# Technical system of units

1. Aug 28, 2014

### Karol

1. The problem statement, all variables and given/known data
The specific mass of iron doesn´t seem right in the technical system.
I know the weight of 1[m3] steel is about 8 tons.

2. Relevant 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

3. 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

2. Aug 28, 2014

### PhanthomJay

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.

3. Aug 29, 2014

### 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?

4. Aug 29, 2014

### PhanthomJay

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.

5. Aug 29, 2014

### Karol

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

6. Aug 31, 2014

### PhanthomJay

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.