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?
I will be happy to critique your thinking. Review what I did for you on the last two.
To determine the distance from the top of the block to the water, we need to consider the principles of buoyancy and the density of the wood block.
1. Freshwater:
In freshwater, the average density is approximately 1000 kg/m^3. For the block to float, its average density should be less than that of freshwater. We can find the average density of the block by using the density formula: density = mass/volume.
Given that the block has dimensions of 10 cm x 10 cm x 10 cm, its volume can be calculated by multiplying the dimensions: volume = 10 cm x 10 cm x 10 cm = 1000 cm^3.
Now, to convert the volume from cubic centimeters to cubic meters, we divide by 1,000,000 (since there are 1,000,000 cubic centimeters in a cubic meter): volume = 1000 cm^3 / 1,000,000 = 0.001 m^3.
Since the block weighs 700 kg/m^3 (density), we can determine its mass by multiplying its volume by its density: mass = density x volume = 700 kg/m^3 x 0.001 m^3 = 0.7 kg.
To determine the buoyant force acting on the block, we use Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object. The block will displace its own volume of water, so the weight of the water displaced can be calculated by multiplying the volume of water displaced by the density of water.
Given that the density of water is 1000 kg/m^3, the volume of water displaced is equal to the volume of the block, which is 0.001 m^3. Therefore, the weight of the water displaced is: weight = volume x density = 0.001 m^3 x 1000 kg/m^3 = 1 kg.
Since the weight of the block is 0.7 kg and the weight of the water displaced is 1 kg, the buoyant force acting on the block is equal to the weight of the water displaced, which is 1 kg.
For the block to float in freshwater, the buoyant force must be equal to or greater than the weight of the block. Since the buoyant force is 1 kg, which is greater than the weight of the block (0.7 kg), the block will float entirely above the water surface in freshwater. Therefore, the distance from the top of the block to the water surface will be the height of the block itself, which is 10 cm or 0.1 m.
2. Seawater:
Seawater has a higher density than freshwater, typically around 1025 kg/m^3. To determine the distance from the top of the block to the water surface in seawater, we follow a similar process as before.
The calculations for the volume, mass, and weight of the block remain the same (since they depend on the dimensions and the block's density). However, when calculating the weight of the water displaced, we use the density of seawater, which is 1025 kg/m^3.
Using the same volume of water displaced (0.001 m^3), the weight of the water displaced in seawater is: weight = volume x density = 0.001 m^3 x 1025 kg/m^3 = 1.025 kg.
Since the weight of the block is 0.7 kg and the weight of the water displaced in seawater is 1.025 kg, the buoyant force acting on the block is less than the weight of the water displaced. Therefore, the block will sink partially, with a part of the block submerged in seawater.
To determine the distance from the top of the block to the water surface in seawater, we subtract the submerged height from the total height of the block.
To find the submerged height, we equate the weight of the block to the buoyant force by solving the equation: weight of the water displaced = weight of the block.
weight of the water displaced in seawater = 1.025 kg
weight of the block = 0.7 kg
The submerged weight is less than the weight of the block, so the block sinks partially. The submerged weight is 0.7 kg, so the distance from the top of the block to the water's surface would be 10 cm - (submerged height).