A metal weighs 20N in air and 12N in water. Calculate the relative density of the metal
The relative density of an object is the ratio of its density to the density of a reference substance, which is usually water.
We know that the weight of the metal in air is 20N and its weight in water is 12N.
The weight of an object in a fluid (such as water) is equal to the weight of the object in air minus the buoyant force acting on it. The buoyant force is equal to the weight of the fluid displaced by the object.
Therefore, the buoyant force acting on the metal in water can be calculated as:
Buoyant force = Weight in air - Weight in water
Buoyant force = 20N - 12N
Buoyant force = 8N
The weight of the fluid displaced by the metal is equal to the buoyant force, so the weight of the fluid displaced is 8N.
The relative density can be calculated as the ratio of the density of the metal to the density of water:
Relative density = density of metal / density of water
The density of the metal can be calculated using the weight of the object in air and its volume:
Density = Mass / Volume
Density of metal = Weight in air / Volume
Since the weight of the fluid displaced is equal to the weight of the metal in water, we can equate the weight of the fluid displaced to the weight of an equal volume of water:
Weight of fluid displaced = Weight of equal volume of water
8N = Density of water * Volume of fluid displaced
We can rearrange this equation to solve for the volume of fluid displaced:
Volume of fluid displaced = 8N / Density of water
Now we have the volume of fluid displaced, which is also the volume of the metal, so we can calculate the density of the metal:
Density of metal = Weight in air / Volume of fluid displaced
Density of metal = 20N / (8N / Density of water)
Density of metal = 20N * (Density of water / 8N)
Density of metal = 2.5 * Density of water
Finally, we can substitute the density of the metal into the relative density equation:
Relative density = Density of metal / Density of water
Relative density = (2.5 * Density of water) / Density of water
Relative density = 2.5
Therefore, the relative density of the metal is 2.5.
To calculate the relative density of the metal, we can use the following formula:
Relative density = Weight in air / (Weight in air - Weight in water)
Given that the weight of the metal in air is 20N and the weight of the metal in water is 12N, we can substitute these values into the formula:
Relative density = 20N / (20N - 12N)
Relative density = 20N / 8N
Relative density = 2.5
Therefore, the relative density of the metal is 2.5.