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The following is a problem from Hobbie, Russell K. and Bradley J.Roth. 2007. Intermediate Physics for Medicine and Biology, Fourth Edition. New York: Springer Science and Business Media, p. 45, Exercise 28.When an animal of mass m falls in air, two forces act on it: gravity, m*g, and a force due to air friction. Assume that the frictional force is proportional to the speed v.
- Write a differential equation for v based on Newton' s second law, F = m (dv/dt).
- Solve this differential equation.
- Assume that the animal is spherical, with radius a and density rho. Also, assume that the frictional force is proportional to the surface area of the animal. Determine the terminal speed (speed of descent in steady state) as a function of a.
- Use your result in part (c) to interpret the following quote by J.~B.~S.~Haldane ``You can drop a mouse down a thousand - yard mine shaft; and arriving at the bottom, it gets a slight shock and walks away. A rat is killed, a man is broken, a horse splashes.''
- Added: Offer any comments on how a given animal may mitigate or at least reduce this terminal velocity.
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