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I am confusing about some data for calculus.
First, the equivalence of weight: 1kgf=9.8N
Second, the mass of 1 Newton is: 1N/(9.8m/s$^2$).
And finally, to get the mass of 1kgf, I have to divide by the gravity.
An example of a weight of P=10N:
P=10N$\cfrac{\text{1kgf}}{9.8N}\approx1$kgf; its mass: $m=\cfrac{P}{g}=\cfrac{1kgf}{9.8m/s^2}\approx0.1kg$
While, directly from Newtons: $m=\cfrac{10N}{9.8m/s^2}\approx1kg$
What I am doing wrong?
Pay attention to the units. There is no such unit in the SI system as kgf. kg is mass, in kilograms. Force is Newtons. Acceleration is m/s^2. The three variables are tied together with Newton's 2nd Law, which is F=ma.
Having said that, weight is the force that gravity exerts on an object, and is defined by the equation W=mg, where W takes the place of F, and g takes the place of a, in Newton's 2nd Law.
Now, in case I haven't answered the question, take the units of g, and multiply them by kg/kg, which gives an answer of g=9.8kg-m/(s^2-kg). Since a Newton has units of kg-m/s^2 (from the units of F=ma), this means that g also has units of N/kg. So, from your last calculation, solving Newton's 2nd Law for mass yields m=F/a, which for a 1 kg mass yields 9.8N/(9.8N/kg).
