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A solid brass sphere is initially surrounded by air, and the air pressure exerted on it is 1.00 x 10° N/m2 (normal atmospheric pressure). The sphere is lowered into the ocean to a depth where the pressure is 2.00 x 107 N/m2. The volume of the sphere in air is 0.35 m3. By how much does this volume change once the sphere is submerged? SOLUTION Conceptualize Think about movies or television shows you have seen in which divers go to great depths in the water in submersible vessels. These vessels must be very strong to withstand the large pressure under water. This pressure squeezes the vessel and --Select--- its volume. Categorize We perform a simple calculation involving the following equation, so we categorize this example as -Select--- problem. AF AP volume stress B = volume strain A = - AV Δν Vi Vi Solve the equation above for the volume change of the sphere: VAP AV = - B Substitute the numerical values (Enter your answer in m.): AV = m3 The negative sign indicates that the volume of the sphere decreases. Typical Values for Elastic Moduli Substance Young's Modulus (N/M2) Shear Modulus (N/m²) Bulk Modulus (N/m²) Tungsten 3.5 x 1011 1.4 x 1011 2.0 x 1011 Steel 2.0 x 1011 8.4 x 1010 6 x 1010 Copper 1.1 x 1011 4.2 x 1010 1.4 x 1011 Brass 9.1 x 1010 3.5 x 1010 6.1 x 1010 Aluminum 7.0 x 1010 2.5 x 1010 7.0 x 1010 Glass 6.5-7.8 x 1010 2.6-3.2 x 1010 5.0-5.5 x 1010 Quartz 5.6 x 1010 2.6 x 1010 2.7 x 1010 Water 2.1 x 109 Mercury 2.8 x 1010 EXERCISE The volume of the copper sphere is measured to be 0.64 m3 in air at standard atmospheric pressure. Now we put it in a vacuum jar (pressure assumed to be zero). What is the change in volume? Hint AV = m3

A solid brass sphere is initially surrounded by air, and the air pressure exerted on it is 1.00 x 10° N/m2 (normal atmospheric pressure). The sphere is lowered into the ocean to a depth where the pressure is 2.00 x 107 N/m2. The volume of the sphere in air is 0.35 m3. By how much does this volume change once the sphere is submerged? SOLUTION Conceptualize Think about movies or television shows you have seen in which divers go to great depths in the water in submersible vessels. These vessels must be very strong to withstand the large pressure under water. This pressure squeezes the vessel and --Select--- its volume. Categorize We perform a simple calculation involving the following equation, so we categorize this example as -Select--- problem. AF AP volume stress B = volume strain A = - AV Δν Vi Vi Solve the equation above for the volume change of the sphere: VAP AV = - B Substitute the numerical values (Enter your answer in m.): AV = m3 The negative sign indicates that the volume of the sphere decreases. Typical Values for Elastic Moduli Substance Young's Modulus (N/M2) Shear Modulus (N/m²) Bulk Modulus (N/m²) Tungsten 3.5 x 1011 1.4 x 1011 2.0 x 1011 Steel 2.0 x 1011 8.4 x 1010 6 x 1010 Copper 1.1 x 1011 4.2 x 1010 1.4 x 1011 Brass 9.1 x 1010 3.5 x 1010 6.1 x 1010 Aluminum 7.0 x 1010 2.5 x 1010 7.0 x 1010 Glass 6.5-7.8 x 1010 2.6-3.2 x 1010 5.0-5.5 x 1010 Quartz 5.6 x 1010 2.6 x 1010 2.7 x 1010 Water 2.1 x 109 Mercury 2.8 x 1010 EXERCISE The volume of the copper sphere is measured to be 0.64 m3 in air at standard atmospheric pressure. Now we put it in a vacuum jar (pressure assumed to be zero). What is the change in volume? Hint AV = m3

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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Squeezing a Brass Sphere A solid brass sphere is initially surrounded by air, and the air pressure exerted on it is 1.00 x 105 N/m2 (normal atmospheric pressure). The sphere is lowered into the ocean to a depth where the pressure is 2.00 x 10' N/m2. The volume of the sphere in air is 0.35 m³. By how much does this volume change once the sphere is submerged? SOLUTION Conceptualize Think about movies or television shows you have seen in which divers go to great depths in the water in submersible vessels. These vessels must be very strong to withstand the large pressure under water. This pressure squeezes the vessel and ---Select--- its volume. Categorize We perform a simple calculation involving the following equation, so we categorize this example as ---Select-- problem. ΔF ΔΡ volume stress A B = = - AV Δν volume strain Solve the equation above for the volume change of the sphere: VAP AV = - B Substitute the numerical values (Enter your answer in m3.): AV = m3 The negative sign indicates that the volume of the sphere decreases. Typical Values for Elastic Moduli Substance Young's Modulus (N/M2) Shear Modulus (N/m2) Bulk Modulus (N/m2) Tungsten 3.5 x 1011 1.4 x 1011 2.0 x 1011 8.4 x 1010 6 x 1010 Steel 2.0 x 1011 Copper 1.1 x 1011 4.2 x 1010 1.4 x 1011 Brass 9.1 x 1010 3.5 x 1010 6.1 x 1010 Aluminum 7.0 x 1010 2.5 x 1010 7.0 x 1010 Glass 6.5-7.8 x 1010 2.6-3.2 x 1010 5.0-5.5 x 1010 Quartz 5.6 x 1010 2.6 x 1010 2.7 x 1010 Water 2.1 x 109 Mercury 2.8 x 1010 EXERCISE The volume of the copper sphere is measured to be 0.64 m3 in air at standard atmospheric pressure. Now we put it in a vacuum jar (pressure assumed to be zero). What is the change in volume? Hint AV = m3 Need Help? Read It
Transcribed Image Text:Squeezing a Brass Sphere A solid brass sphere is initially surrounded by air, and the air pressure exerted on it is 1.00 x 105 N/m2 (normal atmospheric pressure). The sphere is lowered into the ocean to a depth where the pressure is 2.00 x 10' N/m2. The volume of the sphere in air is 0.35 m³. By how much does this volume change once the sphere is submerged? SOLUTION Conceptualize Think about movies or television shows you have seen in which divers go to great depths in the water in submersible vessels. These vessels must be very strong to withstand the large pressure under water. This pressure squeezes the vessel and ---Select--- its volume. Categorize We perform a simple calculation involving the following equation, so we categorize this example as ---Select-- problem. ΔF ΔΡ volume stress A B = = - AV Δν volume strain Solve the equation above for the volume change of the sphere: VAP AV = - B Substitute the numerical values (Enter your answer in m3.): AV = m3 The negative sign indicates that the volume of the sphere decreases. Typical Values for Elastic Moduli Substance Young's Modulus (N/M2) Shear Modulus (N/m2) Bulk Modulus (N/m2) Tungsten 3.5 x 1011 1.4 x 1011 2.0 x 1011 8.4 x 1010 6 x 1010 Steel 2.0 x 1011 Copper 1.1 x 1011 4.2 x 1010 1.4 x 1011 Brass 9.1 x 1010 3.5 x 1010 6.1 x 1010 Aluminum 7.0 x 1010 2.5 x 1010 7.0 x 1010 Glass 6.5-7.8 x 1010 2.6-3.2 x 1010 5.0-5.5 x 1010 Quartz 5.6 x 1010 2.6 x 1010 2.7 x 1010 Water 2.1 x 109 Mercury 2.8 x 1010 EXERCISE The volume of the copper sphere is measured to be 0.64 m3 in air at standard atmospheric pressure. Now we put it in a vacuum jar (pressure assumed to be zero). What is the change in volume? Hint AV = m3 Need Help? Read It
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