Plotting problem 3 (Pillow).mws

1. A Falling Pillow.

The data below is from an experiment in which a pillow was dropped onto a "motion detector" and the results recorded using a TI-CBL, the first coordinate is time and the second coordinate is height (distance). The distance measurements were initially taken at intervals of 0.10 seconds. This is Data1 . Then the distance measurements were taken at intervals of 0.04 seconds. This is Data2 . Finally the distance measurements were taken at intervals of 0.02 seconds.

> Data1:=[[0., 4.18803], [.10, 4.07639], [.20, 3.71629], [.30, 3.08970], [.40, 2.24706]]:

> Data2:=[[0., 4.18803], [.04, 4.17722], [.08, 4.11241], [.12, 4.02958], [.16, 3.89634], [.20, 3.71629], [.24, 3.49662], [.28, 3.23015], [.32, 2.94566], [.36, 2.60716], [.40, 2.24706], [.44, 1.85454], [.48, 1.44762]]:

> Data3:=[[0., 4.18803], [.02, 4.18083], [.04, 4.17722], [.06, 4.15202], [.08, 4.11241], [.10, 4.07639], [.12, 4.02958], [.14, 3.96836], [.16, 3.89634], [.18, 3.81352], [.20, 3.71629], [.22, 3.61186], [.24, 3.49662], [.26, 3.36699], [.28, 3.23015], [.30, 3.08970], [.32, 2.94566], [.34, 2.77281], [.36, 2.60716], [.38, 2.43071], [.40, 2.24706], [.42, 2.05260], [.44, 1.85454], [.46, 1.64928], [.48, 1.44762]]:

Submission:

Plot Data3 using style=point. Using this data only, estimate the instantaneous speed at 0.20 seconds. Do you think this estimate is better or worse than the estimates that you could make from Data1 or Data2? Explain!

Submission worksheet:

 

2. A theoretical value for the Instantaneous speed.

For the situation of the falling pillow in the previous activity, the data points can be fit reasonably well to a quadratic function, i.e., to a function of the form y = a*t^2+b*t+c for suitable values of a, b, c .

Submission:

Use trial/error together with your mathematical knowledge about the graph of a quadratic function to fit the curve to Data3. Use methods of Plotting points/section 3.4 of the tutorial to visually see your fit, and refine your quadratic function until it the fit looks good.

Once you get a good fit, plot the quadratic function over a short interval x = `0.2`-delta .. `0.2`+delta . Pick delta small enough so that the curve looks straight. By figuring out the value of your quadratic function at t = `0.2` and at `0.2`+delta estimate the slope of the curve y = f(t) at t = `0.2` . In principle, what is the relationship between this slope and the instantaneous speed? Address physical limitations.

Submission worksheet: