A 10cm times 10cm times 10cm wood block with a density of 700kg/m^{3} floats in water. What is the distance from the top of the block to the water if the water is fresh? and If it's seawater?
Gonzalez?
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To determine the distance from the top of the wood block to the water, we need to consider the buoyant force acting on the block. The magnitude of the buoyant force depends on the density of the fluid (water), the volume of the displaced fluid (equal to the volume of the block submerged in water), and the acceleration due to gravity.
Let's start by calculating the volume of the wood block. The block's dimensions are given as 10 cm x 10 cm x 10 cm, so the volume can be calculated as:
Volume = length x width x height = 10 cm x 10 cm x 10 cm = 1000 cm³
Next, we need to convert the volume from cubic centimeters (cm³) to cubic meters (m³) since the density is given in kilograms per cubic meter (kg/m³).
1 m³ = 1,000,000 cm³
So the volume of the block in cubic meters is:
Volume = 1000 cm³ / 1,000,000 cm³/m³ = 0.001 m³
To find the buoyant force acting on the wood block, we multiply the volume of the block submerged in water by the density of water and acceleration due to gravity.
Buoyant force = volume submerged x density of water x acceleration due to gravity
Freshwater has a density of approximately 1000 kg/m³. Therefore, for freshwater, the buoyant force can be calculated as:
Buoyant force (freshwater) = 0.001 m³ x 1000 kg/m³ x 9.8 m/s² = 9.8 N
The buoyant force acts vertically upward and equals the weight of the block, which can be calculated as:
Weight of the block = density of wood x volume of the block x acceleration due to gravity
The density of the wood is given as 700 kg/m³:
Weight of the block = 700 kg/m³ x 0.001 m³ x 9.8 m/s² = 6.86 N
Since the buoyant force is greater than the weight of the block in freshwater, the block will float. The distance from the top of the block to the water surface will be equal to the distance submerged in water.
To find this distance, we need to rearrange the equation for the volume of the block submerged in water:
Volume submerged = buoyant force / density of water / acceleration due to gravity
Substituting the values, we get:
Volume submerged = 9.8 N / 1000 kg/m³ / 9.8 m/s² = 0.001 m³
Now, let's calculate the height of the submerged part of the block:
Height submerged = Volume submerged / (length x width)
Since the shape of the block is a rectangular prism, the height submerged is equal to the height of the block, which is 10 cm or 0.1 m.
Therefore, the distance from the top of the block to the water surface is 0.1 meters (10 cm) in freshwater.
Now, let's consider seawater, which has a higher density of approximately 1025 kg/m³. We can repeat the same calculations as above using this density.
The buoyant force in seawater:
Buoyant force (seawater) = 0.001 m³ x 1025 kg/m³ x 9.8 m/s² = 10.078 N
In this case, the weight of the block remains the same at 6.86 N.
Since the buoyant force is still greater than the weight of the block in seawater, the block will still float. The distance from the top of the block to the water surface will also be equal to the height submerged.
Using the same formula as above, we can calculate the height submerged in seawater:
Height submerged = Volume submerged / (length x width)
Height submerged = 10.078 N / 1025 kg/m³ / 9.8 m/s² = 0.001 m³
Therefore, the distance from the top of the block to the water surface is 0.1 meters (10 cm) in seawater as well.