Most modern counterfeits are not pure silver. You can see from Table 1 that this density is very close to that of pure silver, appropriate for this type of ancient coin. We can now find the density of the coin using the definition of density: This is also the volume of the coin, since it is completely submerged. As noted, the mass of the water displaced equals the apparent mass loss, which is m w = 8. The volume of water is where m w is the mass of water displaced. The volume of water displaced V w can be found by solving the equation for density for V. The volume of the coin equals the volume of water displaced. To calculate the coin’s density, we need its mass (which is given) and its volume. Calculate its density, given that water has a density of 1.000 g/cm 3 and that effects caused by the wire suspending the coin are negligible. When the coin is submerged in water as shown in Figure 7, its apparent mass is 7.800 g. The mass of an ancient Greek coin is determined in air to be 8.630 g. The next example illustrates the use of this technique. That isĪpparent weight loss = weight of fluid displacedĪpparent mass loss = mass of fluid displaced. Alternatively, on balances that measure mass, the object suffers an apparent mass loss equal to the mass of fluid displaced. The object suffers an apparent weight loss equal to the weight of the fluid displaced. This, in turn, means that the object appears to weigh less when submerged we call this measurement the object’s apparent weight. Archimedes’ principle states that the buoyant force on the object equals the weight of the fluid displaced. All of these calculations are based on Archimedes’ principle. This same technique can also be used to determine the density of the fluid if the density of the coin is known. The density of the coin, an indication of its authenticity, can be calculated if the fluid density is known. These two measurements are used to calculate the density of the coin.Īn object, here a coin, is weighed in air and then weighed again while submerged in a liquid. (b) The apparent weight of the coin is determined while it is completely submerged in a fluid of known density.
Now we can obtain the relationship between the densities by substituting into the expression. The volume submerged equals the volume of fluid displaced, which we call V fl. The fraction submerged is the ratio of the volume submerged to the volume of the object, or We can derive a quantitative expression for the fraction submerged by considering density. In Figure 4, for example, the unloaded ship has a lower density and less of it is submerged compared with the same ship loaded. The extent to which a floating object is submerged depends on how the object’s density is related to that of the fluid. Likewise, an object denser than the fluid will sink. The buoyant force, which equals the weight of the fluid displaced, is thus greater than the weight of the object. This is because the fluid, having a higher density, contains more mass and hence more weight in the same volume. If its average density is less than that of the surrounding fluid, it will float. The average density of an object is what ultimately determines whether it floats. The buoyant force is always present whether the object floats, sinks, or is suspended in a fluid.ĭensity plays a crucial role in Archimedes’ principle. 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 2.) 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. (a) Even objects that sink, like this anchor, are partly supported by water when submerged.