Final answer:
The density of the metal can be found by determining its mass from its weight in air and then finding the volume of water it displaces, which is equal to its own volume. The metal's density is then calculated as 3566.43 kg/m³.
Step-by-step explanation:
To find the density of the metal, we'll use the concept of buoyant force and Archimedes' principle. The weight difference of the metal in air and water is due to the buoyant force exerted by the water. In air, the weight of the metal is 50.0 N and in water, it is 36.0 N, which means the buoyant force is 50.0 N - 36.0 N = 14.0 N. The buoyant force is equal to the weight of the water displaced by the metal.
First, we'll convert the buoyant force to mass by using the acceleration due to gravity (g = 9.8 m/s²): Mass of water displaced = buoyant force / g = 14.0 N / 9.8 m/s² = 1.43 kg. To find the volume of water displaced, we use the density of water (1,000 kg/m³): Volume of water displaced = mass / density = 1.43 kg / 1,000 kg/m³ = 0.00143 m³.
Since the volume of water displaced is equal to the volume of the metal, we thus have the volume of the metal. Now we can find the density of the metal by dividing its mass by its volume. The mass of the metal can be found by dividing its weight in air by the acceleration due to gravity (we ignore the buoyant force of air since it's negligible): Mass of metal = 50.0 N / 9.8 m/s² = 5.10 kg.
Finally, we calculate the density of the metal: Density of metal = mass of metal / volume of metal = 5.10 kg / 0.00143 m³ = 3566.43 kg/m³.