Question

The raft consists of a uniform platform having a mass of 2 Mg and four floats, each having a mass of 120 kg and a length of 4m. Determine the height h at which the platform floats from the water's surface. Take the density of water to be 1Mg/(m³).

Answer 1

To determine the height at which the platform floats from the water's surface, we need to consider the buoyant force acting on it. The buoyant force is equal to the weight of the water displaced by the platform. Using the formula for the buoyant force, we can set it equal to the weight of the platform and solve for the height h.

Step-by-step explanation:

To determine the height at which the platform floats from the water's surface, we need to consider the buoyant force acting on it. The buoyant force is equal to the weight of the water displaced by the platform.

Each float displaces a volume of water equal to its length multiplied by its cross-sectional area. The total volume of water displaced by the floats adds up to the total volume of the platform.

Using the formula for the buoyant force, we can set it equal to the weight of the platform and solve for the height h:

Buoyant force = Weight of platform

(Density of water) × (Volume of water displaced) × (gravitational acceleration) = (Mass of platform + Mass of floats) × (gravitational acceleration)

Once we solve the equation for h, we will have the height at which the platform floats from the water's surface.