Final answer:
The marble sank and the wood floated in water due to differences in density. Wood has a lower density than water, making it buoyant and able to float, while the marble has a higher density, which causes it to sink as the upward buoyant force is not sufficient to support its weight.
Step-by-step explanation:
The marble and the piece of wood acted differently in water because of their respective densities. Density is defined as mass per unit volume, and it determines whether an object will float or sink when placed in water. The wood has a lower density than water, which allows it to float, while the marble has a higher density than the water, causing it to sink to the bottom of the bucket.
This concept is further explained by the buoyant force, which acts upwards against gravity. When an object is placed in water, it displaces a volume of water equal to its own volume. The displaced water exerts a buoyant force on the object, and if this force is greater than the weight of the object, it will float; otherwise, it will sink. Since the marble's density is greater, the water's buoyant force is not enough to overcome the marble's weight, resulting in it sinking to the bottom. On the other hand, the wood's buoyant force exceeds its weight due to its lower density, hence it floats.
This explanation is based on the principles of physics that describe how objects behave in fluids, such as water. It highlights the importance of buoyant force and density in determining whether an object will float or sink.