Chapter 14 Problems 1, 2 , 3 = straightforward, intermediate, challenging Section 14.1 Pressure 1. Calculate the mass of a solid iron sphere that has a diameter of 3.00 cm. 2. Find the order of magnitude of the density of the nucleus of an atom. What does this result suggest concerning the structure of matter? Model a nucleus as protons and neutrons closely packed together. Each has mass 1.67 × 10 –27 kg and radius on the order of 10 –15 m. 3. A 50.0-kg woman balances on one heel of a pair of high-heeled shoes. If the heel is circular and has a radius of 0.500 cm, what pressure does she exert on the floor? 4. The four tires of an automobile are inflated to a gauge pressure of 200 kPa. Each tire has an area of 0.024 0 m 2 in contact with the ground. Determine the weight of the automobile. 5. What is the total mass of the Earth's atmosphere? (The radius of the Earth is 6.37 × 10 6 m, and atmospheric pressure at the surface is 1.013 × 10 5 N/m 2 .) Section 14.2 Variation of Pressure with Depth 6. (a) Calculate the absolute pressure at an ocean depth of 1 000 m. Assume the density of seawater is 1 024 kg/m 3 and that the air above exerts a pressure of 101.3 kPa. (b) At this depth, what force must the frame around a circular submarine porthole having a diameter of 30.0 cm exert to counterbalance the force exerted by the water? 7. The spring of the pressure gauge shown in Figure 14.2 has a force constant of 1 000 N/m, and the piston has a diameter of 2.00 cm. As the gauge is lowered into water, what change in depth causes the piston to move in by 0.500 cm? 8. The small piston of a hydraulic lift has a cross-sectional area of 3.00 cm 2 and its large piston has a cross-sectional area of 200 cm 2 (Figure 14.4). What force must be applied to the small piston for the lift to raise a load of 15.0 kN? (In service stations, this force is usually exerted by compressed air.) 9. What must be the contact area between a suction cup (completely exhausted) and a ceiling if the cup is to support the weight of an 80.0-kg student? 10. (a) A very powerful vacuum cleaner has a hose 2.86 cm in diameter. With no nozzle on the hose, what is the weight of the heaviest brick that the cleaner can lift? (Fig. P14.10a) (b) What If? A very powerful octopus uses one sucker of diameter 2.86 cm on each of the two shells of a clam in an attempt to pull the shells apart (Fig. P 14.10b). Find the greatest force the octopus can exert in salt water 32.3 m deep.
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