Slope of Force vs Frequency^2 and Radius vs Period^2 Graphs

[Stormblessed]

Homework Statement

An experiment that involved swinging a mass in a circle was conducted. After graphing both sets of data, I obtained linear graphs of which I calculated the slopes for. I got a slope of 3.5 for the force vs frequency^2 graph and a slope of 0.73 for the radius vs period^2 graph. I do not know what these slopes represent though.

Homework Equations

Fc = m(4π^2R/T^2)

The Attempt at a Solution

After looking at the units for the force vs frequency^2 graph, the slope should be 3.5 N/Hz^2, which can be simplified to 3.5 kg(m). I don't know what this would represent though.

For the radius vs period^2 graph, the units for the slope would be 0.73 m/s^2. Would this slope simply represent the centripetal acceleration of the mass being swung?
[/B]

 

[scottdave]

Its hard to understand force vs freq^2, but should be easier to understand what force vs frequency represents (though it will now be a parabola, not a straight line)

 

[haruspex]

Homework Statement

An experiment that involved swinging a mass in a circle was conducted. After graphing both sets of data, I obtained linear graphs of which I calculated the slopes for. I got a slope of 3.5 for the force vs frequency^2 graph and a slope of 0.73 for the radius vs period^2 graph. I do not know what these slopes represent though.

Homework Equations

Fc = m(4π^2R/T^2)

The Attempt at a Solution

After looking at the units for the force vs frequency^2 graph, the slope should be 3.5 N/Hz^2, which can be simplified to 3.5 kg(m). I don't know what this would represent though.

For the radius vs period^2 graph, the units for the slope would be 0.73 m/s^2. Would this slope simply represent the centripetal acceleration of the mass being swung?[/B]

Rearrange your relevant equation to correspond to the graphs. E.g. for force v. frequency², write it in the form force=Constant x frequency².

 

[Stormblessed]

Rearrange your relevant equation to correspond to the graphs. E.g. for force v. frequency², write it in the form force=Constant x frequency².

So the slope of the force vs frequency^2 graph is equal to m(4pi^2)(R)?

 

[haruspex]

So the slope of the force vs frequency^2 graph is equal to m(4pi^2)(R)?

That would seem right, except for one thing. Is the force you measured the centripetal force?

 

[Stormblessed]

That would seem right, except for one thing. Is the force you measured the centripetal force?

The force was not measured in Newtons, instead it was the number of small masses (washers) that were attached to the bottom of the rope (which I assume is supposed to emulate centripetal force). Also, is my idea about the slope of the radius vs period^2 graph correct (represents acceleration)?

 

[haruspex]

it was the number of small masses (washers) that were attached to the bottom of the rope

Ok, but you can convert that to a force by multiplying by the weight of each washer. That will be the tension in the string, but still not the centripetal force. If you really want to understand what the slope represents you have to get the right equation, derived from your relevant equation, connecting whatever your x and y variables are, maybe (number of washers) = slope / (period)².

the slope of the radius vs period^2 graph correct (represents acceleration)?

As I wrote, rearrange the equation to match your graph, so in this case with radius as a function of period².