A large, bronze statue of Newton falls from the deck of a ship and sinks until it rests on the bottom of the ocean. The density of bronze is 8.2x10^3kgm^-3, the density of seawater is 1.02×10^3kgm^-3 and the volume of the statue is 0.14m^3. When the statue reaches a depth of 20m, what is the magnitude of the buoyancy force on the statue (in N)?
A large, bronze statue of Newton falls from the deck of a ship and sinks until it rests on the bottom of the ocean. The density of bronze is 8.2x10^3kgm^-3, the density of seawater is 1.02×10^3kgm^-3 and the volume of the statue is 0.14m^3. When the statue reaches a depth of 20m, what is the magnitude of the buoyancy force on the statue (in N)?
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![### Problem Statement
A large, bronze statue of Newton falls from the deck of a ship and sinks until it rests on the bottom of the ocean. The density of bronze is \( 8.2 \times 10^3 \, \text{kg/m}^3 \), the density of seawater is \( 1.02 \times 10^3 \, \text{kg/m}^3 \), and the volume of the statue is \( 0.14 \, \text{m}^3 \). When the statue reaches a depth of 20 meters, what is the magnitude of the buoyancy force on the statue (in N)?
### Solution
To determine the buoyancy force acting on the statue, we can use Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. The formula for buoyancy force (\( F_b \)) is:
\[ F_b = \rho_{\text{fluid}} \times V_{\text{object}} \times g \]
Where:
- \( \rho_{\text{fluid}} \) is the density of the fluid (seawater in this case),
- \( V_{\text{object}} \) is the volume of the object (the statue),
- \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)).
Given data:
- Density of seawater, \( \rho_{\text{fluid}} = 1.02 \times 10^3 \, \text{kg/m}^3 \)
- Volume of the statue, \( V_{\text{object}} = 0.14 \, \text{m}^3 \)
- Acceleration due to gravity, \( g = 9.8 \, \text{m/s}^2 \)
Substituting the values into the formula:
\[ F_b = 1.02 \times 10^3 \, \text{kg/m}^3 \times 0.14 \, \text{m}^3 \times 9.8 \, \text{m/s}^2 \]
Calculating the buoyant force:
\[ F_b = 1.02 \times 0.14 \times 9.8 \times 10^3 \, \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7be57ba7-aca5-4231-94a7-c86a6ecf18d3%2F3f5c3fce-4ece-48b0-aff5-83a9cc757563%2Fx5yqjab_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
A large, bronze statue of Newton falls from the deck of a ship and sinks until it rests on the bottom of the ocean. The density of bronze is \( 8.2 \times 10^3 \, \text{kg/m}^3 \), the density of seawater is \( 1.02 \times 10^3 \, \text{kg/m}^3 \), and the volume of the statue is \( 0.14 \, \text{m}^3 \). When the statue reaches a depth of 20 meters, what is the magnitude of the buoyancy force on the statue (in N)?
### Solution
To determine the buoyancy force acting on the statue, we can use Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. The formula for buoyancy force (\( F_b \)) is:
\[ F_b = \rho_{\text{fluid}} \times V_{\text{object}} \times g \]
Where:
- \( \rho_{\text{fluid}} \) is the density of the fluid (seawater in this case),
- \( V_{\text{object}} \) is the volume of the object (the statue),
- \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)).
Given data:
- Density of seawater, \( \rho_{\text{fluid}} = 1.02 \times 10^3 \, \text{kg/m}^3 \)
- Volume of the statue, \( V_{\text{object}} = 0.14 \, \text{m}^3 \)
- Acceleration due to gravity, \( g = 9.8 \, \text{m/s}^2 \)
Substituting the values into the formula:
\[ F_b = 1.02 \times 10^3 \, \text{kg/m}^3 \times 0.14 \, \text{m}^3 \times 9.8 \, \text{m/s}^2 \]
Calculating the buoyant force:
\[ F_b = 1.02 \times 0.14 \times 9.8 \times 10^3 \, \
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