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I know that $F = mg$ so $2,00 \textrm{ KG m} \cdot 9,81 \textrm{ N g} = 19,62 \textrm{ N F}$

Why does my book say that the weight of a $2,00 \textrm{ KG}$ object is $19,62\textrm{ N}$, the mass is $2,00\textrm{ KG}$ and the gravity is also $19,62\textrm{ N}$?

$F = mg,$ so $\hspace{.1in} 2,00 \textrm{ KG m} \cdot 19,62\textrm{ N g} = \textrm{ NOT } 19,62 \textrm{ N F}$

$m = F/g$ should be 2 but this example says 1

So confused

F = Gravity in N
m = Mass in KG
g = Earths Gravity (= 9,81 N*KG-1)

I'm Dutch so my signs may be different to yours.

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    $\begingroup$ Your units are confusing me. What do you mean by "N F" and "N g"? I can tell you this: The Newton is a unit of force, and nothing else. kg is a unit of mass, and nothing else. g is the acceleration due to gravity, 9.8 N/kg or m/s^2. The phrase "the gravity is 19.62 N" is not a sentence that makes sense in physics. If your book really says that, then I would be suspicious of everything the book says! $\endgroup$
    – garyp
    Commented Nov 9, 2015 at 14:31
  • $\begingroup$ @garyp, Kg is a unit of mass and nothing else in strict scientific usage, but in every-day life, and even sometimes in engineering, the kgf is a unit of force equal to the weight of a 1 kg mass at some unspecified location somewhere close to the surface of the Earth. $\endgroup$
    – Solomon Slow
    Commented Nov 9, 2015 at 15:16
  • $\begingroup$ @Naowut, welcome to Physics.SE! Please take a look at this post which discusses formatting mathematics on the site. $\endgroup$
    – DilithiumMatrix
    Commented Nov 9, 2015 at 15:18
  • $\begingroup$ It all depends on what you mean by gravity. Owen Boyle in his answer below agrees with the book saying that gravity is a force. However, I agree with you that gravity is rather an acceleration. That is the unchanging quality of a given body as regards gravity. And that is what Einstein's equivalence principle (gravity down is undistinguishable from acceleration up) is all about. $\endgroup$
    – bright magus
    Commented Nov 9, 2015 at 15:24
  • $\begingroup$ I didn't say "gravity" was a force - I said weight has units of force. Gravity is a phenomenon that causes massive objects to experience a force that leads to an acceleration. $\endgroup$
    – Oscar Bravo
    Commented Nov 9, 2015 at 15:29

1 Answer 1

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Mass is the scientific term. It's a measure of how much inertia a body has; that is, how hard it is to push around if it was sitting floating in space. It is a fundamental quantity and has units of kilogram.

Weight is not really a scientific term. It's a common-speech term that means Force due to gravity. So strictly speaking, a weight should be in units of force, i.e., Newtons.

However, we usually express weights in kilograms as well - we simply don't bother doing the multiplication by $9.81 ms^{-2}$ to get it into Newtons. We skip this bit to keep it simple since almost all calculations are done on Earth and gravity is (practically) the same everywhere.

Getting back to your book - I don't see the problem. A 2kg mass has a weight of 19.62N and that means that the force of gravity on it is 19.62N. Be careful to realise that the "9.81" is a acceleration due to gravity - it's the rate of change of speed of any object that falls freely under gravity. If you multiply a mass by an acceleration you get a force - that's Newton's Second Law.

Post back if I haven't cleared this up...

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    $\begingroup$ Because gravity and weight are not both 19.62. g = 9.81. The "g" is the acceleration due to gravity - it's a constant value for all things. $\endgroup$
    – Oscar Bravo
    Commented Nov 9, 2015 at 14:56

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