A large suitcase full of gold sits at the bottom of a lake....

A large suitcase full of gold sits at the bottom of a lake. A team of treasure hunters uses a crane to recover the suitcase and finds that a force of $3.0 \times 10^{5} \mathrm{N}$ is required to lift the suitcase to the surface. What is the volume of the suitcase?

Key Concepts

Fluid Density

Fluid density is the mass per unit volume of a fluid and is a critical factor in calculating the buoyant force. Since the buoyant force depends on the weight of the fluid displaced, knowing the density of the fluid allows one to determine how much weight is counteracted by the upward force for a given volume.

Apparent Weight

The apparent weight of an object in a fluid is the net weight felt by the object when buoyancy is taken into account. It is calculated by subtracting the buoyant force from the object's actual gravitational weight. Understanding apparent weight is essential for solving problems involving the lifting or sinking of objects in fluids.

Buoyant Force

The buoyant force is the upward force exerted by a fluid on a submerged object, which acts against the force of gravity. This force is equal to the weight of the displaced fluid and plays a crucial role in reducing the apparent weight of the object when it is submerged, thereby affecting the net force required to lift it.

Archimedes' Principle

Archimedes' Principle states that any object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by it. This principle is fundamental in determining how fluids interact with submerged bodies and is key to calculating the buoyant force that offsets the object's weight in the fluid.

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