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Zorluk: OrtaBuoyancy and Archimedes' Principle

A technician drops two completely sealed metal canisters into a large vat of testing fluid. Canister A is completely hollow. Canister B has the exact same exterior dimensions and shape as Canister A, but is filled completely with solid lead weights. Both canisters are pushed down and held completely stationary underwater. Which of the following statements is true regarding the upward buoyant force acting on the canisters?

  1. The buoyant forces acting on both canisters are exactly equal because they displace the same volume of fluid.Cevap
  2. B
    The buoyant force on Canister B is greater because its higher mass interacts more strongly with the surrounding fluid.
  3. C
    The buoyant force on Canister A is greater because its lower weight provides less resistance to the upward push of the fluid.
  4. D
    Canister B experiences no buoyant force because its total weight overcomes the lifting capacity of the fluid.

Cevap

The buoyant forces acting on both canisters are exactly equal because they displace the same volume of fluid.
According to Archimedes' principle, the buoyant force on an object is equal to the weight of the fluid it displaces. Since both canisters are perfectly sealed, completely submerged, and have identical exterior dimensions, they displace the exact same volume of testing fluid. Therefore, the fluid exerts the exact same upward force on both, despite the fact that Canister B is much heavier.

Adım Adım Çözüm

1
Identify the physics principle governing the situation.
Archimedes' principle states that the upward buoyant force is equal to the weight of the fluid displaced by the object.
To determine what variables influence buoyant force.
2
Determine the factors that affect the volume of fluid displaced.
The displaced volume depends strictly on the exterior dimensions of the completely submerged object.
The formula for buoyant force is FB=ρ⋅V⋅gF_B = \rho \cdot V \cdot g, where VV is the displaced volume.
3
Compare the exterior volumes of Canister A and Canister B.
The problem states both canisters have the exact same exterior dimensions and shape, meaning they displace the exact same volume of fluid.
To establish the relationship between the two displaced volumes.
4
Evaluate the buoyant force based on the displaced volumes.
Because the displaced volumes are equal, the upward buoyant forces exerted by the fluid must also be equal, regardless of the internal mass.
To reach the final conclusion regarding the buoyant forces.

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Buoyancy and Archimedes' Principle
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Buoyancy and Archimedes' Principle

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