Fluid Mechanics with teacher's notes

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$Holt Math Minnesota Test Prep Workbook for Grade 9$

$Math Skills: More Practice$

PROBLEM SOLUTION 1. DEFINE 2. PLAN 3. CALCULATE 4. EVALUATE Buoyant force A bargain hunter purchases a “gold” crown, like the one shown in Figure 9-5, at a flea market. After she gets home, she hangs the crown from a scale and finds its weight to be 7.84 N. She then weighs the crown while it is immersed in water, and the scale reads 6.86 N. Is the crown made of pure gold? Explain. Given: F g = 7.84 N apparent weight = 6.86 N r f = r water = 1.00 × 10 3 kg/m 3 Unknown: r o = ? Diagram: Copyright © by Holt, Rinehart and Winston. All rights reserved. 7.84 N 6.86 N F T,1 F g Choose an equation(s) or situation: Because the object is completely submerged, consider the ratio of the weight to the buoyant force. F g − F B = apparent weight Fg ⎯⎯ = ⎯ FB ro ⎯ rf Rearrange the equation(s) to isolate the unknown(s): F B = F g − (apparent weight) Fg ro = ⎯⎯rf FB Substitute the values into the equation(s) and solve: F B = 7.84 N − 6.86 N = 0.98 N Fg ro = ⎯⎯rf = ⎯ FB 7. 84 N ⎯ (1.00 × 10 0. 98 N 3 kg/m 3 ) r o = 8.0 × 10 3 kg/m 3 FB FT,2 From Table 9-1, we know the density of gold is 19.3 × 10 3 kg/m 3 . Because 8.0 × 10 3 kg/m 3 < 19.3 × 10 3 kg/m 3 , the crown cannot be pure gold. F g In air In water SAMPLE PROBLEM 9A Figure 9-5 Fluid Mechanics 323 SECTION 9-1 Alternative Problem- Solving Approach FB = Factual − Fapparent FB = 7.84 N − 6.86 N = 0.98 N FB = rfluidVg V = 0.98 N ⎯⎯⎯⎯ (1.00 × 10 3 kg/m3 )(9.81 m/s2 ) V = 0.00010 m 3 This volume of gold should weigh 18.9 N (0.00010 m 3 × 9.81 m/s 2 × density of gold), which is much greater than the 7.84 N weight given in the problem. Classroom Practice The following may be used as teamwork exercises or for demonstration at the chalkboard or on an overhead projector. PROBLEM Buoyant force Calculate the actual weight, the buoyant force, and the apparent weight of a 5.00 × 10 −5 m 3 iron ball floating at rest in mercury. Answer 3.86 N, 3.86 N, 0 N How much of the ball’s volume is immersed in mercury? Answer 2.89 × 10 −5 m 3 323
SECTION 9-1 PRACTICE GUIDE 9A Solving for: r PE Sample, 1; Ch. Rvw. 8–9, 54 PW 6–8 PB 5–7 m PE 2, 3; Ch. Rvw. 36 PW Sample, 1–3 PB 8–10 F B 324 PE 4; Ch. Rvw. 41*, 43*, 44*, 52*, 53*, 59*, 63*, 64*, 65*, 68*, 69* PW 4–5 PB Sample, 1–4 ANSWERS TO Practice 9A Buoyant force 1. a. 3.57 × 10 3 kg/m 3 b. 6.4 × 10 2 kg/m 3 2. 97 kg 3. 9.4 × 10 3 N 4. a. 6.63 N b. 5.58 N Section Review ANSWERS 1. A solid has a definite shape, while a fluid does not; a liquid has a definite volume, while a gas does not. 2. b, c, and d 3. 4.7 × 10 3 m 3 4. 9.92 × 10 2 kg/m 3 5. The effective density of the kayak includes both the material composing the kayak and the air within the kayak below the level of the water. 324 PRACTICE 9A Section Review Chapter 9 Buoyant force 1. A piece of metal weighs 50.0 N in air, 36.0 N in water, and 41.0 N in an unknown liquid. Find the densities of the following: a. the metal b. the unknown liquid 2. A 2.8 kg rectangular air mattress is 2.00 m long, 0.500 m wide, and 0.100 m thick. What mass can it support in water before sinking? 3. A ferry boat is 4.0 m wide and 6.0 m long. When a truck pulls onto it, the boat sinks 4.00 cm in the water. What is the combined weight of the truck and the ferry? 4. An empty rubber balloon has a mass of 0.0120 kg. The balloon is filled with helium at 0°C, 1 atm pressure, and a density of 0.179 kg/m 3 .The filled balloon has a radius of 0.500 m. a. What is the magnitude of the buoyant force acting on the balloon? (Hint: See Table 9-1 for the density of air.) b. What is the magnitude of the net force acting on the balloon? 1. What is the difference between a solid and a fluid? What is the difference between a gas and a liquid? 2. Which of the following objects will float in a tub of mercury? a. a solid gold bead b. an ice cube c. an iron bolt d. 5 mL of water 3. A 650 kg weather balloon is designed to lift a 4600 kg package. What volume should the balloon have after being inflated with helium at 0°C and 1 atm pressure to lift the total load? (Hint: Use the density values in Table 9-1.) 4. A submerged submarine alters its buoyancy so that it initially accelerates upward at 0.325 m/s 2 . What is the submarine’s average density at this time? (Hint: the density of sea water is 1.025 × 10 3 kg/m 3 .) 5. Physics in Action Many kayaks are made of plastics and other composite materials that are denser than water. How are such kayaks able to float in water? 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: SECTION 9-1 Demonstration 4 Lifting
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 and 28: Chapter 9 Summary Teaching Tip Ask
Page 29 and 30: 9 REVIEW & ASSESS 12. because the p
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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