An 8,000 cm³ block of wood is fully immersed in a deep water tank, then tied to the bottom. When the block is released and reaches equilibrium, you measure the tension on the string to be 12 N. What is the density of the wood?

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.]

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(III) 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.

When an object of unknown mass and volume is fully immersed in large oil (800 kg/m³ ) container and released from rest, it stays at rest. Calculate the density of this object.

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?

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?