Why is the Conversion Factor for kg-force 0.1?

[Karol]

Homework Statement

The specific mass of iron doesn´t seem right in the technical system.
Iron is about 8[gr/cm³]
I know the weight of 1[m³] steel is about 8 tons.

Homework Equations

The definition of the kilogram-force unit in the tehnical system is the weight of a mass of 1 kilogram:
1[kgf]=>1[kg]x10

The Attempt at a Solution

`
That was the definition, now:
1[kgf]=0.1[kg-mass]x10
=>1[kg]=0.1[kg-mass]
8[gr/cm³]=8000[kg/m³]
I have to divide the mass with 10 to get gk-mass:
8000[kg/m³]=800[kg-mass/m³]
And in a book it´s written that a certain metal wire has a density of 10,300[kg-mass/m³]
So my solution is about 10 times too low

 

[PhanthomJay]

Homework Statement

The specific mass of iron doesn´t seem right in the technical system.
Iron is about 8[gr/cm³]
I know the weight of 1[m³] steel is about 8 tons.

Homework Equations

The definition of the kilogram-force unit in the tehnical system is the weight of a mass of 1 kilogram:
1[kgf]=>1[kg]x10

The Attempt at a Solution

`
That was the definition, now:
1[kgf]=0.1[kg-mass]x10
=>1[kg]=0.1[kg-mass]
8[gr/cm³]=8000[kg/m³]
I have to divide the mass with 10 to get gk-mass:
8000[kg/m³]=800[kg-mass/m³]
And in a book it´s written that a certain metal wire has a density of 10,300[kg-mass/m³]
So my solution is about 10 times too low

one kgf (which is not an SI unit) is the weight of one kg of mass on planet earth.
A kilogram of mass (designated as kg) has a weight of about 9.8 Newtons (call it 10 N) in SI units. But you are not using SI, so you are dividing by 10 when you shouldn't be.

 

[Karol]

I don´t talk about Newtons, only kg and kg-mass.
If 1[kgf]=0.1[kg-mass]x10 is correct (is it?) and with the definition of kgf, then to convert from kg-mass to kg i have to multiply by ten, no?

 

[PhanthomJay]

I don´t talk about Newtons, only kg and kg-mass.
If 1[kgf]=0.1[kg-mass]x10 is correct (is it?) and with the definition of kgf, then to convert from kg-mass to kg i have to multiply by ten, no?

No, that is not correct. A kg-mass and a kg are one and the same. If you multiply kg-mass , which is a kg, by 10 (or actually 9.8 m/sec^2, let's use 10), you get the weight of one kg in the SI unit of Newtons, on Earth.

It gets very confusing when using different systems of measure like SI, metric, technical, or Imperial units.

A kg of force is actually F = (m/g)(a), where m is in kilograms, g is 10, and a is the acceleration in m/sec^2. On Earth, when you calculate the weight of 1 kg of mass, the acceleration is g or 10 m/sec^2, so the equation becomes F = (m/g)(g), the g's cancel, so F =m. That is , one kg of mass weighs one kg of force, on Earth. The book answer is correct.

 

[Karol]

Why is F=(m/g)a? especially why (m/g)? does it come from the definition of kg-force?

 

[PhanthomJay]

Why is F=(m/g)a? especially why (m/g)? does it come from the definition of kg-force?

yes, it's a conversion factor. Another way to look at it is to rewrite Newtons 2nd Law as
F = kma and W = kmg. m is in kg and a or g is in m/s^2. If you want your force or weight in Newtons , k= 1. If you want your force or weight in kg-force, k = 0.1 (in round numbers). The kg- force unit should be avoided whenever possible.