a raft is consttructed of wood having a density of 6000kg/m3. the surface area of the bottom of the raft is 5.7m2, and the volume of the raft is .60m3. when the raft is placed in fressh water having a density of 1000kg/m3, how deep is the bottom of the raft below water level.
To determine the depth of the bottom of the raft below the water level, we need to consider the principles of buoyancy and Archimedes' principle.
Step 1: Calculate the weight of the raft
The weight of an object can be calculated using the formula: Weight = Mass × Gravity
Given:
Density of wood = 6000 kg/m³
Volume of the raft = 0.60 m³
The mass of the raft can be calculated using the formula: Mass = Density × Volume
Mass of the raft = 6000 kg/m³ × 0.60 m³
Step 2: Calculate the buoyant force acting on the raft
The buoyant force can be calculated using the formula: Buoyant force = Volume of fluid displaced × Density of the fluid × Gravity
Given:
Density of fresh water = 1000 kg/m³
Surface area of the bottom of the raft = 5.7 m²
The volume of fluid displaced is equal to the volume of the raft because the entire raft is submerged in water.
Volume of fluid displaced = Volume of the raft = 0.60 m³
Buoyant force = 0.60 m³ × 1000 kg/m³ × 9.8 m/s²
Step 3: Calculate the depth of the bottom of the raft below the water level
The buoyant force is equal to the weight of the raft when the raft is in a state of equilibrium.
Weight of the raft = Buoyant force
Now we can equate the two values:
Weight of the raft = Mass of the raft × Gravity
Solve for the weight of the raft first:
Weight of the raft = 6000 kg/m³ × 0.60 m³ × 9.8 m/s²
Finally, we can calculate the depth of the bottom of the raft below the water level using the formula for pressure at a certain depth:
Pressure = Density × Gravity × Depth
The pressure on the bottom of the raft is the same as the pressure at that depth.
Pressure on the bottom of the raft = Pressure of the fluid at the water level
Solve for the depth:
Pressure on the bottom of the raft = Density of fresh water × Gravity × Depth
Now we can equate the weight of the raft to the pressure on the bottom of the raft and solve for the depth:
6000 kg/m³ × 0.60 m³ × 9.8 m/s² = 1000 kg/m³ × 9.8 m/s² × Depth
Simplify the equation and solve for Depth:
Depth = (6000 kg/m³ × 0.60 m³) / 1000 kg/m³
Calculating the above equation:
Depth = 3.6 meters
Therefore, the bottom of the raft is located 3.6 meters below the water level.