Physics questions are the most fun when people don’t immediately agree on the answer. What feels intuitive or obvious—sometimes isn’t. We can argue over the solution for hours of entertainment, and we might even learn something in the end.
Here’s one of these seemingly obvious questions that’s been around a long time: Suppose a large rock is on a boat that is floating in a very small pond. If the rock is dumped overboard, will the water level of the pond rise, fall, or remain unchanged?
Go ahead and debate it with your friends and family. While you convince them that your answer is correct, here is a picture of my boat with a rock in it:
OK, it’s not actually a boat, it’s part of a plastic bottle. Also, the “rock” is a lead weight and the “pond” is a beaker. But this way we can see what happens to the water level when we drop an object into it.
When a boat is floating on water, two forces are acting on it. First, there is the downward-pulling gravitational force, which is equal to the mass of the boat and everything on it (m) times the gravitational field (g = 9.8 newtons per kilogram). We often call this product the “weight.”
The other force is the upward-pushing buoyancy interaction with the water. Two things are true about this buoyancy force. First, if the boat is floating, then the upward buoyancy must be equal to the weight of the boat. Second, the buoyancy force is equal to the weight of the water displaced by the boat.
We can calculate this buoyancy force by taking the volume of the water displaced (Vd) and using the density of water (ρw) along with the gravitational field (g).