Final answer:
To calculate the buoyant force acting on the wooden block, we need to determine the volume of the block and use the formula: Buoyant force = weight of fluid displaced. The fraction of the block that is submerged can be found by comparing the buoyant force to the weight of the block. In this case, the buoyant force is approximately 1.69 times the weight of the block.
Step-by-step explanation:
To determine the buoyant force on the block, we need to calculate the volume of the block first. The volume of a rectangular block can be found by multiplying its three dimensions together, so here the volume would be 10 cm x 15 cm x 36 cm = 5,400 cm^3. To find the volume in cubic meters, we convert using the conversion factor that 1 m^3 = 1,000,000 cm^3, resulting in a volume of 0.0054 m^3.
The buoyant force can be calculated using the formula: Buoyant force = weight of fluid displaced = density of fluid x volume of fluid displaced x g (acceleration due to gravity).
In this case, the weight of fluid displaced can be calculated using the buoyant force formula as weight of fluid displaced = density of fluid x volume of fluid displaced x g (acceleration due to gravity).
Here, the density of fresh water is about 1000 kg/m³ and the acceleration due to gravity is 9.8 m/s². Plugging in these values, the buoyant force can be calculated as 1000 kg/m³ x 0.0054 m³ x 9.8 m/s² = 52.92 N.
To find the fraction of the block that is submerged, we need to compare the weight of the block to the buoyant force. The weight of the block can be calculated using the formula: Weight = density of block x volume of block x g. Here, the density of the block can be found using the formula: density of block = specific gravity x density of water. Plugging in the values, the density of block = 0.60 x 1000 kg/m³ = 600 kg/m³.
Using the density of the block, volume of the block and acceleration due to gravity, the weight of the block can be calculated as 600 kg/m³ x 0.0054 m³ x 9.8 m/s² = 31.392 N.
To find the fraction of the block that is submerged, we divide the buoyant force by the weight of the block as follows: Fraction submerged = buoyant force / weight of block = 52.92 N / 31.392 N ≈ 1.69.