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

• Stormblessed
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]

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)

Stormblessed said:

## 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.

haruspex said:
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)?

Stormblessed said:
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?

haruspex said:
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)?

Stormblessed said:
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.
Stormblessed said:
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.

## 1. What is the relationship between the slope of the force vs frequency^2 graph and the radius vs period^2 graph?

The slope of the force vs frequency^2 graph and the radius vs period^2 graph have an inverse relationship. This means that as the slope of the force vs frequency^2 graph increases, the slope of the radius vs period^2 graph decreases and vice versa.

## 2. How can the slope of these graphs be calculated?

The slope of these graphs can be calculated by dividing the change in the y-axis values by the change in the x-axis values. This can be done by selecting two points on the graph and using the formula: slope = (y2-y1)/(x2-x1).

## 3. What does the slope value represent in these graphs?

The slope value represents the relationship between the two variables being plotted. In the case of the force vs frequency^2 graph, the slope represents the relationship between force and frequency^2. Similarly, in the radius vs period^2 graph, the slope represents the relationship between radius and period^2.

## 4. How does the slope of these graphs affect the motion of an object?

The slope of these graphs can provide information about the motion of an object. A steeper slope indicates a stronger relationship between the variables and a faster rate of change. This can indicate a more rapid or forceful motion of an object.

## 5. Are there any limitations to using slope values in these graphs?

Yes, there are limitations to using slope values in these graphs. The slope value is only a measure of the relationship between two variables and does not provide information about the cause and effect of that relationship. Additionally, the slope may change at different points on the graph, so it is important to consider the entire graph when interpreting the slope value.

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