Problem 1: Floating Wooden Cube

A wooden cube has side length $0.50\text{ m}$ and specific gravity $0.60$. Determine the submerged depth when it floats in water.

Problem 2: Cable Tension on a Submerged Concrete Block

A $500\text{ kg}$ concrete block with density $2400\text{ kg/m}^3$ is fully submerged in water and supported by a vertical cable. Determine the cable tension.

Problem 3: Apparent Weight of a Submerged Steel Object

A steel object has volume $0.020\text{ m}^3$ and density $7850\text{ kg/m}^3$. Determine its true weight and apparent weight when fully submerged in water.

Problem 4: Draft of a Rectangular Pontoon

A rectangular pontoon is $8\text{ m}$ long and $4\text{ m}$ wide and weighs $400\text{ kN}$. Determine its draft in seawater with specific weight $10.05\text{ kN/m}^3$.

Problem 5: Metacentric Height of a Loaded Pontoon

A pontoon is $10\text{ m}$ long, $7\text{ m}$ wide, and $2.5\text{ m}$ deep. The pontoon weighs $700\text{ kN}$ with its center of gravity at mid-depth. A $300\text{ kN}$ load has its center of gravity $3\text{ m}$ above the deck. The pontoon floats in seawater with $\gamma=10.104\text{ kN/m}^3$. Determine the transverse metacentric height.

Problem 6: Heel Caused by a Transverse Load Shift

The pontoon in Problem 5 has displacement weight $1000\text{ kN}$ and $GM=1.070\text{ m}$. A $50\text{ kN}$ load is shifted $3.0\text{ m}$ sideways. Estimate the small heel angle.

Problem 7: Hydrometer Reading

A hydrometer weighs $0.020\text{ N}$ and has a uniform stem diameter of $6\text{ mm}$. Its stem immersion is $50\text{ mm}$ in water and $70\text{ mm}$ in an unknown liquid. Determine the unknown liquid specific gravity, assuming the same bulb volume in both cases.

Problem 8: Fraction of an Iceberg above Seawater

Ice has density $917\text{ kg/m}^3$ and seawater has density $1025\text{ kg/m}^3$. Determine the percentages of an iceberg volume below and above the water surface.