Stokes' Law For a spherical object falling in a medium, the drag force is F} = 6717, where r is the radius of the object, 17 is the viscosity of the fluid, and v is the object's velocity. Good examples of Stokes' law are provided by microorganisms, pollen, and dust particles. Because each of these objects is so small, we find that many of these objects travel unaided only at a constant (terminal) velocity. Terminal velocities for bacteria (size about 1 pm) can be about 2 um/s. To move at a greater speed, many bacteria swim using flagella (organelles shaped like little tails) that are powered by little motors embedded in the cell. Sediment in a lake can move at a greater terminal velocity (about 5 pm/s), so it can take days for it to reach the bottom of the lake after being deposited on the surface. If we compare animals living on land with those in water, you can see how drag has influenced evolution. Fish, dolphins, and even massive whales are streamlined in shape to reduce drag forces. Birds are streamlined and migratory species that fly large distances often have particular features such as long necks. Flocks of birds fly in the shape of a spearhead as the flock forms a streamlined pattern (see b). In humans, one important example of streamlining is the shape of sperm, which need to be efficient in their use of energy. Geese fly in a V formation during their long migratory travels. This shape reduces drag and energy consumption for individual birds, and also allows them a better way to communicate. (credit: modification of work by "Julo"/Wikimedia Commons) R6_2 1/1 point (graded) Find the terminal velocity of a 50-kg skydiver falling in spread-eagle fashion (i.e. belly first). Assume that the cross sectional area is 0.70m2 Give your answer in m/s to two significant figures without units. 34 V 34
Key Equations Magnitude of static friction Magnitude of kinetic friction Centripetal force F = m, or Fc = manu2 Ideal angle of a banked curve 3/2 Drag force Fo - CpAv2 Stokes' law F. - ?????