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

$$\frac{Fs^2}{V^2} = \frac{6\times 10^8}{F\times10^{-9}} = \frac{6\times10^{17}}{F}$$

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!