Fluid Mechanics with teacher's notes

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$Holt Math Minnesota Test Prep Workbook for Grade 9$

$Math Skills: More Practice$

DENSITY AND BUOYANCY Conceptual questions 1. If an inflated beach ball is placed beneath the surface of a pool of water and released, it shoots upward, out of the water. Use Archimedes’ principle to explain why. 2. Will an ice cube float higher in water or in mercury? (Hint: See Table 9-1, on page 319.) 3. An ice cube is submerged in a glass of water. What happens to the level of the water as the ice melts? 4. Will a ship ride higher in an inland freshwater lake or in the ocean? Why? 5. Steel is much denser than water. How, then, do steel boats float? 6. A small piece of steel is tied to a block of wood. When the wood is placed in a tub of water with the steel on top, half the block is submerged. If the block is inverted so that the steel is underwater, will the amount of the wooden block that is submerged increase, decrease, or remain the same? 7. A fish rests on the bottom of a bucket of water while the bucket is being weighed. When the fish begins to swim around, does the reading on the scale change? Practice problems 8. An object weighs 315 N in air. When tied to a string, connected to a balance, and immersed in water, it weighs 265 N. When it is immersed in oil, it weighs 269 N. Find the following: a. the density of the object b. the density of the oil (See Sample Problem 9A.) Copyright © by Holt, Rinehart and Winston. All rights reserved. CHAPTER 9 Review and Assess 9. A sample of an unknown material weighs 300.0 N in air and 200.0 N when submerged in an alcohol solution with a density of 0.70 × 10 3 kg/m 3 . What is the density of the material? (See Sample Problem 9A.) PRESSURE Conceptual questions 10. After a long class, a physics teacher stretches out for a nap on a bed of nails. How is this possible? 11. If you lay a steel needle horizontally on water, it will float. If you place the needle vertically into the water, it will sink. Explain why. 12. A typical silo on a farm has many bands wrapped around its perimeter, as shown in Figure 9-18. Why is the spacing between successive bands smaller toward the bottom? 13. Which dam must be stronger, one that holds back 1.0 × 10 5 m 3 of water 10 m deep or one that holds back 1000 m 3 of water 20 m deep? 14. In terms of the kinetic theory of gases, explain why gases do the following: a. expand when heated b. exert pressure 15. When drinking through a straw, you reduce the pressure in your mouth and the atmosphere moves the liquid. Could you use a straw to drink on the moon? Fluid Mechanics Figure 9-18 343 Chapter 9 Review and Assess ANSWERS TO Chapter 9 Review and Assess 1. The weight of the water displaced is greater than the weight of the ball. 2. mercury, because r mercury > r water 3. The level falls because r ice < r water. 4. in the ocean; Because r sea water > r fresh water, F B is greater in sea water. 5. because the average density of the boat, including air inside the hollow hull, is less than the density of the water 6. The amount of the block that is submerged will decrease. The volume of water displaced remains the same when the block is inverted. When the block is inverted, the steel occupies some of the displaced volume. Thus, the amount of wood displaced is less than half the block. 7. The weight may vary slightly because of impulses by the fish’s tail, but the mass of the system will stay the same. 8. a. 6.3 × 10 3 kg/m 3 b. 9.2 × 10 2 kg/m 3 9. 2.1 × 10 3 kg/m 3 10. The force opposing F g is spread out over a large number of nails, so no single nail exerts very much pressure. 11. In the horizontal case, the weight of the needle is spread out along the length of the needle so that the surface tension is greater than the weight at each point. 343
9 REVIEW & ASSESS 12. because the pressure the grains exert increases with increasing depth 13. 20 m deep, because pressure increases with increasing depth 14. a. Molecules are moving faster, so the particles collide more often and, in the absence of any other force, push each other outward. b. As particles move about in a gas, they exert a force F ⎯) on the walls of the (P = ⎯ A container. 15. No, there would be no way to get the pressure in your mouth lower than the zero atmospheric pressure outside the liquid. 16. 1.9 × 10 4 N 17. 6.28 N 18. 14 N downward 19. a. 2.61 × 10 6 Pa b. 1.84 × 10 5 N 20. The air flow causes the pressure over the entrance in the mound to be lower than the pressure over the other entrance. Thus, air is pushed through the mound by the higher-pressure area. 21. The water on the first floor has only kinetic energy (⎯ 1 2 ⎯ rv 1 2 ), whereas the water on the second floor has both kinetic and potential energy (⎯ 1 2 ⎯ rv 2 2 + rgh). Thus, because energy is conserved, v 1 > v 2. 22. The moving air above the ball creates a low pressure area so that the air below the ball exerts a force that is equal and opposite F g. 23. 2.4 m/s 24. 12.6 m/s 25. Pressure decreases, so volume increases. 344 Practice problems 16. The four tires of an automobile are inflated to an absolute pressure of 2.0 × 10 5 Pa. Each tire has an area of 0.024 m 2 in contact with the ground. Determine the weight of the automobile. (See Sample Problem 9B.) 17. A pipe contains water at 5.00 × 10 5 Pa above atmospheric pressure. If you patch a 4.00 mm diameter hole in the pipe with a piece of bubble gum, how much force must the gum be able to withstand? (See Sample Problem 9B.) 18. A piston, A, has a diameter of 0.64 cm, as in Figure 9-19. A second piston, B, has a diameter of 3.8 cm. In the absence of friction, determine the force, F, necessary to support the 500.0 N weight. (See Sample Problem 9B.) 19. A submarine is at an ocean depth of 250 m. a. Calculate the absolute pressure at this depth. Assume that the density of water is 1.025 × 10 3 kg/m 3 and that atmospheric pressure is 1.01 × 10 5 Pa. (See Sample Problem 9C.) b. Calculate the magnitude of the total force exerted at this depth on a circular submarine window with a diameter of 30.0 cm. (See Sample Problem 9B.) FLUID FLOW Conceptual questions 20. Prairie dogs live in underground burrows with at least two entrances. They ventilate their burrows by building a mound around one entrance, which is open to a stream of air. A second entrance at ground level is open to almost stagnant air. Use Bernoulli’s principle to explain how this construction creates air flow through the burrow. 344 Chapter 9 B 500.0 N F A Figure 9-19 21. Municipal water supplies are often provided by reservoirs built on high ground. Why does water from such a reservoir flow more rapidly out of a faucet on the ground floor of a building than out of an identical faucet on a higher floor? 22. If air from a hair dryer is blown over the top of a table-tennis ball, the ball can be suspended in air. Explain how this suspension is possible. Practice problems 23. A dairy farmer notices that a circular water trough near the barn has become rusty and now has a hole near the base. The hole is 0.30 m below the level of the water that is in the tank. If the top of the trough is open to the atmosphere, what is the speed of the water as it leaves the hole? (See Sample Problem 9D.) 24. The hypodermic syringe shown in Figure 9-20 contains a medicine with the same density as water. The barrel of the syringe has a cross-sectional area of 2.50 × 10 −5 m 2 . The cross-sectional area of the needle is 1.00 × 10 −8 m 2 . In the absence of a force on the plunger, the pressure everywhere is atmospheric pressure. A 2.00 N force is exerted on the plunger, making medicine squirt from the needle. Determine the speed of the emerging fluid. Assume that the pressure in the needle remains at atmospheric pressure, that the syringe is horizontal, and that the speed of the emerging fluid is the same as the speed of the fluid in the needle. (See Sample Problem 9D.) F P1 A1 Figure 9-20 GASES AND THE IDEAL GAS LAW Conceptual questions 25. Why do underwater bubbles grow as they rise? 26. What happens to a helium-filled balloon released into the air? Does it expand or contract? Does it stop rising at some height? P2 A2 v2 Copyright © by Holt, Rinehart and Winston. All rights reserved.
Page 1 and 2: Chapter 9 Overview Section 9-1 defi
Page 3 and 4: Section 9-1 Demonstration 1 Volume
Page 5 and 6: SECTION 9-1 The Language of Physics
Page 7 and 8: SECTION 9-1 Demonstration 4 Lifting
Page 9 and 10: SECTION 9-1 PRACTICE GUIDE 9A Solvi
Page 11 and 12: SECTION 9-2 STOP 326 Misconception
Page 13 and 14: SECTION 9-2 Visual Strategy Figure
Page 15 and 16: SECTION 9-2 Classroom Practice The
Page 17 and 18: Section 9-3 Demonstration 7 Fluid f
Page 19 and 20: SECTION 9-3 Misconception STOP Aler
Page 23 and 24: Section 9-4 Demonstration 10 Temper
Page 27: Chapter 9 Summary Teaching Tip Ask
Page 31 and 32: 9 REVIEW & ASSESS 42. 7.1 m 43. 17
Page 33 and 34: 9 REVIEW & ASSESS 63. 60.9 m/s 2 64
Page 35 and 36: Chapter 9 Laboratory Exercise NOTE
Page 37 and 38: CHAPTER 9 LAB Boyle’s Law Apparat

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