AP Physics--Graphing

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Graphing AssignmentDue July 6, 2012WHAT IF THE GRAPH IS CURVED?Here is where the fun begins. If we get a nonlinear relationship between our physical quantities, we will need toinvestigate further to figure out the exact model for this relationship. This is where your graphing calculator comes invery handy. However, while you may be able to obtain a graph on the calculator, you will need to be able to properlytransfer it to the graph paper on the AP exam.LINEARIZING DATAThe process described in the previous example is called linearizing data. It is a simple five-step process:1) Graph the original data.2) Look at the shape of the type of relationship it represents (quadratic, cubic, square root, and inverse are themost common).3) Create a second set of data for the type of relationship you determined your graph represents. These data willhave different x values. In the previous example, x changed from time to time squared. If the graphed shapewould have been a square root curve, the altered x would have been the square root of x.4) Create a graph of the new data.5) Use the slope-intercept form of the line to create the exact relationship for your data. You can see why thisprocess is called linearizing the data.This is the most important data analysis skill you can learn in an AP Physics course. You will be practicing it byworking with graphs that present you with interesting relationships we have seen throughout the course. The followingare the most common relationships:1) y = kx2) y = kx 23) y = k/x4) y = k/x 25) y = k√xPROBLEM 2Here is a sample set of position v. time data. Graph position as a function of time. Then create a second graph tolinearize the data by manipulating time (t 2 , 1/t, 1/t 2 , t ½ ). For the linear graph, determine the slope (with units)and the equation for the linear plot.Position (m)Time (t)5 0.010 1.016 1.526 2.036 2.551 3.0SLOPE = _________ EQUATION = _______________2
Graphing AssignmentDue July 6, 2012From our data, we were able to figure out the exact relationship between position and time and obtained theacceleration value from our analysis. The point of graphing is to find the average for the data. You should avoidsimply picking a set of points in the table and calculating an average value. This is not proper lab technique andwill get you in trouble on the AP exam. The purpose of graphing is to understand the relationship between twophysical quantities. Therefore, use your graphs to determine other quantities that directly come from the graphs, suchas acceleration.PROBLEM 3We are considering an experiment in which we put a series of masses on a spring and then set the spring/mass systeminto motion. The resulting motion is simple harmonic motion. We measure each mass we place on the spring and theperiod of the SHM. The period is always constant for any one mass. Here is a set of data that was gathered. Graphthe data of Period vs. Mass. Then, linearize the data to determine the proper relationship and apply meaning tothe relationship. Fill in the data table. Plot Period vs. Manipulated Mass and Manipulated Period vs. Mass.Both plots should be linear. Determine the slope (with units) and equation for each linear graph.Mass (kg)Period (s)0.1 0.600.2 0.840.3 1.020.4 1.200.5 1.380.8 1.681.0 1.98SLOPE = _________EQUATION = _______________SLOPE = _________EQUATION = _______________3
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AP Physics--Graphing

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