A raft is constructed of wood havig a density of 600kg/m^3. The surface area of the bottom of the raft is 5.7m^2 and the volume of the raft is .60m^3. When the raft is placed in fresh water having a density of 1000kg/m^3, how deep is the bottom of the raft below water level ?
To find out how deep the bottom of the raft is below the water level, we need to consider the buoyant force acting on the raft.
The buoyant force is the force exerted by a fluid (in this case, fresh water) on an object immersed in it, and it is equal to the weight of the fluid displaced by the object.
To find the buoyant force, we need to calculate the weight of the fresh water displaced by the raft. The weight of an object is equal to its mass multiplied by the acceleration due to gravity.
The mass of the fresh water displaced can be found using the density of fresh water (1000 kg/m³) and the volume of the raft (0.60 m³). The formula to calculate mass is:
mass = density * volume
mass = 1000 kg/m³ * 0.60 m³
Next, we need to calculate the weight of the fresh water displaced by multiplying the mass by the acceleration due to gravity (9.8 m/s²). The formula to calculate weight is:
weight = mass * gravity
weight = (1000 kg/m³ * 0.60 m³) * 9.8 m/s²
Now that we have the weight of the fresh water displaced, we can use this value to find the buoyant force. The buoyant force is equal to the weight of the fresh water displaced. So:
buoyant force = weight of fresh water displaced
Now, the buoyant force acting on the raft is equal to the weight of the raft. The weight of the raft can be found using the density of the raft (600 kg/m³) and its volume (0.60 m³). The formula to calculate weight is:
weight = density * volume * gravity
weight = 600 kg/m³ * 0.60 m³ * 9.8 m/s²
This weight of the raft is opposing the buoyant force. Since the two forces are equal, we can equate them:
buoyant force = weight of the raft
Now we can solve for the depth of the bottom of the raft below the water level. The depth is the difference between the height of the water level and the height of the bottom of the raft. We can find the height of the water level by dividing the buoyant force by the surface area of the bottom of the raft. The formula to calculate depth is:
depth = (buoyant force / surface area of bottom of raft) - height of bottom of raft
Substituting the values we have:
depth = (buoyant force / 5.7 m²) - 0
Now you can substitute the calculated values and complete the calculation to find the depth of the bottom of the raft below the water level.
To find out how deep the bottom of the raft is below the water level, we can calculate the buoyant force acting on the raft.
Buoyant force (Fb) = weight of water displaced by the raft.
The weight of water displaced by the raft can be calculated as the difference in weight of the raft in air and the weight of the raft in water.
Weight of water displaced = Weight of raft in air - Weight of raft in water.
Now let's break down the calculation step by step:
Step 1: Calculate the weight of the raft in air.
Weight (W) = mass (m) x gravitational acceleration (g).
Given that the density of the raft is 600 kg/m^3 and the volume of the raft is 0.60 m^3, we can calculate the mass of the raft using the formula:
Mass (m) = density (ρ) x volume (V).
Mass of the raft (m) = 600 kg/m^3 x 0.60 m^3.
Step 2: Calculate the weight of the raft in water.
Since we know that the raft is completely submerged in water, the volume of the water displaced will be equal to the volume of the raft.
Volume of water displaced = 0.60 m^3.
Density of water (ρw) = 1000 kg/m^3.
Weight of water displaced = Volume of water displaced x Density of water.
Weight of water displaced = 0.60 m^3 x 1000 kg/m^3.
Now we can calculate the weight of the raft in air.
Step 3: Calculate the buoyant force.
Buoyant Force (Fb) = Weight of water displaced - Weight of raft in air.
Step 4: Calculate the depth of the bottom of the raft below water level.
Since the buoyant force is equal to the weight of the water displaced, we can calculate the depth of the bottom of the raft below the water level using the equation:
Depth = Buoyant force / (Surface Area of the bottom of the raft x Density of water).
Now let's perform the calculations:
Step 1: Calculate the mass of the raft.
Mass (m) = 600 kg/m^3 x 0.60 m^3.
Step 2: Calculate the weight of the raft in water.
Weight of water displaced = 0.60 m^3 x 1000 kg/m^3.
Step 3: Calculate the buoyant force.
Buoyant Force (Fb) = Weight of water displaced - Weight of raft in air.
Step 4: Calculate the depth of the bottom of the raft below water level.
Depth = Buoyant force / (Surface Area of the bottom of the raft x Density of water).
Please note that the units for the answer will depend on the units used for the calculations.