Four cube-shaped blocks are floating in equilibrium in a tank of water. Blocks A, B, and C have the same size. Block D is larger than the others. The masses of the blocks are unknown.Part (a) Rank the magnitudes of the buoyant forces acting on blocks A, B, C, and D in order of greatest to smallest.Part (b) Rank the masses of the blocks from greatest to smallest.Part (c) Rank the densities of the blocks from greatest to smallest.

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08-12-2022
Physics

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Four cube-shaped blocks are floating in equilibrium in a tank of water. Blocks A, B, and C have the same size. Block D is larger than the others. The masses of the blocks are unknown.Part (a) Rank the magnitudes of the buoyant forces acting on blocks A, B, C, and D in order of greatest to smallest.Part (b) Rank the masses of the blocks from greatest to smallest.Part (c) Rank the densities of the blocks from greatest to smallest.

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AnnuG AnnuG · Answer 1 · 2022-12-15T07:26:22-05:00

The ranking of magnitude of buoyant forces of the four boxes from greatest to smallest is FD>FA=FB>FC. The ranking of masses of the blocks from greatest to smallest is mD>mA=mB>mC and the ranking of densities of the blocks from greatest to smallest is pA=pB=pD>pC.

(a) The buoyant force is the upward force exerted on an object wholly or partly immersed in a fluid. This upward force is also called Upthrust. Due to the buoyant force, a body submerged partially or fully in a fluid appears to lose its weight, i.e. appears to be lighter. It depends on acceleration due to gravity, volume of fluid and fluid density.

Thus, the order of force on the block from greatest to smallest is FD>FA=FB>FC.

(b) Mass (symbolized m) is a dimensionless quantity representing the amount of matter in a particle or object. The standard unit of mass in the International System (SI) is the kilogram (kg). If an object's average density is less than that of the surrounding fluid, it will float. The reason is that the fluid, having a higher density, contains more mass and hence more weight in the same volume. The buoyant force, which equals the weight of the fluid displaced, is thus greater than the weight of the object.

Thus, the order of mass on the block from greatest to smallest is mD>mA=mB>mC.

(c) Buoyant force is directly proportional to the density of the liquid displaced. So, greater the density of the liquid, greater is the buoyant force due to the liquid. So, the order of density on the block from greatest to smallest is pA=pB=pD>pC.

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