1kg mass = 1kg weight?

[isaac]

1kg mass = 1kg weight?
Where's the proof?
If in the gravitational field of the Earth a mass weighs 1 kg (weight), then in the gravitational field of that mass the Earth weighs the same 1 kg (weight)! What is the mass of the Earth, and what is the mass that weighs 1 kg of weight?
The gravitational force is the sum of the forces in those two gravitational fields:
The total gravitational force FG between two gravitational fields is 2 kg (weight).
FG = 1 kg + 1 kg = 2 kg (weight) = 2 * 9.81 N
While our convention for the relationship between weight and mass says:
FG = 1 kg mass * 9.81 m/(s^2) = 9.81 N = 1 kg weight (free fall - g - relative acceleration!)
Physicists today claim: "1 kg of mass = 1 kg of weight," as if it were some natural law ?!

The above convention was adopted without prior definition of what is mass and what is weight!
The concept of relative and absolute acceleration in the gravitational field is also not defined!
When a mass is at rest (on scale), it is acted upon by an absolute acceleration a!
Absolute acceleration a is equal to half of the relative acceleration g!
FG/2 = 1kg weight * relative acceleration (on scale)
How does the scale weigh 1 kg of weight?
The gravitational force of 2 kg weight is divided into the force of 1 kg weight in the center of gravity of the scale and 1 kg weight of the mass we are weighing!
Therefore, only the relative acceleration g/2 acts on the mass at rest!
Therefore it will be:
m * a = 1 kg (weight)
a = g/2
m * g/2 = 1 kg (weight)
m * g = 2 kg (weight)
that is, our convention for the ratio of mass to weight should be:
m * g/2 = 1 kg (weight)
m/2 * g = 1 kg (weight) = 9.81 N
From here Newton's second law would be (w = weight, m = mass):
w/2 * g = m * g ,
w/2 = m ,
whence the ratio of the actual mass m to the weight w is equal to:
w/m = 2/1 (1 kg of weight = 1/2 kg of mass),(weight and mass are not equal and are not the same!)
therefore Newton's Law of Force should be corrected to F = w/2 * a , if the mass is entered using the weight w. In calculations where mass is calculated, all weights should be divided by two to get the correct masses!
Where is the mistake?
 

Dear OceanBreeze, thank you for replying to my post, but I don't think you understood it at all. You might have understood my question more easily if I had used an equivalence sign instead of an equals sign, but that wouldn't have changed my question. You say: "In science ... we work with tested and verified theory", but you haven't cited a single experiment that confirms that the convention "1 kg mass = 1 kg weight" is correct.
You accuse me of confusing mass and weight. So how is it even possible to confuse this when every body has mass, and every mass has weight? So how can this fact be "outside of science and engineering"? Every person who steps on a scale has both mass and weight. The fact that we are free to "measure" mass in everyday speech either by a kilogram of mass or by the equivalent weight of that mass (depending on the calibration of the scale on our measuring device) does not mean that we have confused anything. Newton didn't confuse anything either when he said: "Force = mass times acceleration".
My question that you didn't understand is: "What is the mass and what is the acceleration in Newton's force equation if the Force is equal to 9.81 N?"
Every body freely falls to Earth with the same acceleration regardless of mass (all bodies fall at the same speed). This fact was experimentally demonstrated to us by Galileo. In addition to this fact, Galileo also introduced the concept of "relativity" into physics. Galileo says: if two bodies move towards each other at a certain speed, the speed that we measure relative to one of these bodies is the relative speed, while the actual absolute speeds can be any. We can say the same for acceleration. The acceleration of free fall is therefore relative acceleration and is the same for all masses! Relative speed and relative acceleration are apparent speeds and accelerations. What makes masses perceptibly different from each other is their weights. If we measure a relative acceleration of g = 9.81 m/s^2 between two masses of equal weight, then each mass contributes g/2 to this interaction, which is the amount of absolute acceleration in the gravitational field of each of the masses.
It is not at all gibberish to say that in the gravitational field of the Earth a mass weighs 9.81 N, and it is also not gibberish to say that then the Earth in the gravitational field of that mass also weighs 9.81 N. The total gravitational force between these two fields is 2*9.81 N! If we include this result in Newton's equation of force for a unit mass, we will get that:
9.81 N = (m)(g/2) = (m/2)g
If m = 1 kg mass then it is
9.81 N = 1 kg weight = (1/2) kg mass * g , or
2*9.81 N = 2 kg weight = 1 kg mass x g

Conclusion: Gravitational force on the Earth's surface of 9.81 N is given by a mass of (1/2) kg!

Therefore, OceanBreeze, please re-read what I wrote, as well as what you wrote and "defined"! Greetings!
 

Edited March 20 by isaac
reply

[OceanBreeze]

1kg mass = 1kg weight?

Not in Physics or Engineering!

Only in the home, or in most commerce, loads are usually expressed in kilograms by custom. As a marine engineer, when a ship is taking on a load expressed in kilograms, it must be  converted into force units( 1 kilogram = 9.8 Newtons ). All ship design work is done in Newtons. Only by using Newtons can the marine engineer know if the load is within the ship’s design parameters.

Where's the proof?

What exactly would you like to see proved? Remember, in science there are no absolute proofs; we work with tested and verified theory.

If in the gravitational field of the Earth a mass weighs 1 kg (weight), then in the gravitational field of that mass the Earth weighs the same 1 kg (weight)! What is the mass of the Earth, and what is the mass that weighs 1 kg of weight?

You are mixing up mass and weight. As I already mentioned, this is customary outside of science and engineering. This is a Science Forum so you should use the proper scientific definitions:

Mass is the quantity of matter possessed by a body and is proportional to the volume and density of that body. The basic unit of mass is the kilogram. The kilogram can be defined in terms of a fixed value of the Planck constant, h, plus the existing definitions of the meter and the second.

Weight of a body is the gravitational force on the mass of that body; usually the force of gravitational attraction exerted on the body by the Earth. The basic unit of weight is the Newton, which is a unit of Force.

Calculation of the weight of a one kilogram mass on the surface of the Earth:

Weight is a Force. Near the Earth’s surface:   Weight [N] = Mass [Kg]  X  g [9.8 m/s^2]

Where g is the Earth’s acceleration = GMe/r^2

G is the gravitational constant = 6.67E-11, Me = Earth's mass 5.98E24 kg, r = Earth’s radius 6.37E6 m

A one kilogram mass near the surface of the Earth weighs 9.81 Newtons.

Now reverse the calculation and calculate the weight of the Earth on a one kilogram mass:

Weight [N] = Mass [Kg]  X  g [9.8 m/s^2]

Me X Gm/r^2 = 9.81 Newtons   Me is Earth’s mass, m is the mass of the one kilogram object.

Confirming Newton’s Third Law: Forces always exist in pairs in such a way that if body A exerts a force on body B, then body B exerts an equal force on body A, with these forces being in opposite directions.

One caveat to keep in mind; the distance between the 1 kg mass and the Earth is always the radius of the Earth, so r is the same in both calculations.

The below in brackets is gibberish and I will not respond to such:

[The gravitational force is the sum of the forces in those two gravitational fields:

The total gravitational force FG between two gravitational fields is 2 kg (weight).

FG = 1 kg + 1 kg = 2 kg (weight) = 2 * 9.81 N

While our convention for the relationship between weight and mass says:

FG = 1 kg mass * 9.81 kg(m^-1)(s^-2) = 9.81 N = 1 kg weight (free fall – g – relative acceleration!)]

Physicists today claim: “1 kg of mass = 1 kg of weight,” as if it were some natural law ?!

Physicists claim no such thing.

More gibberish follows:

[The above convention was adopted without prior definition of what is mass and what is weight!

The concept of relative and absolute acceleration in the gravitational field is also not defined!

When a mass is at rest (on scale), it is acted upon by an absolute acceleration a!

Absolute acceleration a is equal to half of the relative acceleration g!

FG/2 = 1kg weight * relative acceleration (on scale)]

 

How does the scale weigh 1 kg of weight?

Finally, a reasonable question! The scale indicates 1 Kg of “weight” because that is how the dial and spring are calibrated because most people are accustomed to having their “weight” expressed in kilograms. This is technically incorrect but it is far enough outside the field of Physics and Engineering that it has become an acceptable custom.

You will never catch a marine engineer designing the hull of a ship based on kilograms of force! (At least I hope not!) Designers use Newtons for force and Kilograms for mass.

Warning, more gibberish follows:

[The gravitational force of 2 kg weight is divided into the force of 1 kg weight in the center of gravity of the scale and 1 kg weight of the mass we are weighing!

Therefore, only the relative acceleration g/2 acts on the mass at rest!

Therefore it will be:

m * a = 1 kg (weight)

a = g/2

m * g/2 = 1 kg (weight)

m * g = 2 kg (weight)

that is, our convention for the ratio of mass to weight should be:

m * g/2 = 1 kg (weight)

m/2 * g = 1 kg (weight) = 9.81 N

From here Newton’s second law would be (w = weight, m = mass):

w/2 * g = m * g ,

w/2 = m ,

whence the ratio of the actual mass m to the weight w is equal to:

w/m = 2/1 (1 kg of weight = ½ kg of mass),(weight and mass are not equal and are not the same!)

therefore Newton’s Law of Force should be corrected to F = w/2 * a , if the mass is entered using the weight w. In calculations where mass is calculated, all weights should be divided by two to get the correct masses!]

Where is the mistake?

In my opinion, your biggest mistake is questioning Newton’s Laws without first trying to understand them. I do admit that the unfortunate popular custom of expressing weight in kilograms is confusing. However, most people are not scientifically or mathematically literate enough to know that this is wrong and their weight should be expressed in Newtons.