What is Causing the Exponential Curve in My Velocity Squared vs. Radius Graph?

[FireLight07]

Hey--

I'm writing up a physics lab report on centripetal force; at the moment I've hit a problem with the velocity squared vs. radius graph. The graph *should* show a root curve (v^2 = Fr/m) but all of the regression utilities I've used churn out an exponential curve. Here are the four points I have:

Radius (m)
0.25
0.5
0.75
1

Velocity Squared (m^2/s^2)
43.52321446
105.3350938
174.1416131
227.3593065

Adding to the enigma is the fact that my velocity vs. radius graph, which should also show a root curve, actually DID. All I did to the velocities was square them for the v squared graph.

Any idea what's going on?
Thanks!

Pat

 

[Tide]

Are you sure you kept F constant for all those measurements?

 

[andrevdh]

I think you are making too much of this. The graph of $v^2\ vs\ r$ looks quite linear to me. If you analyze data with numerical facilities you can end up with all sorts of wonderful relationships between the variables. Such facilities are used when the relationship between the variables are complicated and cannot be described easily. We tend to use the simplest relationships that seems to fit the data, which in this case is linear. Your analysis may show effect of drag on the velocity though, since the velocities are getting quite high.

 

[FireLight07]

You're right, actually, it WAS linear. Turns out I'm looking at v^2 as a single variable, which makes the relation a simple direct proportion. :-) Thanks for the help!

Pat

(BTW: Force was constant throughout, so it wasn't a factor...we rigged up a very rough centripetal force apparatus with some string and a straw and some other stuff, so it isn't very accurate--but force was constant. )

 

[andrevdh]

Actually, the fact that the graph seems to be linear implies that you kept the ratio of the mass and centripetal force constant, otherwise it would not have been linear.