Final answer:
To find the density of the object, calculate the buoyant force, translate this to the mass of the water displaced, and then find the volume of the object from this mass. The density of the object is then found by dividing its mass by its volume, with the final calculation showing the object's density to be 1448.0 kg/m³.
Step-by-step explanation:
The question asks to find the density of a solid object given that it weighs 13.50 N in air and 4.18 N when submerged in water, using the density of water as 1000.0 kg/m³. To calculate the density of the object, we first determine the buoyant force by the difference in weight in air and in water (13.50 N - 4.18 N). This buoyant force is equal to the weight of the water displaced by the object.
Next, we use Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid it displaces. Using the known density of water, we calculate the volume of water displaced, and from there, we can find the volume of the object. Finally, we use the formula density = mass/volume to find the density of the object.
Example:
Calculate the buoyant force: 13.50 N - 4.18 N = 9.32 N.
Convert the buoyant force to mass (since weight is mass times the acceleration due to gravity, and g=9.8 m/s²): Mass = 9.32 N / 9.8 m/s² = 0.951 kg.
Since the density of water is 1000 kg/m³, the volume of water displaced by the object is equal to its mass: Volume = Mass / Density of water = 0.951 kg / 1000 kg/m³ = 0.000951 m³.
Now, find the mass of the object in kg (since weight is mass times gravity): Mass of object = 13.50 N / 9.8 m/s² = 1.377 kg.
Finally, calculate the density of the object: Density = Mass / Volume = 1.377 kg / 0.000951 m³ = 1448.0 kg/m³.