Question

1.How does the buoyant force determined from the mass of the fluid displaced compare with the difference in the dry and wet weights of each object? Is Archimedes' priciple verified?

2.How does the density determined for each object compare with its accepted value? You will have to look up the densities of Al, Cu, and Pb. Note : Discuss with the percent error

Answer 1

a)

Buoyancy arises from the fact that fluid pressure increases with depth and from the fact that the increased pressure is exerted in all directions (Pascal's principle) so that there is an unbalanced upward force on the bottom of a submerged object.

                Since the "water ball" at left is exactly supported by the difference in pressure and the solid object at right experiences exactly the same pressure environment, it follows that the buoyant force on the solid object is equal to the weight of the water displaced (Archimedes' principle).

b )

Suppose you had equal sized balls of cork, aluminum and lead, with respective specific gravities of 0.2, 2.7, and 11.3 . If the volume of each is 10 cubic centimeters then their masses are 2, 27, and 113 gm.

Each would displace 10 grams of water, yielding apparent masses of -8 (the cork would accelerate upward), 17 and 103 grams respectively.

The behavior of the three balls would certainly be different upon release from rest in the water. The cork would bob up, the aluminum would sink, and the lead would sink more rapidly. But the buoyant force on each is the same because of identical pressure environments and equal water displacement. The difference in behavior comes from the comparison of that buoyant force with the weight of the object.