Deriving an Equation from a graph

[Murdoc88]

Homework Statement

Hello everyone,

I'm in need of some assistance in regards to deriving an equation from a graph. I have been tasked to graph information which I've collected through experimentation and then write an equation to represent the graph.

1 Plot a graph of centripetal force versus frequency ( frequency is the independent variable)

2 Using graphical analysis, rearrange the values of the frequency until a linear plot is obtained. Include a table of values.

3 Write a proportionality statement (in words) relating the centripetal force and frequency

4 write the equation relating centripetal force and frequency, inclued the value of the constant and units.

5 using the eq^, determine the force (including units and direction) required to maintain a stoppers (item swung) of the same mass in a horizontal circle of radius 1.0 m with a frequency of 6 Hz. a complete solution is required

I'm stuck at steps 3 and 4 and I am not really sure on how to approach the questions. I know that I have a power graph and if I square the frequencies that I obtained I come to a linear graph.

Here is a direct link to the graphs that I've made:

http://s7.photobucket.com/albums/y266/murdoc8888888/?action=view&current=hmwrk2.jpg

Homework Equations

$Fc=(mv^2)/r$

$f= 1 / T$

The Attempt at a Solution

I'm not exactly sure on how to derive an equation from curved graph at all, the linear graph though is simple.

(Y2 - Y1) / (X2 - X1)

is the equation to find slope and from there I would use 'y' intercept form and derive that equation.

I don't know how to do this with a power graph though.

 

[Hootenanny]

Firstly, you only need to derive an equation from linear graph (the one with the straight line), not the curved one. So looking at you graph, you have a (roughly :s) straight line when you plot F_c vs. f² and therefore you can say that that F_c$\propto$f². Now, you should be able to write an expression with a constant of proportionality, and what is the general expression for a straight line...?

 

[Murdoc88]

Well the general expression for a straight line is Ax + By + C = 0, or y = mx + b.I know it's a very rough linear graph but my teacher only wants the use of whole numbers such as 2 or 3 rather than decimals as exponents. So from here how would I write the proportionality statement of Fc$\propto$f^2 using the equation of the linear graph?

Fc$\propto$f^2 if I remember correctly, becomes an equation such as $Fc = Kf^2$ where K is a constant. Is this true?

P.S. I'm new to the latex system so please bare with me ...

 

[drpizza]

Well, on your straight line graph, what is represented by "y" in y=mx+b?
What is represented by "x" in y=mx+b?

 

[Murdoc88]

y is the same as f (x) where f is centripetal force, and x represents frequency. So could I then say that Fc(frequency) = mx + b ? or am I missing something here?

 

[Murdoc88]

I was just wondering if my logic is correct.

 

[Hootenanny]

Your very close but not quite there. What did you plot on your linear graph? Did you really plot F_c vs. f, or did you plot F_c vs. f²...?

 

[Murdoc88]

Alright,

$Fc v f^2$ becomes an equation when you add a constant. I'll make it 'k', would 'k' then represent the slope of the linear line?

$Fc = kf^2$ ?

 

[Hootenanny]

Looks good to me . Depending on your data you may have to add in a constant (which would be the y-axis intercept + C), but this constant would be due to the standard error of your data. And yes k would represent the gradient of the line, if you have a proper line fitting program I would use that, but failing that excel does a reasonable job of plotting lines of bet fit.

P.S. What is your academic level?

 

[Murdoc88]

I'm not sure what you mean academic level. I'm currently a senior student in high school.

 

[Hootenanny]

Then my guess would be the line of best fit drawn by excel would be sufficient for High School level, but it might be worth checking with your teacher.

 

[Murdoc88]

I see I see,

Nope my teacher won't accept excel, it needs to be hand drawn.

Thanks for the help!

 

[Hootenanny]

I see I see,

Nope my teacher won't accept excel, it needs to be hand drawn.

Thanks for the help!

Ahh, the fun of hand plotting graphs It was a pleasure