Applied Statistics - Project 1

Project description:
It is the year 1679, and Hooke is (following a suggestion from Newton) trying to prove the rotation of Earth by the Coriolis force on falling bodies. Your team has an other (better?) idea, namely to measure the gravitational pull on Earth at different latitudes.
However, to obtain the necessary funding to travel south and repeat a measurement of g near equator, you have to prove that you can do it with the necessary precision. The size of the effect is somewhere around 0.5%, and you want to prove the difference with 5 sigma certainty, which thus requires sub-per-mille precision.

Your mission - and you have little choice, but to accept it - is to take up the challenge of making these measurements and proving that at least one of your two experimental setups has the required/desired precision...


Left: Robert Hooke (1655-1705), Right: The distribution of land and ocean, if Earth's rotation stopped!

Experiments:
  • Experiment 1: Ball rolling down an incline (or dropping freely)
  • Experiment 2: Simple pendulum with a mass at the end

    Suggestions for initial macros:
    The following two macros are suggestions for a place to start data analysis. They run on the datasets provided, which should look a bit what you will get!
  • Rolling Ball: g_RollingBall.py, data_RollingBall_exmple.txt
  • Pendulum: g_Pendulum.py data_Pendulum_example.txt

    For the pendulum experiment, I suggest copying this analysis macro, and "empty" it. Also, for illustrating the period measurement, you may let yourself be inspired by the following plot macro snippet (i.e. piece of code that does NOT run by itself - it needs data!), which produces this figure.

    Measurements to make:
    Below is a list of measurements to make, all of which should of course have well determined uncertainties. Make sure that you report all the "raw" measurements you performed (i.e.\ for each group member), possibly with uncertainty, if one was available. Otherwise, you obtain the uncertainty from the RMS of the typically four independent (make sure they are!) measurements.
  • Pendulum length: Measured both with measuring tape and laser.
  • Pendulum period: Measured over several (e.g. 25) swings.
  • Timing precisions: Accuracy of timing of each team member.
  • Rolling ball timing gate distances: From all members!
  • Rolling ball acceleration: I.e. combining above with times.
  • Rolling ball incline angle: Note: This is the hard part!
  • Rolling ball table angle: Measured by turning the experiment. Was it level?
    And finally, you should of course combine your measurements to one value of g for each setup.

    Writing up results:
    The project should be written in Physical Review Letter style (or something close to it, if you don't like Latex) thus not more than 3-4 pages! The aim should be to answer the questions above also given on page two of the introduction slides. You do not need to describe the experiments themselves (assume the reader is a fellow student, who has also done the experiments), but of course all measurements, details and results should be described, such that the reader can follow (i.e. calculate themselves) your results fully and reproduce what you have done.

    Below you can find the files needed (works with pdftex as well, except for the figures, which needs to be converted into .pdf or .png):
  • PRL Latex template.
  • Test figure.
  • Result using current template.

    For each of the two results, I would like to see a table with the errors from each of the variables listed. So for each variable used in determining g, list their value, their uncertainty, and their impact on g (i.e. if they were the only uncertainty on g, how large would it then be), so that one can compare source of error. An example in LaTeX can be found in the PRL template above.

    The group should send the project by mail in PDF format to me by Thursday the 4th of December, 22:00.
    The projects will be corrected by us, but you will also yourself be asked to consider one of the others projects. Below is a link to the list of groups and the group members, and if you are in group N, then you should consider the project from group (N+1) (modulo number of groups).
    The list of groups Project1_Groups.pdf

    Notes:
    For measuring time to (better than) 1/100 of a second with lap time and the option of saving the result to a file on your computer, please use the following Python stop watch script: stopwatch.py.

    Comments:
    Enjoy, have fun, and throw yourself boldly at the data.



    Last updated: 22nd of November 2015.