(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?

(II) A crane lifts the 21,000-kg steel hull of a sunken ship out of the water. Determine

(a) the tension in the crane’s cable when the hull is fully submerged in the water , and

(III) A 3.75-kg block of wood (SG = 0.50) floats on water. What minimum mass of lead, hung from the wood by a string, will cause the block to sink?

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?

A raft is made of 12 logs lashed together. Each is 45 cm in diameter and has a length of 6.5 m. How many people can the raft hold before they start getting their feet wet, assuming the average person has a mass of 68 kg? Do not neglect the weight of the logs. Assume the specific gravity of wood is 0.60.

(b) To ensure that a ship is in stable equilibrium, would it be better if its center of buoyancy was above, below, or at the same point as its center of gravity? Explain.

<IMAGE>

A simple model (Fig. 13–62) considers a continent as a block ( density ≈ 2800 kg/m³) floating in the mantle rock around it ( density ≈ 3300 kg/m³) . Assuming the continent is 35 km thick (the average thickness of the Earth’s continental crust), estimate the height of the continent above the surrounding mantle rock.

<IMAGE>

A copper (Cu) weight is placed on top of a 0.40-kg block of wood (density = 0.60 x 10³ kg/m³) floating in water, as shown in Fig. 13–60. What is the mass of the copper if the top of the wood block is exactly at the water’s surface?

<IMAGE>

(II) A scuba tank, when fully submerged, displaces 15.7 L of seawater. The tank itself has a mass of 14.0 kg and, when “full,” contains 3.00 kg of air. Assuming only its weight and the buoyant force act on the tank, determine the net force (magnitude and direction) on the fully submerged tank at the beginning of a dive (when it is full of air) and at the end of a dive (when it no longer contains any air).