The goal of this project is to examine a standard commercial video cassette (or audio cassette). Experiments will be performed an a mathematical model constructed to profile the performance of the cassette, and a computer model will be generated to predict it's behaviour. A detailed report including all experimentation, calculations, and simulations will be produced.
1.) When being rewound (or fast-forwarded), one spool in the cassette is being driven by the motor at a constant RPM, making the speed the actual tape moves variable (this is not true when the tape is playing, when the tape is actually pulled past the head reading the media; the system driving the spool slips to allow this).
2.) The thickness of commercial videotape is 20 mm (2 extra credit points to anyone finding a more accurate value, through research or experimentation).
3.) It takes exactly 6 hours to play the whole tape.
Using a standard video (or audio) cassette, measure the width of the tape on the spool when the tape is at it's end. Then rewind the tape for a number of known periods of time and measure the width on the spool for each time.
Using just your brain and knowledge of basic geometry, determine the equations that to calculate:
1. The width of the tape on the spool as a function of time and RPM.
2. The linear speed of the tape (speed it moves past the head) as a function of the width of tape on the spool and RPM.
3. The rate the spool is turning (RPM) given two widths at particular times and the thickness of the tape
4. The amount of tape rewound given the elapsed time
5. The speed the tape plays.
Enter your experimental data into Excel and produce a plot of it. Use Excel and/or your calculator to fit a curve to your data. Determine the best possible model. Use your equation to predict the time it would take to rewind completely. Check this value against your measured data and your theoretical result. Use this data with equation (3) of your model to compute the RPM for the spool at several different times. See if the rate remains constant.
Use your computed value for RPM and your equations from your theoretical model to write a Matlab program to simulate the tape. The program should accept a ``rewind time'' (always assuming you start from the end of the tape), compute the total length of tape that is rewound during this time period, determine how many minutes of program time this would correspond to, and produce a plot of linear tape speed over the time interval, and the average ``rewind speed'' in (minutes of tape play time per second of rewind time) over the time interval.
Write a detailed report outlining the goals of the project, the procedures you followed and any problems you encountered. Include all of your data, plots, equations, program code, and demonstrations of your simulation. Try to explain any discrepancies in your data between measured, theoretical, and simulated values. In particular, reconcile the equation you obtained by curve-fitting your data to the equation your theoretical model predicted. Refer to your Technical Communication book for information on format of a technical report. All parts of the report should be typed.