The bottom of a flat-bottomed aluminum boat has an area of 4.20 m² and the boat's mass is 63.0 kg.When set afloat in water,how far below the water surface is the boat bottom? (water density = 1.00 × 10³ kg/m³)

Question

Quizplus · Accepted Answer

To find how far below the water surface the boat bottom is, we use the principle of buoyancy, which states that the weight of the displaced water equals the weight of the boat. The weight of the boat is $63.0 \, \text{kg} \times 9.8 \, \text{m/s}^2$. The volume of water displaced equals the weight of the boat divided by the density of water times gravity. Thus, the depth $d$ is given by $d = \frac{\text{Weight of boat}}{\text{Area} \times \text{Density of water} \times g}$. Substituting the given values, we find $d = 0.0150 \, \text{m}$.

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