When two flat surfaces approach each other, the fluid in between is accelerated and ejected from the sides at large speeds. This situation occurs often in everyday life, such as when you step in a puddle and create splashes of water, or when you clap your hands or close a book and create jets of air. For these systems, the inertia of the fluid resists the acceleration, creating large nonlinear forces on the flat surfaces. In this work, we study the case of a closing book. The fluid motion in this case is relatively easy to model, using the conservation of mechanical energy, and to measure using a MEMS gyroscopic sensor. This study reveals the unusual forces that occur when two plates collide in an experiment that can be performed by students at home.
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The theoretical analysis presented here is motivated by those in Refs. 1, 3, and 4. Their arguments have been adapted to the geometry of a hinged rotating plate, which is easier to realize experimentally. Also, while those discussions used partial differential equations to derive the force, here we use the mechanical energy conservation framework. This method is accessible by a wider range of students and also is more revealing of the approximations involved.
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According to the phyphox database on smartphones, their sampling rate varies by more than a factor of 5.
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2024
Author(s)
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