## Exploration 14.3: Buoyancy and Oil on Water

This Exploration will address the buoyant force in more depth (pun intended). Specifically, what happens if we put an object in two "layers" of fluids? Assume the brown block is a cube (position is given in meters and pressure is given in pascals). Restart.

Note: The format of the pressure is written in shorthand. For example atmospheric pressure, 1.01x105 Pa, is written as 1.01e+005.

Move the pressure indicator and measure the pressure at the bottom of the wooden block and at the top of the block.

1. If the block is a cube, what is the force on the block due to the water (buoyant force)?
2. What, then, is the weight of the block? What is the density of the block?
3. Another method: How much (what percentage) of the block is submerged? Check that the density of the block is that same percentage of the density of water (1000 kg/m3).

Now consider what would happen if we put the block in an oil with a different density.

1. Predict what you expect will happen if we put the block in an oil with a density of 700 kg/m3.
2. Try it. Was your prediction correct? Explain.
3. What is the pressure at the bottom of the block and at the top of the block? What is the buoyant force on the block in the oil?

Now, suppose the wood block is put in a mixture of water on the bottom with oil on the top (the oil floats on the water and doesn't mix with the water).

1. What do you expect will happen? Why?
2. Try it. Is more or less of the block submerged in water in this case compared with the block simply floating in water (without oil)? Why?
3. One way to look at what happened is to measure the pressures. Find the pressure at the bottom of the block and at the top of the block.
4. What is the pressure difference and thus the net buoyant force on the block?
5. In order for a block to float only in water (with air on top), to get the same pressure difference to support the block, why does the block need to be lower in the water? (Think about the density of air compared with the density of oil and, therefore, the change in pressure with depth in air and in the oil.)

Another way to look at this is to compare the buoyant forces.

1. In comparison with the block floating in water only, has the buoyant force increased, decreased, or stayed the same?
2. What is the volume of water that the block displaces?
3. What is the weight of that water?
4. What is the volume of oil that the block displaces?
5. What is the weight of the displaced oil?
6. How do those two compare with the weight of the block? Exploration authored by Anne J. Cox.

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