The average density of an object is what ultimately determines whether it floats. Density and Archimedes’ Principleĭensity plays a crucial role in Archimedes’ principle. (a) What is the mass of this amount of foil? (b) If the foil is folded to give it four sides, and paper clips or washers are added to this “boat,” what shape of the boat would allow it to hold the most “cargo” when placed in water? Test your prediction. Use a piece of foil that measures 10 cm by 15 cm. In equation form, Archimedes’ principle isĪ piece of household aluminum foil is 0.016 mm thick. Stated in words, Archimedes’ principle is as follows: The buoyant force on an object equals the weight of the fluid it displaces. 287–212 B.C.) that he stated this principle long before concepts of force were well established. It is a tribute to the genius of the Greek mathematician and inventor Archimedes (ca. This weight is supported by the surrounding fluid, and so the buoyant force must equal w fl w fl, the weight of the fluid displaced by the object. The space it occupied is filled by fluid having a weight w fl w fl. That is, F B = w fl F B = w fl,a statement of Archimedes’ principle. Since this weight is supported by surrounding fluid, the buoyant force must equal the weight of the fluid displaced. (b) If the object is removed, it is replaced by fluid having weight w fl w fl. If F B F B is less than the weight of the object, the object will sink. If F B F B is greater than the weight of the object, the object will rise. The buoyant force is always present whether the object floats, sinks, or is suspended in a fluid.įigure 11.19 (a) An object submerged in a fluid experiences a buoyant force F B F B. If the buoyant force equals the object’s weight, the object will remain suspended at that depth. If the buoyant force is less than the object’s weight, the object will sink. (See Figure 11.18.) If the buoyant force is greater than the object’s weight, the object will rise to the surface and float. There is a net upward, or buoyant force on any object in any fluid. This means that the upward force on the bottom of an object in a fluid is greater than the downward force on the top of the object. (credit: Crystl)Īnswers to all these questions, and many others, are based on the fact that pressure increases with depth in a fluid. (credit: Allied Navy) (c) Helium-filled balloons tug upward on their strings, demonstrating air’s buoyant effect. (b) Submarines have adjustable density (ballast tanks) so that they may float or sink as desired. Figure 11.17 (a) Even objects that sink, like this anchor, are partly supported by water when submerged.
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