The bottom of a flat-bottomed aluminum boat has an area of 4.0 m²,and the boat's mass is 120 kg.When set afloat in water,how far below the water surface is the boat bottom? (water density = 1.0 × 10³ kg/m³)

Question

Quizplus · Accepted Answer

The buoyant force acting on the boat is equal to the weight of displaced water, which can be calculated using Archimedes' principle as:

Buoyant force = Density of water x Volume of displaced water x g
Buoyant force = 1000 kg/m^3 x (4.0 m^2 x 0.030 m) x 9.81 m/s^2
Buoyant force = 1177.2 N

Since the boat is in equilibrium, the buoyant force must be balanced by the weight of the boat. Therefore:

Weight of boat = Mass of boat x g
Weight of boat = 120 kg x 9.81 m/s^2
Weight of boat = 1177.2 N

Thus, the boat will sink until its weight is equal to the buoyant force, which means that the bottom of the boat will be at the water surface. Therefore, the boat bottom will be 0.030 m below the water surface.

Therefore, the answer is C.

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