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A buoyant force of 26 newton acts on a piece of metal that is completely immersed in ethyl alcohol. what is the volume of metal piece..? (density of ethanol=785.06kg/m³)
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Understanding Buoyant Force
Buoyant force is the upward force exerted by a fluid on an object that is immersed in it. This principle is explained by Archimedes’ Principle, which states that the buoyant force on an object is equal to the weight of the fluid that it displaces.
Given Data
- Buoyant Force (F_b) = 26 N
- Density of Ethyl Alcohol (ρ) = 785.06 kg/m³
Volume of the Metal Piece
To find the volume of the metal piece (V), we can use the formula:
F_b = ρ × g × V
Where:
- F_b = buoyant force
- ρ = density of the fluid (ethyl alcohol)
- g = acceleration due to gravity (approximately 9.81 m/s²)
- V = volume of the object
Rearranging the formula to solve for volume (V) gives:
V = F_b / (ρ × g)
Calculating Volume
Now, substituting the values:
1. **Convert density to appropriate units**:
- ρ = 785.06 kg/m³
2. **Use g = 9.81 m/s²**.
Now, plug in the values:
V = 26 N / (785.06 kg/m³ × 9.81 m/s²)
Calculating the denominator:
- 785.06 kg/m³ × 9.81 m/s² = 7716.46 N/m³
Now, calculate the volume:
V = 26 N / 7716.46 N/m³
V ≈ 0.00337 m³
Conclusion
The volume of the metal piece is approximately 0.00337 m³. This calculation illustrates the principles of buoyancy and demonstrates how the weight of the displaced fluid correlates with the buoyant force acting on the submerged object.
Buoyant force is the upward force exerted by a fluid on an object that is immersed in it. This principle is explained by Archimedes’ Principle, which states that the buoyant force on an object is equal to the weight of the fluid that it displaces.
Given Data
- Buoyant Force (F_b) = 26 N
- Density of Ethyl Alcohol (ρ) = 785.06 kg/m³
Volume of the Metal Piece
To find the volume of the metal piece (V), we can use the formula:
F_b = ρ × g × V
Where:
- F_b = buoyant force
- ρ = density of the fluid (ethyl alcohol)
- g = acceleration due to gravity (approximately 9.81 m/s²)
- V = volume of the object
Rearranging the formula to solve for volume (V) gives:
V = F_b / (ρ × g)
Calculating Volume
Now, substituting the values:
1. **Convert density to appropriate units**:
- ρ = 785.06 kg/m³
2. **Use g = 9.81 m/s²**.
Now, plug in the values:
V = 26 N / (785.06 kg/m³ × 9.81 m/s²)
Calculating the denominator:
- 785.06 kg/m³ × 9.81 m/s² = 7716.46 N/m³
Now, calculate the volume:
V = 26 N / 7716.46 N/m³
V ≈ 0.00337 m³
Conclusion
The volume of the metal piece is approximately 0.00337 m³. This calculation illustrates the principles of buoyancy and demonstrates how the weight of the displaced fluid correlates with the buoyant force acting on the submerged object.
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A buoyant force of 26 newton acts on a piece of metal that is completely immersed in ethyl alcohol. what is the volume of metal piece..? (density of ethanol=785.06kg/m³) Related: Pascal's Law, Buoyancy and Archimedes Principle? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A buoyant force of 26 newton acts on a piece of metal that is completely immersed in ethyl alcohol. what is the volume of metal piece..? (density of ethanol=785.06kg/m³) Related: Pascal's Law, Buoyancy and Archimedes Principle? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A buoyant force of 26 newton acts on a piece of metal that is completely immersed in ethyl alcohol. what is the volume of metal piece..? (density of ethanol=785.06kg/m³) Related: Pascal's Law, Buoyancy and Archimedes Principle?.
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