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The can in the given image floats in the position shown. The diameter of the can is 19 cm. What is its weight in newtons? 3 cm 1 8 cm Water

The can in the given image floats in the position shown. The diameter of the can is 19 cm. What is its weight in newtons? 3 cm 1 8 cm Water

Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)
Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)
5th Edition
ISBN:9781305084766
Author:Saeed Moaveni
Publisher:Saeed Moaveni
Chapter10: Force And Force-related Variables In Engineering
Section: Chapter Questions
Problem 22P
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**Floating Can Problem** **Description:** The can in the given image floats in the position shown. The diameter of the can is 19 cm. What is its weight in newtons? **Diagram Details:** - The can is partially submerged in water. - The submerged height of the can is labeled as 8 cm. - The height of the part of the can above water is labeled as 3 cm. - The total height of the can is therefore 11 cm (8 cm submerged + 3 cm above water). - The diameter of the can is given as 19 cm. - The depth of the water is not specified, but it is sufficient to submerge part of the can. **Key Considerations:** - To determine the weight of the can in newtons, use the principle of buoyancy. - According to Archimedes' principle, the upward buoyant force on the can is equal to the weight of the water displaced by the submerged portion of the can. **Steps to Calculate the Weight:** 1. **Determine the volume of the submerged part of the can:** - Volume of submerged part (V_submerged) = π × (radius)^2 × (submerged height) - Radius = Diameter/2 = 19 cm / 2 = 9.5 cm - Submerged height = 8 cm - V_submerged ≈ π × (9.5 cm)^2 × 8 cm 2. **Find the weight of the displaced water:** - Assume the density of water (ρ_water) = 1000 kg/m³ - Convert the volume from cm³ to m³ (1 cm³ = 1 × 10^-6 m³) - Volume in m³ = V_submerged × 1 × 10^-6 - Weight of displaced water (Buoyant Force) = V_submerged × ρ_water × g (where g is the acceleration due to gravity ≈ 9.8 m/s²) 3. **Weight of the can (W_can):** - Since the can is floating, the weight of the can is equal to the buoyant force. **Result:** - Substitute the values and compute the results to find the weight of the can in newtons. **Note:** - Ensure all units are consistent when performing the calculations. - Use appropriate significant figures based on the given measurements
Transcribed Image Text:**Floating Can Problem** **Description:** The can in the given image floats in the position shown. The diameter of the can is 19 cm. What is its weight in newtons? **Diagram Details:** - The can is partially submerged in water. - The submerged height of the can is labeled as 8 cm. - The height of the part of the can above water is labeled as 3 cm. - The total height of the can is therefore 11 cm (8 cm submerged + 3 cm above water). - The diameter of the can is given as 19 cm. - The depth of the water is not specified, but it is sufficient to submerge part of the can. **Key Considerations:** - To determine the weight of the can in newtons, use the principle of buoyancy. - According to Archimedes' principle, the upward buoyant force on the can is equal to the weight of the water displaced by the submerged portion of the can. **Steps to Calculate the Weight:** 1. **Determine the volume of the submerged part of the can:** - Volume of submerged part (V_submerged) = π × (radius)^2 × (submerged height) - Radius = Diameter/2 = 19 cm / 2 = 9.5 cm - Submerged height = 8 cm - V_submerged ≈ π × (9.5 cm)^2 × 8 cm 2. **Find the weight of the displaced water:** - Assume the density of water (ρ_water) = 1000 kg/m³ - Convert the volume from cm³ to m³ (1 cm³ = 1 × 10^-6 m³) - Volume in m³ = V_submerged × 1 × 10^-6 - Weight of displaced water (Buoyant Force) = V_submerged × ρ_water × g (where g is the acceleration due to gravity ≈ 9.8 m/s²) 3. **Weight of the can (W_can):** - Since the can is floating, the weight of the can is equal to the buoyant force. **Result:** - Substitute the values and compute the results to find the weight of the can in newtons. **Note:** - Ensure all units are consistent when performing the calculations. - Use appropriate significant figures based on the given measurements
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