## The Displacement Problem Of the Rock in the Boat - Question of the Week 1/20-1/24

Suppose that you are in a boat in a closed pond, so no water can flow in or out of the pond. In your boat you have a large rock. A friend marks the water level on the side of the pond, then you throw the rock out of the boat into the pond, and it quickly sinks to the bottom. A model of this situation is shown below, where the boat floats in an aquarium with a lead weight rock; pieces of black tape mark the water level.

Which of the following statements most accurately describes what happens to the water level in the pond after the rock has been taken out of the boat and allowed to sink into the pond?

• (a) The water level in the pond will be higher.
• (b) The water level in the pond will be lower.
• (c) The water level in the pond will remain the same.

After January 20th, 2014, click Read More for the answer.

The answer is (b); the water level in the pond will go down, as seen in the photograph at the right below. The original photograph with the rock in the boat is shown at the left for comparison.

Many middle school students are able to cite the relevant "laws of buoyancy:"

• A floating body displaces its weight in water.
• A submerged body displaces its volume in water.

However, many of those same students have never been taught exactly what "displacement" means. Note that if you push the boat down into the water, it displaces more water, and the water level in the tank (or pond) must rise.

When the rock is in the boat, it is floating, so it displaces its weight in water - a large amount of water. However, after it has sunk to the bottom of the pond, it displaces its volume in water - much less water, because the lead weight (or a rock) is much more dense than water.