Final answer:
The pail with a piece of wood floating in it has a greater weight because it includes the additional mass of the wood on top of the water, which doesn't displace an equivalent weight of water due to its lower density.
Step-by-step explanation:
When considering two identical pails of water, one with only water and the other with a piece of wood floating in it, we need to understand the concept of density to determine which has the greater weight. Density is the mass per unit volume of a substance. Since both pails are filled to the brim, they contain the same volume of water. However, the pail with the piece of wood has the additional mass of the wood. Therefore, the pail with the wood floating in it weighs more because the wood's mass is added to the total mass of the pail of water. The floating wood does not displace water equal to its own weight since the wood has a lower density than water, so the pail overflows less.