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11. A proud yacht owner makes an anchor from 145 kg of pure gold. a) If gold has a density of 19,600 kg/m³, calculate the volume of this anchor. b) When the golden anchor is stored inside the yacht, the water's buoyant force must support the

11. A proud yacht owner makes an anchor from 145 kg of pure gold. a) If gold has a density of 19,600 kg/m³, calculate the volume of this anchor. b) When the golden anchor is stored inside the yacht, the water's buoyant force must support the

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### Buoyancy and Density: Practical Applications #### Problem Statement A proud yacht owner makes an anchor from 145 kg of pure gold. ##### a) **Calculation of the Volume of the Anchor:** Given: - Mass of gold anchor: \(145 \, \text{kg}\) - Density of gold: \(19,600 \, \text{kg/m}^3\) **Solution:** The volume (V) can be calculated using the formula: \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \implies \text{Volume} = \frac{\text{Mass}}{\text{Density}} \] Therefore, \[ \text{Volume} = \frac{145 \, \text{kg}}{19,600 \, \text{kg/m}^3} \] ##### b) **Calculation of Volume of Water Displaced by the Anchor Stored Inside the Yacht:** Given: - The volume of the anchor calculated in part (a) When the anchor is stored inside the yacht, the buoyant force from the water supports the anchor. The volume of water displaced will be equivalent to the volume of the anchor. ##### c) **Why Shipping Companies Struggle to Transport Large Quantities of Solid Metal Across Oceans:** Based on the calculations in parts (a) and (b): - Metals, particularly heavy ones like gold, have high densities, resulting in small volumes but very large masses. - The high density of metals means that even relatively small amounts can be exceptionally heavy, making transportation challenging due to the weight constraints of shipping vessels. - Significant buoyant forces are encountered when dealing with heavy metals, affecting the stability and buoyancy of ships. This practical scenario illustrates the fundamental physics principles of density and buoyancy and their impact on real-world applications, particularly in maritime transport. *Ensure you understand the calculation processes and the implications of these principles on logistical challenges faced by shipping companies.*
Transcribed Image Text:### Buoyancy and Density: Practical Applications #### Problem Statement A proud yacht owner makes an anchor from 145 kg of pure gold. ##### a) **Calculation of the Volume of the Anchor:** Given: - Mass of gold anchor: \(145 \, \text{kg}\) - Density of gold: \(19,600 \, \text{kg/m}^3\) **Solution:** The volume (V) can be calculated using the formula: \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \implies \text{Volume} = \frac{\text{Mass}}{\text{Density}} \] Therefore, \[ \text{Volume} = \frac{145 \, \text{kg}}{19,600 \, \text{kg/m}^3} \] ##### b) **Calculation of Volume of Water Displaced by the Anchor Stored Inside the Yacht:** Given: - The volume of the anchor calculated in part (a) When the anchor is stored inside the yacht, the buoyant force from the water supports the anchor. The volume of water displaced will be equivalent to the volume of the anchor. ##### c) **Why Shipping Companies Struggle to Transport Large Quantities of Solid Metal Across Oceans:** Based on the calculations in parts (a) and (b): - Metals, particularly heavy ones like gold, have high densities, resulting in small volumes but very large masses. - The high density of metals means that even relatively small amounts can be exceptionally heavy, making transportation challenging due to the weight constraints of shipping vessels. - Significant buoyant forces are encountered when dealing with heavy metals, affecting the stability and buoyancy of ships. This practical scenario illustrates the fundamental physics principles of density and buoyancy and their impact on real-world applications, particularly in maritime transport. *Ensure you understand the calculation processes and the implications of these principles on logistical challenges faced by shipping companies.*
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