Final answer:
The density of objects A, B, and C were calculated from their given mass and volume coordinates. Object A is neutrally buoyant, object B will sink, and object C will also sink in water. This is determined by comparing their densities to the density of water and applying Archimedes' principle.
Step-by-step explanation:
Understanding Density and Buoyancy
To determine whether objects A, B, and C float or sink in water, we need to calculate their densities. The density of an object is found by dividing its mass by its volume. According to the coordinates provided for each object: A (5,5), B (10,15), and C (23,24), where the mass is on the y-axis and volume on the x-axis, we can determine the densities by dividing the mass by the volume for each point.
For object A, the density is 5/5 = 1 g/cm³. Since this density is equal to the density of water (1 g/cm³), object A will neither sink nor float but will be neutrally buoyant. For object B, the density is 15/10 = 1.5 g/cm³. Because this density is greater than that of water, object B will sink. Lastly, object C has a density of 24/23 ≈ 1.04 g/cm³, which is slightly greater than that of water, so object C will also sink.
To understand why objects float or sink, it's important to know that this behavior is explained by 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. Objects float when their density is less than that of the fluid they are in, and they sink when their density is more.
To estimate the mass of an object based on its density, you multiply the volume of the object by its density. Likewise, if you know the mass and want to estimate the volume, you would divide the mass by the density.