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11.2.1.2: Explorations

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    Exploration 1: Floating and Density

    How can a boat made out of a material more dense than water float? The block has a mass of \(0.185\text{ kg}\) (position is given in centimeters). If this block is a cube, what is the density of the block? Note that since it is greater than water (\(1000\text{ kg/m}^{3}\)) the block sinks as shown in the animation. Restart.

    We reshape the block so that it has the same depth into the screen, but is wider and taller with walls that are \(0.21\text{-cm}\) thick.

    1. When the animation runs, what is the volume of water displaced (the dimension of the water container into the screen that you cannot see is \(10\text{ cm}\))?
    2. Using the density of water (\(1000\text{ kg/m}^{3}\)), find the mass of the water displaced. Show that it is equal to the mass of the reshaped block. Thus the block floats.
    3. Another way to think about this is that in its new shape the block has an effective density (total mass/total volume) less than that of the water. Divide the mass (\(0.185\text{ kg}\)) by the new volume to find the new effective density of the block.
    4. How does the effective density compare to the density of water?

    The weight (\(\text{mass}\ast 9.8\text{ m/s}^{2}\)) of the water displaced (even if the displaced water leaves the container) is equal to the buoyant force on the block. In the case of a floating object, the buoyant force is equal to the weight of the floating object.

    Exploration authored by Anne J. Cox.

    Exploration 2: Buoyant Force

    When an object is put into a liquid, it experiences a buoyant force that is equal to the weight of the liquid the object displaces. The force on the wire is given as the block is slowly lowered into the liquid (position is given in centimeters and force is given in newtons). You can change the mass of the block between \(0.125\text{ kg}\) and \(0.375\text{ kg}\) and the density of the liquid between \(500\text{ kg/m}^{3}\) and \(1000\text{ kg/m}^{3}\). The object is in static equilibrium when the clock stops. Restart.

    1. What is the weight of the block and the tension in the string when the block is in the liquid? Therefore, what is the value of the buoyant force? The buoyant force and the tension in the string (as the force on the support wire) act upward and the weight acts down.
    2. What is the volume of the block in the liquid—either the submerged part of the block if the block is partially submerged when you paused it or the entire block if it is completely submerged (the dimension of the block that is into the screen is \(5\text{ cm}\))?
    3. What is the volume of the water that is displaced by the block (the dimension of both water containers into the screen is \(10\text{ cm}\))? Verify that this is equal to the answer in (b).
    4. What is the mass of the liquid displaced? What is the weight of the liquid displaced? Check that this is equal to the buoyant force.
    5. Pick two different masses and densities and verify that the buoyant force is equal to the weight of the water displaced.

    Exploration authored by Anne J. Cox.

    Exploration 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, \(1.01\times 10^{5}\text{ Pa}\), 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 (\(1000\text{ kg/m}^{3}\)).

    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 \(700\text{ kg/m}^{3}\).
    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.

    Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.

    This page titled 11.2.1.2: Explorations is shared under a CC BY-NC-ND license and was authored, remixed, and/or curated by Wolfgang Christian, Mario Belloni, Anne Cox, Melissa H. Dancy, and Aaron Titus, & Thomas M. Colbert.