Monday, April 15, 2013

Geophysics Problem of the Day: Garage Doors and Rolling Sheets

I am equal parts awed by and afraid of the parking garage door at my husband’s worksite. The garage door consists of a semiflexible metal sheet that hangs down from a horizontal cylinder. The cylinder rolls very quickly and the garage door whooshes upward. Something about it takes my breath away every time.

Part one of the geophysics problem of the day is to quantify “whoosh”. Calculate the upward velocity as a function of time for a flexible sheet with finite thickness hanging down from a cylinder as it rotates. What is the garage door upward velocity as a function of time? The upward linear acceleration of the sheet will be related to the sheet thickness, the initial radius of the cylinder and the its rotation rate.  As necessary for all decent homework-type problems, first draw yourself a cartoon. My picture is here:


Part two is to apply this physics problem to plate tectonics. Take a look at a plate-reconstruction animation, and keep your eye on India.
Can you see India whooshing into Eurasia? Pretend that the Indian plate is the garage door, and use your above derivation to calculate the relationship between plate velocity,  plate thickness, and cylinder rotation, using rates from plate-reconstructions.  Is there a giant cylinder within the Earth?


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