Surface Tension of Water.

[gamerboy290]

I'm, doing the Measuring the Surface Tension of water experiment. I need to finish my results. I have to convert my measurments form grams into the equation F=2sd. F is the force in Newtons/gram. I convert my grams into that by mutliplying them by 9.83*10(-3) N/g. (the -3 means the negative third power.) How do I do this?
Here is th elink to the project itself. https://www.sciencebuddies.org/mentorin ... p012.shtml

[gamerboy290]

BTW, the -3 in 9.83*10(-3) is not times -3, it is to the negative third power.
Thanks

[deleted-71588]

What grade are you in?
Have you had algebra yet?

Based on your question, I'm going to assume you haven't had algebra.
The equation F = 2 s d when written with units in [] looks like:

F [N] = 2 s [N/m] d [m]

Ignoring the numbers and just dealing with the units you get:
[Newtons] = [Newtons / meter] * [meters]
and canceling units on the right hand side of the = you get
[Newtons] = [Newtons]

If you divide both sides by 2 d [m], you get:
F [N] / 2 d [m] = s [N/m]

combining units on the left hand side, you get:

(F / 2 d) [N/m] = s [N/m]

Now for converting grams to N

1 [g] = 9.83 x 10**-3 [N]

10**-3 is just the scientific notational way of writing 1/1000, so

1 [gram] = .00983 [Newtons]

If you divide both sides by .00983, you get
1/.00983 [grams] = 1 [Newton]

or
101.73 [grams] = 1 [Newton]

Combining these two equations, you get
F / 2 x 101.73 d [g/m] = s [N/m]

or
F [grams] / 203.46 d [meters] = s [Newton/meters]

Have somebody who knows algebra check mine!

[deleted-71588]

Sorry, I didn't show all the intermediate steps

101.73 [grams] = 1 [Newton]
or written as a conversion factor
1 [gram/Newton]= 1 /101.73

Combining these two equations by multiplying the left side by the conversion factor equvalent of 1, you get
(F / 2 x 101.73 d) [N/m][g/N] = s [N/m]
and simplifying units (caceling out Newtons)
(F / 2 x 101.73 d) [g/m] = s [N/m]