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I'm currently taking a Physics class in college, we just had our fourth lab which was about forces. We did experiments and collected data about the relationship between the variables in the equation F = ma. I have three variables in my dataset: Force (N), Mass (g), and Acceleration (m/s^2). How can I plot these three variables using a scatter plot (teacher's choice) and show a relationship between the three (if any)?

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    $\begingroup$ Could you explain the design a little more clearly. e.g. How many different masses did you use? (yes, it can make a difference to the choice of display). Do you have some values for measurement error on any of the variables? $\endgroup$
    – Glen_b
    Commented Oct 2, 2018 at 6:49
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    $\begingroup$ How did you measure force? $\endgroup$
    – Aksakal
    Commented Oct 2, 2018 at 17:53

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You do not necessarily need to plot only two single variables against each other in a plot.

You can also plot groups of variables against each other. For instance $F$ versus $m \cdot a$


This is done a lot in engineering where often several, more than two, (dimensionless) numbers are related with each other, using emperical correlations. (often some power law equation, for instance take the expressions for the rate of heat transfer in terms of dimensionless numbers $Nu = Re^a Pr^b$)

So imagine you would have some phyical law like:

$$F \propto m^xa^y$$

Then you might:

  • wish to show that for those coefficients you have constant $x=y=1$
  • wish to explore that $x$ and $y$ may be varying (e.g. show different laws in the same graph)
  • wish to show how $x$ and $y$ are varying with respect to some standard

In the first case you would have a very strong visual representation when you plot $F$ versus $m \cdot a$ because you get a straight line which people can interpret very easily.

In the second case you can not plot so easily versus $m \cdot a$ because the coefficients $x$ and $y$ may vary. Or at least you should not expect everything to be on a single straight line.

In the third case you may not have a constant $x$ and $y$ but you might still choose to F plot versus some product, e.g. $m \cdot a$. E.g. because it makes the graph easier, or you want to stress some difference (say you want to show that $F \neq m a$, then plotting $F$ vs $m a$ would be a very effective visual representation) .

example

If you browse these images (keywords Nusselt Reynolds Prandtl) on google you may get an idea/feeling of the different representations.

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You will be doing what can be called an EDA step. Having three variants you can plot up to 9 scatter plots where half of them would be repeating (3 unique) from which your goal is to find (show) the dependent and the invariant variables.

If you find the works of astronomers in 1600s, their research was mostly tabling their observations in writing and looking for a constant. Having visualization tools now your teacher is hoping you figure out the relations, here linear with m as a constant, using scatter plots. This homework would only make sense if you don’t know the relationship ahead.

Here is one simulated experiment data set, three weight groups (0.8kg, 1kg, 1.25kg) and for each weight, 30 students of the class are measuring acceleration while applying pretty much same force. Each student submits its 3 observation in the end to the teacher. What is the take outs from the plot from all the observations? That is what you are looking to figure out here. enter image description here

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