What happens to the water level when you throw a rock overboard of a boat?

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Physics questions are the most fun when people don't immediately agree on the answer. What seems intuitive and obvious is sometimes not. We could argue about the solution for hours, and even learn something at the end.

Here's one of those seemingly obvious questions that's been aro Phone Number List und for a long time: Suppose you're carrying a huge rock in a boat floating in a very small pond. If you throw it overboard, will the water level rise, fall, or stay the same?

The physics behind the movement of water as you float on it
Go ahead and discuss 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:

Measuring glass within a larger measuring glass
My boat with a rock inside. RHETT ALLAIN
Okay, it's not a jar, it's part of a plastic bottle. Furthermore, the “rock” is a lead object and the “pond” is a laboratory beaker. But this way we will see what happens to the water level when we drop an object into it.

When a boat floats on water, two forces act on it. First, the gravitational force, which pulls downward and is equal to the mass of the ship, and everything on it (m), multiplied by the gravitational field (g = 9.8 newtons per kilogram). We normally call this result “ weight ”.

The other force is the interaction of buoyancy with water, which pushes upward. Two facts are true regarding this buoyant force . First, if the boat floats, the upward buoyant force must be equal to the weight of the boat. Second, the buoyant force is equal to the weight of the water displaced by the boat.

We can calculate this buoyant force by taking the volume of displaced water (V d ) and using the density of the water (ρ w ) along with the gravitational field (g).

Formula to calculate buoyant force
Buoyancy force. RHETT ALLAIN
Once this is done, we can see our tiny boat in a small pond. To simplify the situation as much as possible, let's assume that it has massless walls, which is not a crazy approximation, since my boat is actually a plastic bottle. That means the only weight is the rock. But don't worry, I'll give you a more realistic example later. Below I show you a diagram of the forces:



Since this rock is much smaller than the boat, it displaces less water than when it was on the floating vehicle. This means that the buoyant force pushing up is also smaller, and is no longer strong enough to balance the gravitational force pushing down. The rock therefore rests on the floor of the pond (or beaker), providing an additional upward force (F f ).

With a lower buoyant force, the water displaced is less. That means the time has come to reveal the answer to our question: the water level will go down !

Are you surprised? People usually think that the water level will rise, because the rock will displace it and cause the level to rise, but they are wrong, and it doesn't matter. We often base our answers on our previous life experiences, and chances are you've done something like adding rocks to a glass of water to raise its level. It seems reasonable to imagine that the same thing will happen in this case.

But putting pebbles in a glass is different from our boat situation, because these are not floating on a boat, they are not in the water in the first place. You will have them in your pocket, or something similar, and taking one out of it has no influence on the water level. When you put that rock in the glass, the water has nowhere to go but up and the water level rises. It's the same thing that would happen if you threw a stone into a pond from the shore.

On the other hand, a rock on a boat is already displacing water before it falls into it. That's why the two cases are different, and that's what makes this a fun physics question.