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Buoyancy: Upward Force by Fluids (page 2)

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Author: Janice VanCleave

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The paper cup floats in the water. The water pushed out by the paper cup spills over into the measuring cup. You used this volume of water to calculate the buoyancy of the paper cup. For the example, an object that displaces 0.015 L of water has a buoyancy of 0.147 N.

Why?

The paper cup floats in the water, with about half of the paper cup below the surface of the water. The paper cup displaced (pushed aside) the amount of water equal to the volume of the paper cup below the water's surface. Buoyancy is the upward force of a fluid (a substance, a gas, or liquid, that flows and offers little resistance to a change in its shape when under pressure) on an object placed in it. The buoyancy of the water on the paper cup equals the weight of the water displaced by the paper cup. The Greek mathematician Archimedes (298-212 B.C.) is credited with discovering the law of buoyancy, which states that any object submerged or floating in a fluid is buoyed (lifted) by a force equal to the weight of the fluid displaced. Once you know the amount of water displaced, you can calculate the weight of the water displaced, which is equal to the buoyancy in newtons.

Try New Approaches

1. An object will float as long as its weight is equal to the weight of water it displaces. Compare the weight of the cup and coins with the weight of the water it displaces determined from the original experiment. Determine the weight of the cup and coins by using a food scale to measure the mass of the cup and the coins in grams. Then convert the gram measure to kilograms and use the equation F wt = m × g to determine the weight of the cup and coins in newtons.
2. What is the maximum weight at which the paper cup and its contents can remain afloat? Repeat the original experiment placing the paper cup in the water. As you add one coin at a time, make note of any change of position of the cup in the water. Continue to add coins until one more coin makes the paper cup sink. Remove one coin, then determine the weight of the dry cup and coins as before. Determine the weight of the water displaced by the cup. How do the two weights compare?

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1. If Archimedes' principle is correct, buoyancy on an object in water causes the object to have an apparent weight (FA) equal to the actual weight (Fwt) of the object as measured in air minus the weight of the water displaced by the object (FB), which is equal to buoyancy. An equation that expresses this relationship is: FA = (Fwt) – (FB).
2. Design a way to test this. One way is to determine the actual weight of a rock in air (Fwt) in newtons. Do this by using the previous method of measuring the mass of the rock on a food scale in kg, then calculate the weight using the equation F wt = m × g. Record the rock's weight (Fw) in a Buoyancy Data table like Table 12.1. Repeat the original experiment to determine the weight of the displaced water (FB)when the rock is placed in water. Record the weight (Fs) in the data table. Calculate the apparent weight (FA)of the rock using the equation FA = (Fwt) – FB) and record the results in the data table.

3. If two items of identical volume but different weights are submerged in water, would the buoyancy on each be the same? Design a way to determine this, such as by using a container that can be closed. Fill the container with different contents to change its weight.
4. How does the density of the fluid affect its buoyancy? Repeat the investigation using fluids with different densities, such as different concentrations of salt water. Since the density differences between the fluid concentrations may be slight, determine the densities by asking your teacher or maybe a pharmacist to measure the mass of a certain volume of each fluid on a scale accurate to at least 0.01 g. For more information about how things float, see Robert L. Lehrman, Physics the Easy Way (Hauppauge, N.Y.: Barron's, 1998), pp. 158–159.

Get the Facts

1. Most fish are able to remain suspended at depths beneath the surface of the water. They remain stable due to a condition known as neutral buoyancy. What forces create neutral buoyancy? How is a fish able to maintain neutral buoyancy? For information, see Mary and Geoff Jones, Physics (New York: Cambridge University Press, 1997), p. 56.
2. Air is a very light fluid with a density of only 1.25 × 10-3 glml (1.25 kg/m3). A few things, such as a balloon filled with helium or hot air, are light enough to float in air. Why can a balloon filled with hot air float in air? What is the flight ceiling for a hot-air balloon? For information, see Louis A. Bloomfield, How Things Work: The Physics of Everyday Life (New York: Wiley, 1997), pp. 128–134.
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