I also thought of titling this post "Teaching how to think about the drag equation in biophysics by demonstration", but it's more verbose and less amusing to write.
As it is nearing the end of my teaching semester I reminisce (and procrastinate setting the question paper) about the fun I had teaching Cellular Biophysics 2 (Out of equilibrium approaches to cellular scale biophysics) at IISER Pune, I am reminded probably of a demo-experiment that actually worked quite well.
Borrowing heavily from the excellent book by Sunjoy Mahajan [1], a professor at Olin College of Engineering and visiting faculty at MIT, Boston, this is a mixture of DIY and order of magnitude estimates, to hone the intuition of the class. Our day to day intuition suggests that dropping cones of different sizes will result in differing amounts of drag and weight of the cone, and hence possibly lead to a different time of arrival. Indeed in a vote I took in class (2019-Jan), we had a 1:6 split (same time:different times of arrival).
Doing the experiment in a classroom:
The first step was to get paper, a ruler (foot-rule, scale) and scissors. Indeed, the need for a this high-school equipment was part of the excitement of doing the experiment. Also, a break in normal classroom teaching is a delight- for both students and professors.
Once the semi-circles were ready, we glued their overlapping edges together, such that we had atleast a pair of cones with 2-fold differences in base-diameters (big-cone, small-cone).
Finally it was time to let it all fly- off to the bridge (literally) we went. The bridge is a part of the lecture hall complex (LHC - yes, really!) which connects the ellipsoid corridor across the short axis. From the second floor (Indian 2nd, USAmerican 3rd) at about the height of 7-10 metres, we then held our hands out and let the cones drift.
For any good experiment we needed repeats. So the same cones with little damage were allowed to fly down three times. Also considering the class lasts only 55 minutes, we really had to keep it tight.
And (not so surprisingly) our average measurements of the time of arrival at the bottom, which allowed us to estimate a mean velocity (which we consider to be terminal velocity). And these turned out to be THE SAME for both big and small cones.
In the next post, I will discuss the maths of this very exciting result. And perhaps, if time permits interpret what that could mean for biological systems - animals flying and fish moving.
References:
[1] Mahajan S. 2010 Street Fighting Mathematics OpenAccess & FREE https://mitpress.mit.edu/books/street-fighting-mathematics
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| Compass required for drawing a circle, to make a well proportioned cone (screen grab from Amazon.in. Easily purchased in a local stationery shop). |
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| Foot rule |
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| Paper cone (Image taken from https://www.cutoutandkeep.net/projects/cone-shaped-frog) based on the half-circle using the compass (above) and a simple measuring scale to mark the straight part. |
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| Big cone, small cone: Paper cones made using the same sizes of semi-circle with different overlaps to ensure mass was the same. |
The first step was to get paper, a ruler (foot-rule, scale) and scissors. Indeed, the need for a this high-school equipment was part of the excitement of doing the experiment. Also, a break in normal classroom teaching is a delight- for both students and professors.
Once the semi-circles were ready, we glued their overlapping edges together, such that we had atleast a pair of cones with 2-fold differences in base-diameters (big-cone, small-cone).
Finally it was time to let it all fly- off to the bridge (literally) we went. The bridge is a part of the lecture hall complex (LHC - yes, really!) which connects the ellipsoid corridor across the short axis. From the second floor (Indian 2nd, USAmerican 3rd) at about the height of 7-10 metres, we then held our hands out and let the cones drift.
For any good experiment we needed repeats. So the same cones with little damage were allowed to fly down three times. Also considering the class lasts only 55 minutes, we really had to keep it tight.
And (not so surprisingly) our average measurements of the time of arrival at the bottom, which allowed us to estimate a mean velocity (which we consider to be terminal velocity). And these turned out to be THE SAME for both big and small cones.
In the next post, I will discuss the maths of this very exciting result. And perhaps, if time permits interpret what that could mean for biological systems - animals flying and fish moving.
References:
[1] Mahajan S. 2010 Street Fighting Mathematics OpenAccess & FREE https://mitpress.mit.edu/books/street-fighting-mathematics
