How to show that Nkg-1 and ms-2 are equivalent to each other?

AlistairOvereem

Just studying mass and force at the moment.

my book says the two quantities are linked by the following equation:

W=mg

W is weight (N)
M is mass (kg)
g is gravitational field strength (Nkg-1)


g is 9.81 Nkg-1.however sometimes g is quotes as 9.81 ms-2. This is the acceleration of free fall and is the acceleration of an object falling freely towards the earth without any air resistance.

Question: show that the units Nkg-1 and ms-2 are equivalent to each other.


so basically the book states that they are both equivalent but then asks me to prove it? how would i do this?

Thanks

Delphi91

Use the equation derived from Netwon's Second law, i.e.[latex]F=m a[/latex]

If you re-arrange this, you get

[latex] \displaystyle a=\frac{F}{m}[/latex]

Putting in units on the right hand side gives [latex] a=\frac {N}{kg}[/latex] or [latex] a=N kg^{-1}[/latex].(*)

Now, from the original equation [latex]\displaystyle F=m a[/latex], putting in units on each side you get [latex]\displaystyle N=kg ms^{-2}[/latex]

Use this fact to replace [latex]N[/latex] in (*).

This gives
[latex]\displaystyle a=(kg ms^{-2})(kg^{-1})[/latex]

Therefore [latex] a = ms^{-2}[/latex]

This shows that you can get [latex]a=ms^{-2}[/latex] from [latex]a=N kg^{-1}[/latex].


Hope this helps?

p.s. - Apologies for the fact that some of the latex seems to be in "superscript" mode