The bottom of a flat-bottomed aluminum boat has an area of 4.4 m² and the boat's mass is 62 kg.When set afloat in water,how far below the water surface is the boat bottom? (water density = 1.0 × 10³ kg/m³)

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Quizplus · Accepted Answer

The buoyant force on the boat is equal to the weight of the water displaced by the boat. The volume of water displaced is equal to the area of the bottom of the boat times the distance that the boat is submerged. The density of water is 1.0 × 10³ kg/m³, so the mass of the water displaced is equal to the volume of water displaced times the density of water. The mass of the water displaced is equal to the mass of the boat, so the volume of water displaced is equal to the mass of the boat divided by the density of water. The distance that the boat is submerged is equal to the volume of water displaced divided by the area of the bottom of the boat.$$V = \frac{m}{ ho} = \frac{62 ext{ kg}}{1.0 imes 10^3 ext{ kg/m}^3} = 0.062 ext{ m}^3$$$$d = \frac{V}{A} = \frac{0.062 ext{ m}^3}{4.4 ext{ m}^2} = 0.014 ext{ m}$$

The Bottom of a Flat-Bottomed Aluminum Boat Has an Area