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A Merry-Go-Round as an Alternative to the Wind Tunnel
||Upper and lower secondary
||Individual Learning, Partner/Team Work, Discussion
For a given model, the air resistance force F(v) as a function of the velocity v can be determined by placing it in a wind tunnel and reading F for a number of v-es. The merry-go-round gives the same, rather accurately, by clever combinations of several different fundamental ideas. Hopefully this gives a feeling for the power of these ideas.
The role of modelling, intuition and assumptions can be pursued: The equivalent car introduced in sec. 5 is a mathematical model of the merry-go-round. The way its mass is determined builds on an idea of inertia which is purely intuitive ( although founded rigorously in appendix B). The air resistance force against the model on the merry-go-round is determined by subtracting a force found in a run without the model. This is easily understood when explained in terms of the equivalent car. So is the assumption that the air stream around the merry-go-round does not affect the air stream around the model - and vice versa. If that is not so, a so-called systematic error goes with the method. Another systematic error could enter by the turbulence in the air caused by a passing model: Does this calm down before the next passage? That error cannot be foreseen in terms of the equivalent car. A young inexperienced student can understand the basic idea of the graphically illustrated computer fittings, neglecting the mathematics behind. The student with some knowledge Newton's 2. law as an equation of motion can improve his understanding. The more advanced student can start studying the rotation of a rigid body around of fixed axis and Reynolds model law.
Suggestions for methodology
Clearly the merry-go-round is well suited when a small group of students is supposed to work on their own for a fairly long time. If a whole class wishes to use it in minor groups, one possibility is the following. With all the students watching, the teacher himself balances the empty merry-go-round, measures the periods for the harmonic oscillations as well as a set of decreasing velocities. Then the students take these data to the computer and start doing the calculations. They should use some time on trying to find a good least squares fit before they let the computer find the optimal one. This takes some time, but gives a good feeling of the method. Can be arranged as a competition: Who finds the smallest least square error? While this work takes place, the groups can - one by one - return to the merry-go-round, mount a model of their own choice and carry out the corresponding measurements themselves.
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