment. Suppose you are in a small elevator car with no windows. You have a bevy of accelerometers, ring laser gyros, and other sensing equipment that enable you to test conditions inside the car. None of them can tell what is going on outside the care. Let's look at four cases:

1. The car is at rest on the surface of a non-rotating planet with a surface gravity of 1g.
2. The car is in orbit above this planet.
3. The car is attached to a rocket in deep, deep space (far from any pesky gravitational source). The rocket is accelerating at 1g.
4. The car is attached to a rocket in deep, deep space (far from any pesky gravitational source). The rocket's thrusters are quiescent.

You can define a reference frame with the center of the car as the origin of the frame and the car's nice orthogonal edges defining the axes of the frame. Newtonian mechanics would deem this frame to be an inertial frame in cases #1 and #4 but not in cases #2 and #3. General relativity uses a different definition of an inertial frame from that provided by Newtonian mechanics. An inertial frame in general relativity is not rotating and in which an accelerometer affixed to the frame reads zero acceleration. General relativity would deem cases #2 and #4 to be inertial, #1 and #3 to be non-inertial.

In general relativity, an object in free-fall is not accelerating (from the perspective of an inertial frame).

 

[tuoni]

A "g" is the gravitational acceleration, the standard accepted value is 9.80665 m/s^2. In reality, g changes with location and altitude.

Also, I would also like to point out that mass and weight is not the same. There are several ways you could define mass -- can quickly get complicated -- but let's use "mass is the amount of matter; where matter is a quantity that possesses space and is affected by gravity."

Mass is mass, a primary measurement, and does not "change", 1 kg on Earth is 1 kg on the moon and 1 kg a billion-gazillion-super-mega-duper lightyears away.

Weight is a force, mass times acceleration, or in this case, mass times the gravitational acceleration. However, the gravitational acceleration is implicit, you rarely go to the market and ask for "1 kg relative to the moon's gravitation" of vegetables. It is always implicit that we refer to the Earth's gravitation. You can never have weight without an acceleration, but mass is just fine.

"g" is this gravitational acceleration that is implicit when talking about weight. Mass is fine without "g" (an astronaut CANNOT be massless), but weight is not (an astronaut CAN be weightless).

Em...maybe that was a bit offtopic (and messy/incoherent) and not really relevant to "exactly what g" is...oh, well.

 

[Naty1]

As you struggle thru these ideas for the first few times, and most people struggle at first, it can be useful to get a few 'anchors' for yourself...a few rules that make sense to you and from which you begin each analysis.

for example I liked:

The way I like to think of it is that if g is the acceleration due to gravity, then for a stationary object on earth, f=ma (where a=g) is the force required to not accelerate due to gravity!

from Russ Waters.

Another possibly useful idea is "What would an accelerometer (a mechanical device)show in this circumstance?"...say free fall versus sitting in a chair vs floating in space...

 

[pixel01]

for example I liked:
from Russ Waters.

Another possibly useful idea is "What would an accelerometer (a mechanical device)show in this circumstance?"...say free fall versus sitting in a chair vs floating in space...

My thinking is quite close to this idea. Acceleration is some thing that exert inside the object. When you sit in a chair, you are immobilized, but there are forces between parts of your body and thus an accelerometer would show a value (this case is g). In free fall, you are moving at an acceleration of g, but there are no forces between and the accelarometer also show now value. When you drift in space, it's simply you are in free fall.
So if you are in a gravitational field, if you are not moving (with accelaration) you must tolerate some forces within your body and vice versa. If the moving is not at an acceleration of g (in case in the surface of the earth) but a smaller value, you have to bear 'forces' (the reading of an accelerometer) and totally the two values must equal to g.

 

[Nutterbutterz]

To answer the first question quite simply, gravity is a force, but g is the acceleration due to gravity. The force of gravity itself is measured in Newtons, measured quite differently from acceleration.

 

[dr dodge]

A "g" is the gravitational acceleration, the standard accepted value is 9.80665 m/s^2. In reality, g changes with location and altitude.

the value of 9.80665 is considered standard gravity. in actuality it varies, not only by lat/lon/alt location, it also varies by the make up of the Earth under you.
gravity varies in the us by almost 0.2%. This variation makes the use of certain test equipment interesting because the actual value must be known to get accurate measurements. Dead weight testers are one of these devices. also, gravity only gets close to 9.80665 in the north end of the country. At our facility in Houston its 9.7927783.
very close to the value in Denver, Co

dr

 

[dr dodge]

A "g" is the gravitational acceleration, the standard accepted value is 9.80665 m/s^2. In reality, g changes with location and altitude.

the value of 9.80665 is considered standard gravity. in actuality it varies, not only by lat/lon/alt location, it also varies by the make up of the Earth under you.
gravity varies in the us by almost 0.2%. This variation makes the use of certain test equipment interesting because the actual value must be known to get accurate measurements. Dead weight testers are one of these devices. also, gravity only gets close to 9.80665 in the north end of the country. At our facility in Houston its 9.7927783.
very close to the value in Denver, Co

dr