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Large objects have inertia and tend to keep moving-Newton's first law. Life is very different for small microorganisms that swim through water. For them, drag forces are so large that they instantly stop, without coasting, if they cease their swimming motion. To swim at constant speed, they must exert a constant propulsion force by rotating corkscrew-like flagella or beating hair-like cilia. The quadratic model of drag given by the equation, D=(CpAv², direction opposite the motion), fails for very small particles. Instead, a small object moving in a liquid experiences a linear drag force, D= (bv, direction opposite the motion), where b is a constant. For a sphere of radius R, the drag constant can be shown to be b = 6R, where is the viscosity of the liquid. Water at 20°C has viscosity 1.0 x 10-³ N-s/m². Part A A paramecium is about 100 μm long. If it's modeled as a sphere, how much propulsion force must it exert to swim at a typical speed of 0.80 mm/s? Express your answer to two significant figures and include the appropriate units. ▸ View Available Hint(s) n°² μà 3 F = Value Submit ▾ Part B μà F = Value Submit How about the propulsion force of a 2.0-um-diameter E.coli bacterium swimming at 38 μm/s? Express your answer to two significant figures and include the appropriate units. ► View Available Hint(s) → C 1 Units ? Units ? The propulsion forces are very small, but so are the organisms. To judge whether the propulsion force is large or small relative to the organism, compute the acceleration that the propulsion force could give each organism if there were no drag. The density of both organisms is the same as that of water, 1000 kg/m³.

Large objects have inertia and tend to keep moving-Newton's first law. Life is very different for small microorganisms that swim through water. For them, drag forces are so large that they instantly stop, without coasting, if they cease their swimming motion. To swim at constant speed, they must exert a constant propulsion force by rotating corkscrew-like flagella or beating hair-like cilia. The quadratic model of drag given by the equation, D=(CpAv², direction opposite the motion), fails for very small particles. Instead, a small object moving in a liquid experiences a linear drag force, D= (bv, direction opposite the motion), where b is a constant. For a sphere of radius R, the drag constant can be shown to be b = 6R, where is the viscosity of the liquid. Water at 20°C has viscosity 1.0 x 10-³ N-s/m². Part A A paramecium is about 100 μm long. If it's modeled as a sphere, how much propulsion force must it exert to swim at a typical speed of 0.80 mm/s? Express your answer to two significant figures and include the appropriate units. ▸ View Available Hint(s) n°² μà 3 F = Value Submit ▾ Part B μà F = Value Submit How about the propulsion force of a 2.0-um-diameter E.coli bacterium swimming at 38 μm/s? Express your answer to two significant figures and include the appropriate units. ► View Available Hint(s) → C 1 Units ? Units ? The propulsion forces are very small, but so are the organisms. To judge whether the propulsion force is large or small relative to the organism, compute the acceleration that the propulsion force could give each organism if there were no drag. The density of both organisms is the same as that of water, 1000 kg/m³.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Large objects have inertia and tend to keep moving-Newton's first law. Life is very different for small microorganisms that swim through water. For them, drag forces are so large that they instantly stop, without coasting, if they cease their swimming motion. To swim at constant speed, they must exert a constant propulsion force by rotating corkscrew-like flagella or beating hair-like cilia. The quadratic model of drag given by the equation, Ď= (CpAv², direction opposite the motion), fails for very small particles. Instead, a small object moving in a liquid experiences a linear drag force, D = (bv, direction opposite the motion), where b is a constant. For a sphere of radius R, the drag constant can be shown to be b = 6ŋR, where n is the viscosity of the liquid. Water at 20°C has viscosity 1.0 × 10-³ N-s/m². Part A A paramecium is about 100 μm long. If it's modeled as a sphere, how much propulsion force must it exert to swim at a typical speed of 0.80 mm/s? Express your answer to two significant figures and include the appropriate units. ► View Available Hint(s) F = Submit Part B F = LO Submit μÀ Value How about the propulsion force of a 2.0-μm-diameter E.coli bacterium swimming at 38 μm/s? Express your answer to two significant figures and include the appropriate units. ► View Available Hint(s) μA Units Value ? Units ? The propulsion forces are very small, but so are the organisms. To judge whether the propulsion force is large or small relative to the organism, compute the acceleration that the propulsion force could give each organism if there were no drag. The density of both organisms is the same as that of water, 1000 kg/m³.
Transcribed Image Text:Large objects have inertia and tend to keep moving-Newton's first law. Life is very different for small microorganisms that swim through water. For them, drag forces are so large that they instantly stop, without coasting, if they cease their swimming motion. To swim at constant speed, they must exert a constant propulsion force by rotating corkscrew-like flagella or beating hair-like cilia. The quadratic model of drag given by the equation, Ď= (CpAv², direction opposite the motion), fails for very small particles. Instead, a small object moving in a liquid experiences a linear drag force, D = (bv, direction opposite the motion), where b is a constant. For a sphere of radius R, the drag constant can be shown to be b = 6ŋR, where n is the viscosity of the liquid. Water at 20°C has viscosity 1.0 × 10-³ N-s/m². Part A A paramecium is about 100 μm long. If it's modeled as a sphere, how much propulsion force must it exert to swim at a typical speed of 0.80 mm/s? Express your answer to two significant figures and include the appropriate units. ► View Available Hint(s) F = Submit Part B F = LO Submit μÀ Value How about the propulsion force of a 2.0-μm-diameter E.coli bacterium swimming at 38 μm/s? Express your answer to two significant figures and include the appropriate units. ► View Available Hint(s) μA Units Value ? Units ? The propulsion forces are very small, but so are the organisms. To judge whether the propulsion force is large or small relative to the organism, compute the acceleration that the propulsion force could give each organism if there were no drag. The density of both organisms is the same as that of water, 1000 kg/m³.
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