A tub of water rests on a scale as shown in Fig. 13–61. The weight of the tub plus water is 100 N. A 50-N concrete brick is tied by a cord to a fixed arm and lowered into the water but does not touch the bottom of the tub. What does the scale read now? [Hint: Draw two free-body diagrams, one for the brick and a second one for the tub + water + brick.]

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.

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.

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?

(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).

A common effect of surface tension is the ability of a liquid to rise up a narrow tube due to capillary action. Show that for a narrow tube of radius r placed in a liquid of density ρ and surface tension γ, the liquid in the tube will reach a height h = 2γ/ρgr above the level of the liquid outside the tube, where g is the gravitational acceleration. Assume that the liquid “wets” the tube and that the liquid surface is vertical at the contact with the inside of the tube.

Estimate the diameter of a steel needle that can just barely remain on top of water due to surface tension. (See Figs. 13–38 and 13–39a, and Table 13–1.)

Calculate the true mass (in vacuum) of an aluminum sphere whose apparent mass is 4.0000 kg when weighed in air.

How many helium-filled balloons would it take to lift a person? Assume the person has a mass of 72 kg and that each helium-filled balloon is spherical with a diameter of 36 cm.