Graph Linearization

Please make a copy of the sheet HERE.

Additional tabs will be created as we conduct more experiments. 

‘AP Experiment Question Advice’ 

Analyze-data questions…

The student is provided with a set of data from an experiment that has already been completed.

Sometimes the student is asked to adapt the data in a way that will make the interpretation of the resulting graph easier. The student is usually given a very big hint about what to do… the result is (always?) the linearization of the data. 

Then the student is usually asked to ‘graph the data’.  Many students seem to think that all graphs should pass through the origin, and that extrapolation of experiment data is perfectly fine. If the data doesn’t pass through the origin, then it is almost certain that there will be a question asking for the significance of the non-zero intercept (such as in photoelectric effect).

Axes… sometimes the axes are labeled for the student, sometimes not. If the axes are not labeled, it has been known for a point to be given for choosing to use the vertical axis for the independent variable. It’s a smart idea to add appropriate units to the axis label (worth at least a point).

Plotting data and sketching a best fit line… (sometimes, we even plot the data for the student!).  Data points should be clear, in the form of a small cross. We expect to see a single smooth line… if it’s a straight line it should look like one (use a ruler). A pencil is the best tool. Sometimes a best fit line will pass directly over one of the student’s data points; if the data point is not very visible, the student may then lose credit for plotting all of the data points. The best fit line should a ‘sketch’ of one… if the student wants to do regression analysis on his calculator, that’s fine, but no extra points. This means that, if the student is asked later to find the slope of the line, that there a range of acceptable scores that will get full credit.

Finding the slope of the line… if it’s a straight line, and the student is asked to find the slope ‘from the graph’ then the student better show that the graph was used (spring constant= slope of graph = ΔF/Δx = (52 – 0) / (13.3-0) = etc. If the data used in finding the slope is only that supplied in the original data (not the best fit line) then things look decidedly fishy. The slope should include appropriate units. 

‘What would happen if’… an example would be a graph related to the gravitational field strength, showing the relationship between the U_s of a particular mass against the mass of a planet… ‘what would happen if the mass were placed on a planet with a greater mass?’ or ‘a larger mass were used in the experiment’...  well, this is where the physics is tested. Apart from investigating the meaning of the slope and area of the graph (dimensional analysis, scouring brain for a relevant formula etc), no helpful advice here.