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, we need to find the weight of the board.
Volume of the board = (20.0 cm) x (5.00 cm) x (3.00 m) = 0.3 m^3
Weight of the board = Volume x Density = 0.3 m^3 x 350 kg/m^3 = 105 kg
Next, we need to find the buoyant force acting on the board.
Buoyant force = Volume of water displaced x Density of water x Gravity
Volume of water displaced = (20.0 cm) x (3.00 m) x (x m) where x is the fraction of the volume above the surface of the water.
Volume of water displaced = 0.6 m^3 x
Density of water = 1000 kg/m^3
Gravity = 9.81 m/s^2
Buoyant force = (0.6 m^3 x x) x 1000 kg/m^3 x 9.81 m/s^2 = 5886 x x N
Since the board is floating, the weight of the board is equal to the buoyant force acting on it.
105 kg = 5886 x x N
x ≈ 0.0179 or 1.79%
Therefore, the fraction of the volume of the board above the surface of the water is approximately 1.79%, or 0.0179 as a decimal. The fraction of the volume below the surface of the water is approximately 98.21%, or 0.9821 as a decimal. Therefore, the fraction of the volume above the surface of the water is 0.9821, which is closest to choice B, 0.650.

A Board That Is 20