19. Fluid Mechanics

A block floats with 40% of its volume above water. When you place it on an unknown liquid, it floats with 30% of its volume above. What is the density of the unknown liquid?

(II) A cube of side length 10.0 cm and made of unknown material floats at the surface between water and oil. The oil has a density of 810 kg/m³. If the cube floats so that it is 72% in the water and 28% in the oil, what is the mass of the cube and what is the buoyant force on the cube?

A slab of ice floats on a freshwater lake. What minimum volume must the slab have for a 65.0-kg woman to be able to stand on it without getting her feet wet?

Why will a block of iron float in mercury but sink in water?

Which property do all floating objects have in common when placed in a fluid?

(II) Archimedes’ principle can be used not only to determine the specific gravity of a solid using a known liquid (Example 13–10). The reverse can be done as well. (a) As an example, a 3.80-kg aluminum ball has an apparent mass of 2.10 kg when submerged in a particular liquid: calculate the density of the liquid. (b) Determine a formula for finding the density of a liquid using this procedure.

A coin is dropped into a shallow lake. As the coin sinks deeper, the buoyant force acting on the coin:

A cubical block of wood, 10.0 cm on a side, floats at the interface between oil and water with its lower surface 1.50 cm below the interface (Fig. E12.33). The density of the oil is 790 kg/m³. (a) What is the gauge pressure at the upper face of the block? (b) What is the gauge pressure at the lower face of the block?

You want to build a large storage container, with outer walls and an open top, as shown, so that you can load things into it, while it floats on fresh water, without any water getting inside. If the bottom face of the container measures 3.0 m by 8.0 m, how high should the side walls be, such that the combined mass of container and inside load is 100,000 kg?

A 950-kg cylindrical can buoy floats vertically in sea-water. The diameter of the buoy is 0.900 m. Calculate the additional distance the buoy will sink when an 80.0-kg man stands on top of it.

A ship, carrying fresh water to a desert island in the Caribbean, has a horizontal cross-sectional area of 2240 m² at the waterline. When unloaded, the ship rises 8.55 m higher in the sea. How much water (m³) was delivered?

The average density of the body of a fish is 1080 kg/m³ . To keep from sinking, a fish increases its volume by inflating an internal air bladder, known as a swim bladder, with air. By what percent must the fish increase its volume to be neutrally buoyant in fresh water? The density of air at 20°C is 119 kg/m³.

A 6.00-cm-diameter sphere with a mass of 89.3 g is neutrally buoyant in a liquid. Identify the liquid.