Computing Project — Natural Sciences Computing Workshops
Computing Project
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Introduction
Instructions
Submission
For the rest of this course you will put together the concepts and skills you have
learnt so far in order to conduct a simple (but genuine) scientific experiment.
Introduction
It is well known that the value of acceleration due to gravity at the Earth’s surface (
) is approximately . But how accurately can you measure the value of
this physical constant using just a handheld video camera and your nascent
programming skills?
Perform an experiment to determine an estimate of the value of , using a
handheld camera to capture the experimental results and Python to
perform the analysis.
Instructions
These instructions are one suggested way to meet the project goal. There may be
other equally valid ways to achieve the goal, so feel free to adapt them as you wish.
Step 1: Conduct an Experiment
Using a handheld video camera (e.g. the one in your smartphone), record the
motion of an object falling vertically from rest. You can use any object you like, but
I advise against anything breakable or expensive. You might need to experiment a
little to determine a setup which reliably gives a clean and accurate recording (for
example the camera will need to be completely static) but don’t spend a lot of time
tinkering; you can refine the experiment later! The output of this step should be a
movie file (e.g. .mov or .avi).
Step 2: Extract the Data
g 9.81!m/s2
Project Goal!
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Extract the location of the object from the recording in the form of a sequence of x
and y co-ordinates for each frame. First you will need to upload the movie file.
Then you can use the image segmentation techniques studied in the last workshop
to determine the frame-by-frame coordinates. The end result should be two arrays
containing the x- and y-coordinates of the object in each frame.
Step 3: Build and Fit the Model
The motion of an object accelerating uniformly from rest is described by the
following differential equation:
where is the acceleration of the object and is the object’s vertical position at
time . Integrating this equation results in an equation for the vertical position of
the object:
By plotting this curve against the experimental results determined in step 2, find
the value of which best fits.
Optional Extension Activities
You could use the techniques to measure another physical parameter (e.g.
coefficient of friction) or perform error analysis to quantify the accuracy of your
results. You can discuss your extension activity ideas with one of the tutors.
Submission
You should submit your solution to the problem as a Jupyter Notebook, including
code cells and Markdown. Your submission should include enough explanatory text
that the reader can easily understand how you completed the experiment. See
Moodle for the submission deadline and instructions.
Each project group will be awarded a mark as follows.
Grade Criterion
Distinction A solution to the problem which also goes beyond the project
goal by completing an extension activity
Merit A solution to the problem which meets the project goal by
correctly determining a value for
Fail Failed to solve the problem or notebook does not run correctly
y(t) = y0 !
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By Natural Sciences
© Copyright 2022.
09/12/2022 01:59
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