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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?

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  • $\begingroup$ It's the units. Dividing $kgf$ by $m/s^2$ doesn't give you $kg$. $\endgroup$ – Dawood ibn Kareem Aug 4 '16 at 23:15
  • $\begingroup$ I am confused. What happened if I weight 70 kg, I must say 70kgf? I mean, to get my mass, I have to divide my weight by the gravity. What is wrong? $\endgroup$ – Isai Aug 4 '16 at 23:28
  • $\begingroup$ OK, how about if I tell you that gravity is $1 kgf / kg$. Does that help? $\endgroup$ – Dawood ibn Kareem Aug 4 '16 at 23:31
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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).

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  • $\begingroup$ Yes, thanks. I found this in Wikipedia: $1 kp=1 kgf=g_n⋅(1 kg)$. So, in my problem, I must say: $m=\cfrac{P}{g_n}=\cfrac{1 kgf}{g_n}=\cfrac{1 ·g_n⋅(1 kg)}{g_n}=1 kg$ $\endgroup$ – Isai Aug 5 '16 at 15:27

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