**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 cm2. **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

Asked: To determine the weight of the can shown floating in the given figure. Given: Diameter of…

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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

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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**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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