Buoyancy: A board that is 20.0 cm wide, 5.00 cm thick, and 3.00 m long has a density 350 kg/m³. The board is floating partially submerged in water of density 1000 kg/m³. What fraction of the volume of the board is above the surface of the water?

Question

Quizplus · Accepted Answer

First, find the weight of the board using the density and volume:
weight = density x volume x gravity = (350 kg/m^3) x (20.0 cm x 5.00 cm x 3.00 m) x (9.81 m/s^2) = 1029.15 N

Next, find the buoyant force on the board using the displaced water:
buoyant force = weight of water displaced = density of water x volume of displaced water x gravity = (1000 kg/m^3) x (20.0 cm x 3.00 m x x) x (9.81 m/s^2) = (5886 N/m) x x

The board will float when the buoyant force is equal to the weight, so:
1029.15 N = (5886 N/m) x x
x = 0.175 m or 17.5 cm
This means that 17.5 cm of the board is submerged in the water, and the rest is above the surface.

To find the fraction of the volume above water, we need to find the total volume of the board and subtract the volume that is submerged:
volume = length x width x height = 3.00 m x 0.20 m x 0.050 m = 0.03 m^3
volume submerged = length x width x depth = 3.00 m x 0.20 m x 0.175 m = 0.0105 m^3
fraction above water = (volume - volume submerged) / volume = (0.03 m^3 - 0.0105 m^3) / 0.03 m^3 = 0.65
Therefore, the fraction of the volume of the board above the surface of the water is 0.650, or choice (B).

Buoyancy: a Board That Is 20