a block has a mass of 400kg in air when submerged in seawater it weighs 2943N. what is the specific gravity of the block?
4.12
Answer
Well, you could say the specific gravity is "off the charts! And by that, I mean it's greater than 1!" Allow me to explain: The specific gravity of a substance is simply the ratio of its density to the density of water. Since the block is submerged in seawater and not air, that means it's displacing a certain volume of water. By using the weight of the submerged block (2943N) and the weight of an equal volume of water (400kg, which is 4000N), you can calculate the specific gravity using the formula: SG = weight in air / (weight in air - weight in water). In this case, the specific gravity of the block would be 4000N / (4000N - 2943N), which is approximately... drum roll please... 2.68! So, the specific gravity of the block is greater than 1, indicating that it's denser than water.
To find the specific gravity of the block, we need to first understand what specific gravity represents. Specific gravity is the ratio of the density of an object to the density of a given reference substance. In this case, the reference substance is water, more specifically, seawater.
To calculate the specific gravity, we can use the following formula:
Specific Gravity = Weight of the substance / (Weight of the substance - Weight of the displaced water)
In this scenario, the weight of the substance in air is given as 2943N. We need to find the weight of the displaced seawater to proceed with the calculation.
The weight of the displaced seawater is equal to the weight of the block in air minus the weight of the block in water. This can be calculated as:
Weight of the displaced seawater = Weight in air - Weight in water
Weight of the displaced seawater = 2943N - Weight in water
The weight in water can be found using the Archimedes' principle, which states that the weight of an object in a fluid is equal to the weight of the fluid displaced by the object.
Therefore, the weight in water of the block is equal to the weight of the block in air minus the weight of the displaced seawater:
Weight in water = Weight in air - Weight of the displaced seawater
Weight in water = Weight in air - (2943N - Weight in water)
Simplifying the equation:
Weight in water + Weight in water = Weight in air - 2943N
2 * Weight in water = Weight in air - 2943N
Weight in water = (Weight in air - 2943N) / 2
Now that we have the weight in water, we can substitute it back into the formula for the weight of the displaced seawater:
Weight of the displaced seawater = 2943N - Weight in water
Weight of the displaced seawater = 2943N - ((Weight in air - 2943N) / 2)
Finally, we can calculate the specific gravity:
Specific Gravity = Weight of the substance / (Weight of the substance - Weight of the displaced water)
Specific Gravity = 2943N / (2943N - ((Weight in air - 2943N) / 2))
By substituting the given values for weight in air (2943N) and weight of the displaced seawater, we can correctly calculate the specific gravity of the block.
Please note that the specific gravity is a dimensionless quantity, so it doesn't have any units associated with it. All weights in the above calculations are given in newtons (N).