Multiple Choice
Why are some tiny insects able to walk on water?
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19. Fluid Mechanics
Buoyancy & Buoyant Force
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A large rectangular raft with a density of 650 kg/m^3 is floating on a lake. The surface area of the top of the raft is 8.2 m^2 and its volume is 1.80 m^3. Given that the density of the lake water is 1000 kg/m^3, what is the buoyant force acting on the raft?
A
11,760 N
B
18,000 N
C
8,200 N
D
1,170 N
Verified step by step guidance1
Identify the principle that applies: The buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. This is known as Archimedes' principle.
Calculate the volume of water displaced by the raft. Since the raft is floating, the volume of water displaced is equal to the volume of the raft submerged in the water. Use the formula: \( V_{displaced} = V_{raft} \).
Determine the mass of the water displaced using the density of water. The formula is: \( m_{water} = \rho_{water} \times V_{displaced} \), where \( \rho_{water} = 1000 \text{ kg/m}^3 \).
Calculate the weight of the water displaced, which is equal to the buoyant force. Use the formula: \( F_{buoyant} = m_{water} \times g \), where \( g = 9.81 \text{ m/s}^2 \) is the acceleration due to gravity.
Compare the calculated buoyant force with the given options to determine the correct answer.
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