Final answer:
To sink the wood, the buoyant force must be greater than the weight of the wood. By using the formulas for buoyant force and weight, and accounting for the volume and mass of the wood, we can calculate the minimum mass of lead required to sink the wood.
Step-by-step explanation:
To determine the minimum mass of lead required to sink the wood, we need to understand buoyancy. Buoyancy is the upward force exerted on an object immersed in a fluid, such as water. The object will float if the buoyant force is greater than or equal to the weight of the object.
In this case, the wood is floating, which means the buoyant force is equal to the weight of the wood. The buoyant force can be calculated using the equation Fb = ρw × Vo × g, where ρw is the density of water, Vo is the volume of the wood, and g is the acceleration due to gravity.
Since the wood is floating, the buoyant force must be equal to the weight of the wood, which is given by the equation Fw = mw × g, where mw is the mass of the wood.
To calculate the volume of the wood, we can use its density and mass. The density of wood, ρwood, is given as 0.48 times the density of water, ρw. We can use this relationship to find the volume of the wood using the equation ρwood × Vo = ρw × Vw, where Vw is the volume of water displaced by the wood.
Now we can set the buoyant force equal to the weight of the wood and solve for the minimum mass of lead required to sink the wood. This can be done by substituting the equations for the buoyant force and weight of the wood into the equation Fb = Fw + Flead, where Flead is the weight of the lead.