In this buoyancy scenario, we analyze the behavior of two objects—wood and metal—both with the same volume when submerged in water. The key concept here is buoyant force, which is determined by the equation:

\( F_B = \rho \cdot g \cdot V \)

Where \( F_B \) is the buoyant force, \( \rho \) is the density of the liquid, \( g \) is the acceleration due to gravity, and \( V \) is the volume of the object submerged in the liquid. Since both objects are in the same water, the density of the liquid and the gravitational acceleration are constant for both, making them equal factors in the equation.

However, the crucial difference lies in the volume of each object that is submerged. While the wood floats, it has a portion of its volume above the water, meaning only part of it contributes to the buoyant force. In contrast, the metal, which sinks, has its entire volume submerged. This leads to the conclusion that the metal experiences a greater buoyant force because all of its volume is underwater, compared to the wood, which has some of its volume exposed.

It's a common misconception to assume that because the wood floats, it must have a greater buoyant force acting on it. In reality, the floating condition indicates that the weight of the wood is balanced by the buoyant force, but this does not mean the buoyant force is greater than that acting on the metal. Instead, the metal's greater submerged volume results in a stronger buoyant force, despite its sinking behavior.

In summary, when evaluating buoyancy, always refer to the equation and consider the volume submerged to accurately determine the buoyant forces acting on different objects. This approach helps clarify the often counterintuitive nature of buoyancy and floating versus sinking objects.