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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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A buoyant force of 26 newton acts on a piece of metal that is complete...
To determine the volume of the metal piece that experiences a buoyant force of 26 Newtons when immersed in ethyl alcohol, we can use the principles of buoyancy and density.
Understanding Buoyant Force
The buoyant force acting on an object submerged in a fluid is given by Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object.
Formula for Buoyant Force
The formula for buoyant force (F_b) is:
F_b = ρ_f × V × g
Where:
- F_b = Buoyant force (in Newtons)
- ρ_f = Density of the fluid (kg/m³)
- V = Volume of the submerged object (m³)
- g = Acceleration due to gravity (approximately 9.81 m/s²)
Given Values
- Buoyant force (F_b) = 26 N
- Density of ethyl alcohol (ρ_f) = 785.06 kg/m³
- Acceleration due to gravity (g) = 9.81 m/s²
Calculation of Volume
Rearranging the formula to solve for volume (V):
V = F_b / (ρ_f × g)
Substituting the known values:
V = 26 N / (785.06 kg/m³ × 9.81 m/s²)
Calculating the denominator:
ρ_f × g = 785.06 kg/m³ × 9.81 m/s² ≈ 7716.54 kg/(m²·s²)
Now, substituting back to find V:
V ≈ 26 N / 7716.54 kg/(m²·s²) ≈ 0.00337 m³
Conclusion
The volume of the metal piece is approximately 0.00337 m³ or 3.37 liters. This calculation illustrates the application of Archimedes' principle in determining the volume of an object based on the buoyant force it experiences in a fluid.
Understanding Buoyant Force
The buoyant force acting on an object submerged in a fluid is given by Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object.
Formula for Buoyant Force
The formula for buoyant force (F_b) is:
F_b = ρ_f × V × g
Where:
- F_b = Buoyant force (in Newtons)
- ρ_f = Density of the fluid (kg/m³)
- V = Volume of the submerged object (m³)
- g = Acceleration due to gravity (approximately 9.81 m/s²)
Given Values
- Buoyant force (F_b) = 26 N
- Density of ethyl alcohol (ρ_f) = 785.06 kg/m³
- Acceleration due to gravity (g) = 9.81 m/s²
Calculation of Volume
Rearranging the formula to solve for volume (V):
V = F_b / (ρ_f × g)
Substituting the known values:
V = 26 N / (785.06 kg/m³ × 9.81 m/s²)
Calculating the denominator:
ρ_f × g = 785.06 kg/m³ × 9.81 m/s² ≈ 7716.54 kg/(m²·s²)
Now, substituting back to find V:
V ≈ 26 N / 7716.54 kg/(m²·s²) ≈ 0.00337 m³
Conclusion
The volume of the metal piece is approximately 0.00337 m³ or 3.37 liters. This calculation illustrates the application of Archimedes' principle in determining the volume of an object based on the buoyant force it experiences in a fluid.
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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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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? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC 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? covers all topics & solutions for UPSC 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?.
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? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC 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? covers all topics & solutions for UPSC 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?.
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