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Help Save & Exit S Archimedes, when asked by King Hiero if the new crown was pure gold (SG = 19.3), found the crown weight in air to be 24.5 N and in water to be 19.5 N. Was it gold? Yes or No No Yes

Help Save & Exit S Archimedes, when asked by King Hiero if the new crown was pure gold (SG = 19.3), found the crown weight in air to be 24.5 N and in water to be 19.5 N. Was it gold? Yes or No No Yes

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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--- ### Archimedes' Principle and the King's Crown **Question:** Archimedes, when asked by King Hiero if the new crown was pure gold (Specific Gravity = 19.3), found the crown weight in air to be 24.5 N and in water to be 19.5 N. Was it gold? - Yes or No - **Yes** - **No** ### Explanation: To determine if the crown is made of pure gold, Archimedes used the principle of buoyancy which states that the buoyant force on an object submerged in fluid is equal to the weight of the fluid displaced by the object. Here the given data: - Weight in air: 24.5 N - Weight in water: 19.5 N - Specific Gravity (SG) of gold: 19.3 The steps involved: 1. Calculate the loss of weight in water. 2. Use the loss of weight to determine the volume of the crown. 3. Calculate the density of the crown. 4. Compare this density with the known density of gold. **Detailed Calculation:** 1. **Loss of weight in water:** Weight in air - Weight in water = 24.5 N - 19.5 N = 5 N 2. **Volume of the crown (V) using the weight of water displaced:** Weight of displaced water = 5 N Since weight (N) = mass (kg) * gravitational acceleration (9.8 m/s²), Mass of water = 5 N / 9.8 m/s² = 0.51 kg 3. **Volume of water (since density of water = 1000 kg/m³):** Volume = Mass / Density Volume of water = 0.51 kg / 1000 kg/m³ = 0.00051 m³ 4. **Density of the crown:** Density = Mass / Volume Mass of the crown = 24.5 N / 9.8 m/s² = 2.5 kg Density of the crown = 2.5 kg / 0.00051 m³ = 4901.96 kg/m³ The density of the crown (4901.96 kg/m³) is significantly lower than the density of pure gold (19200 kg/m³ using SG). Hence, the crown
Transcribed Image Text:--- ### Archimedes' Principle and the King's Crown **Question:** Archimedes, when asked by King Hiero if the new crown was pure gold (Specific Gravity = 19.3), found the crown weight in air to be 24.5 N and in water to be 19.5 N. Was it gold? - Yes or No - **Yes** - **No** ### Explanation: To determine if the crown is made of pure gold, Archimedes used the principle of buoyancy which states that the buoyant force on an object submerged in fluid is equal to the weight of the fluid displaced by the object. Here the given data: - Weight in air: 24.5 N - Weight in water: 19.5 N - Specific Gravity (SG) of gold: 19.3 The steps involved: 1. Calculate the loss of weight in water. 2. Use the loss of weight to determine the volume of the crown. 3. Calculate the density of the crown. 4. Compare this density with the known density of gold. **Detailed Calculation:** 1. **Loss of weight in water:** Weight in air - Weight in water = 24.5 N - 19.5 N = 5 N 2. **Volume of the crown (V) using the weight of water displaced:** Weight of displaced water = 5 N Since weight (N) = mass (kg) * gravitational acceleration (9.8 m/s²), Mass of water = 5 N / 9.8 m/s² = 0.51 kg 3. **Volume of water (since density of water = 1000 kg/m³):** Volume = Mass / Density Volume of water = 0.51 kg / 1000 kg/m³ = 0.00051 m³ 4. **Density of the crown:** Density = Mass / Volume Mass of the crown = 24.5 N / 9.8 m/s² = 2.5 kg Density of the crown = 2.5 kg / 0.00051 m³ = 4901.96 kg/m³ The density of the crown (4901.96 kg/m³) is significantly lower than the density of pure gold (19200 kg/m³ using SG). Hence, the crown
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