Algebra Homework Help: Solving Equations with Fs^2, F/V^2, and Real Numbers

[Odyssey]

Homework Statement

If I know Fs^2 = 6*10^{-8}, and \frac{F}{V^2} = 10^{-9}, how can I figure out \frac{Fs^2}{V^2}? F, s, V are all real numbers.

Homework Equations

Fs^2 = 6*10^{-8} (equation 1)
\frac{F}{V^2} = 10^{-9}, (equation 2)
\frac{Fs^2}{V^2}

The Attempt at a Solution

I tried dividing equation 1 by equation 2 and vice versa...and mutiplied them...but the best thing I can get is \frac{F^2s^2}{V^2}...

 

[cristo]

Homework Statement

If I know Fs^2 = 6*10^{-8}, and \frac{F}{V^2} = 10^{-9}, how can I figure out \frac{Fs^2}{V^2}? F, s, V are all real numbers.

Homework Equations

Fs^2 = 6*10^{-8} (equation 1)
\frac{F}{V^2} = 10^{-9}, (equation 2)
\frac{Fs^2}{V^2}

The Attempt at a Solution

I tried dividing equation 1 by equation 2 and vice versa...and mutiplied them...but the best thing I can get is \frac{Fs^2}{V^2}...

What do you want to find out? In your first line you say you want "Fs²/V²," whereas in the last line you say the best you can get is Fs²/V². Is this not what you want?

 

[Odyssey]

oh right, sorry. I had a typo...the best I got was \frac{F^2s^2}{V^2}. Lemme correct that.

 

[coalquay404]

You have two equations. The first is

Fs^2 = 6\times 10^8

while the second is

\frac{F}{V^2} = 10^{-9}

Rearranging the second equation gives you

\frac{1}{V^2} = \frac{1}{F\times10^{-9}}

If you now multiply your first equation by this you obtain

\frac{Fs^2}{V^2} = \frac{6\times 10^8}{F\times10^{-9}}<br /> = \frac{6\times10^{17}}{F}

There's a certain redundancy here. Multiplying both sides by F gives you

\left(\frac{Fs}{V}\right)^2 = 6\times 10^{17}

Is this not what you want?

 

[Odyssey]

Hmmm not quite :\ \left(\frac{Fs}{V}\right)^2 = 6\times 10^{17} is the same as \frac{F^2s^2}{V^2}...which was what I got before...I want to get \frac{Fs^2}{V^2}...but I don't know if that's actually possible. Anyway, thanks a bunch for the help! :)

 

[Odyssey]

Going to the root of the problem, I am actually working on my lab report. I need to determine the value of the permittivity of free space from my experiment...and from my results I plotted F with V^2 and I got a linear relationship between them with a slope of 10^-9...which is the number I had up there \frac{F}{V^2} = 10^{-9}. Then I plotted F with \frac{1}{s^2} and I got another relationship...with a slope of Fs^2 = 6*10^{-8}.

My experiment is to deduce the permittivity of free space so I can eventually deduce the speed of light.

F is the attractive force between two parallel plates (capacitor). A is the area of the plate. s is the distance between the plates. V is the voltage between them. My formula I'm dealing with is F=\frac{e_{0}AV^2}{2s^2}

The lab requires me to find the "best" value of \frac{Fs^2}{V^2} ...which is where I was stuck at from the beginning. :\

From then on, once I get \frac{Fs^2}{V^2}, find the permittivity of free space and eventually the speed of light.
Thanks again for the time and effort! :)

 

[HallsofIvy]

You simply don't have enough information. If you could find \frac{Fs^2}{V^2}, since you already know Fs^2, you could divide the second by the first to find V then use \frac{F}{V^2} to find F and finally solve for s. You can't expect to be able to solve 2 equations for 3 values.

 

[Odyssey]

Hmmm...ok...I'll have to check my values again. Thanks!