Ch14 problem

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Unformatted text preview: Print this page PROBLEMS sec. 14-3 Density and Pressure 1 A fish maintains its depth in fresh water by adjusting the air content of porous bone or air sacs to make its average density the same as that of the water. Suppose that with its air sacs collapsed, a fish has a density of 1.08 g/cm 3 . To what fraction of its expanded body volume must the fish inflate the air sacs to reduce its density to that of water? Answer: 0.074 2 A partially evacuated airtight container has a tight-fitting lid of surface area 77 m 2 and negligible mass. If the force required to remove the lid is 480 N and the atmospheric pressure is 1.0 × 10 5 Pa, what is the internal air pressure? 3 Find the pressure increase in the fluid in a syringe when a nurse applies a force of 42 N to the syringe's circular piston, which has a radius of 1.1 cm. Answer: 1.1 × 10 5 Pa 4 Three liquids that will not mix are poured into a cylindrical container. The volumes and densities of the liquids are 0.50 L, 2.6 g/cm 3 ; 0.25 L, 1.0 g/cm 3 ; and 0.40 L, 0.80 g/cm 3 . What is the force on the bottom of the container due to these liquids? One liter = 1 L = 1000 cm 3 . (Ignore the contribution due to the atmosphere.) 5 An office window has dimensions 3.4 m by 2.1 m. As a result of the passage of a storm, the outside air pressure drops to 0.96 atm, but inside the pressure is held at 1.0 atm. What net force pushes out on the window? Answer: 2.9 × 10 4 N 6 You inflate the front tires on your car to 28 psi. Later, you measure your blood pressure, obtaining a reading of 120/80, the readings being in mm Hg. In metric countries (which is to say, most of the world), these pressures are customarily reported in kilopascals (kPa). In kilopascals, what are (a) your tire pressure and (b) your blood pressure? 7 In 1654 Otto von Guericke, inventor of the air pump, gave a demonstration before the noblemen of the Holy Roman Empire in which two teams of eight horses could not pull apart two evacuated brass hemispheres. (a) Assuming the hemispheres have (strong) thin walls, so that R in Fig. 14-29 may be considered both the inside and outside radius, show that the force required to pull apart the hemispheres has magnitude F = π R 2 Δ p , where Δ p is the difference between the pressures outside and inside the sphere. (b) Taking R as 30 cm, the inside pressure as 0.10 atm, and the outside pressure as 1.00 atm, find the force magnitude the teams of horses would have had to exert to pull apart the hemispheres. (c) Explain why one team of horses could have proved the point just as well if the hemispheres were attached to a sturdy wall. Page 1 of 18 Problems 12/23/2010 .. Figure 14-29 Problem 7. ...
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