A steel drum (barrel) has a volume of 200 Liters and a mass of 16 kg. It is filled to the top with an unknown liquid, sealed and thrown into water. It is floating with 50% of its volume underwater. What is the density of the liquid inside the drum? Assume the walls of the drum are very thin.
To find the density of the liquid inside the drum, we need to use the concept of buoyancy. Here's how you can calculate it:
1. Start by calculating the volume of the steel drum that is submerged in water. Since the drum is floating with 50% of its volume underwater, the volume of the submerged part of the drum is 200 Liters * 0.5 = 100 Liters.
2. Convert the volume to cubic meters, as density is typically measured in kilograms per cubic meter. 1 Liter is equal to 0.001 cubic meters, so 100 Liters is 100 * 0.001 = 0.1 cubic meters.
3. Calculate the mass of the water displaced by the submerged part of the drum. According to Archimedes' principle, the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. The buoyant force is equal to the weight of the drum, which is 16 kg. Therefore, the mass of the water displaced is also 16 kg.
4. Use the formula for density to find the density of the liquid inside the drum. Density is mass divided by volume. Hence, density = mass of the liquid / volume of the liquid. In this case, the mass of the liquid is 16 kg (same as the mass of the displaced water) and the volume of the liquid is 0.1 cubic meters (submerged volume of the drum). So, the density of the liquid inside the drum is 16 kg / 0.1 cubic meters = 160 kg/m^3.
Therefore, the density of the liquid inside the drum is 160 kg/m^3.