A piece of metal weighs 51.8 N in air, 37.2 N in water, and 42.6 N in an unknown liquid.
Find the density of the metal.
Answer in units of kg/m^3
Find the density of the unknown liquid.
Answer in units of kg/m^3
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To find the density of the metal, we can use Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
1. Start by finding the apparent weight of the metal in water:
Apparent weight in water = Weight in air - Buoyant force
Buoyant force = Weight in air - Weight in water
Buoyant force = 51.8 N - 37.2 N = 14.6 N
2. Convert the weight of the liquid displaced to the mass of the liquid displaced:
Mass of the liquid displaced = Buoyant force / acceleration due to gravity
Mass of the liquid displaced = 14.6 N / 9.8 m/s^2 = 1.49 kg
3. The volume of the liquid displaced is equal to the volume of the metal. We can calculate the volume of the metal using the formula:
Volume = Mass / Density
Density = Mass / Volume
Density = 1.49 kg / Volume
Now, let's find the density of the unknown liquid:
1. Start by finding the apparent weight of the liquid:
Apparent weight of the liquid = Weight in air - Weight in unknown liquid
Apparent weight of the liquid = 51.8 N - 42.6 N = 9.2 N
2. Convert the weight of the liquid to its mass:
Mass of the liquid = Weight of the liquid / acceleration due to gravity
Mass of the liquid = 9.2 N / 9.8 m/s^2 = 0.94 kg
3. To find the volume of the liquid, we divide the mass of the liquid by its density:
Density = Mass / Volume
Volume = Mass / Density
Volume = 0.94 kg / Density of unknown liquid
So, the density of the metal is 1.49 kg / Volume, and the density of the unknown liquid is 0.94 kg / Volume.