Biomedical Engineering: Bridging Medicine and Technology 1st Edition by Veronique Tran,Mark Saltzman

Exercise 4

The forces that act on a body that is swimming through water are similar to the forces acting on an object flying through the air, as shown in Box 10.1, except that swimming bodies are buoyant, which exactly balances the force of gravity. Assume that we are studying the differences between swimmers of different size: a bacterium, a fish, and a human swimmer. Assume further that the drag force, Fd, acting on any swimmer is proportional to its average "size" a: where µ is the viscosity of the fluid surrounding the swimmer and vx is the speed of swimming. Assume that the viscosity of the fluid through which they are swimming is 0.01 g/cm-s and the following are the characteristics of each swimmer:
a. What is the drag force acting on each swimmer? What is the propulsive force that is produced by each swimmer to swim at the stated speed?
b. Assume that the swimmer suddenly stops exerting energy to swim. At the very instant that it stops, before it has had time to slow down appreciably, what is the drag force on each swimmer? What is the propulsive force?
c. How long will each swimmer "coast"-that is, how long will it keep moving forward before stopping?
d. How far did it travel during the "coasting" phase?