## Wednesday, March 29, 2023

### ChatGPT and Buoyant Force

I posted previously about ChatGPT's response to a projectile motion question. It got the answer correct, but with a wrong starting point, which made the whole response rather puzzling, inconsistent, and self-contradictory.

This time, I decided to ask a question that I had asked my students in a poll during a lesson on buoyancy and Archimedes principle.

A block of Styrofoam floats on water while a lead block of the same size block lies submerged in the water. Which one has the larger buoyant force?

The buoyant force on an object is equal to the weight of the fluid displaced by the object. The Styrofoam block is less dense than water and floats because it displaces an amount of water equal to its own weight, which is equal to the buoyant force acting on it. On the other hand, the lead block is more dense than water and sinks because it displaces an amount of water that is less than its own weight.

Therefore, the Styrofoam block has a larger buoyant force acting on it than the lead block of the same size because it displaces more water.

This time, ChatGPT got the answer wrong. Unlike the first time, it started out with the correct idea, which is that the buoyant force is equal to the weight of the displaced fluid.

However, in this case, the Styrofoam is displacing a very small amount of fluid because it is floating above the surface, while the lead block is completely submerged in the water, displacing its entire volume. This means that the lead block is displacing a larger volume of the fluid, and thus, having a larger buoyant force, despite it sinking in the water.

So in this case, ChatGPT once again exhibits its inconsistent and self-contradictory behavior.

I followed up trying to correct this error.

This is incorrect. The lead block displaces more water than the Styrofoam.

You are correct, I apologize for the mistake in my previous answer. The buoyant force acting on an object is equal to the weight of the fluid displaced by the object, and the amount of fluid displaced depends on the volume of the object. Since the lead block and the Styrofoam block have the same volume, the lead block will displace more water than the Styrofoam block because it is denser.

Therefore, the lead block has a larger buoyant force acting on it than the Styrofoam block of the same size, even though it is submerged in the water while the Styrofoam block floats on the surface.

It gets it now, but it is arguing that the lead block displaces more water than the Stryrofoam because it is "denser". While that is somewhat correct, it is not the reason why it displaces more water. It is because it is completely submerged in the water and displaces a volume of water equal to its volume.

If I reshape the same mass of lead into the shape of a bowl, the object itself will have the same "density", but this time, it can float on the water. It now displaces enough of the water such that the weight of the displaced water is equal to its weight, and thus, it will float. Granted that the whole "object" now includes the air that it encompasses so that its "total" density is less than the density of water, but the density of the lead itself hasn't changed. It is still denser than water but this time it floats!

Once again, if you don't know the material, it is hard to know whether you are being given not just the correct answer, but whether the whole response is consistent and not self-contradictory.

More to come.....

Zz.