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Chapter 6: Q.12 (page 153)
A hand presses down on the book in FIGURE Q6.12. Is the normal force of the table on the book larger than, smaller than, or equal to mg?
The book's usual force is more than.
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A baggage handler drops your kg suitcase onto a conveyor belt running at m/s. The materials are such that and . How far is your suitcase dragged before it is riding smoothly on the belt?
Large objects have inertia and tend to keep moving-Newton's BI0 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 of Equation fails for very small particles. Instead, a small object moving in liquid experiences a linear drag force, , the direction opposite the motion), where is a constant. For a sphere of radius , the drag constant can be shown to be , where is the viscosity of the liquid. Water at has viscosity .
a. A paramecium is about long. If it's modeled as a sphere, how much propulsion force must it exert to swim at a typical speed of ? How about the propulsion force of a --diameter . coli bacterium swimming at ?
b. 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, .
A particle of ma帽s moving along the -axis experiences the net force, where is a constant. The particle has velocity at. Find an algebraic expression for the particle's velocity at a later time
A woman has a mass of 55 kg.
a. What is her weight while standing on earth?
b. What are her mass and her weight on Mars, where g = 3.76 m/s2 ?
Very small objects, such as dust particles, experience a linear drag force,(bv, direction opposite the motion), where is a constant. That is, the quadratic model of drag of Equation fails for very small particles. For a sphere of radius , the drag constant can be shown to be , where is the viscosity of the gas.
a. Find an expression for the terminal speedof a spherical particle of radius and mass falling through a gas of viscosity .
b. Suppose a gust of wind has carrieda -diameter dust particle to a height of . If the wind suddenly stops, how long will it take the dust particle to settle back to the ground? Dust has a density ofrole="math" localid="1647776411884" the viscosity ofair is , and you can assume that the falling dust particle reaches terminal speed almost instantly.
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