How to Find the Density of a Floating Object

To find the density of a floating object, you must determine its mass and its total volume, then divide the mass by the volume.

Understanding Density and the Principle of Flotation

The fundamental way to determine the density of any object, including one that floats, is by using the definition of density:

Density = Mass / Volume

This is the core formula used to calculate density for any substance.
(Reference 3: "To find the object density divide the mass by the volume of an object.")

For an object to float in a liquid, specific physical principles and conditions apply:

• Principle of Flotation: A floating object displaces a volume of liquid such that the weight of the liquid displaced is exactly equal to the object's own weight.
  (Reference 1: "For an object to float in a liquid, the weight of the liquid displaced by this object should be equal to its own weight.")

This principle directly implies that the mass of the floating object is equivalent to the mass of the volume of liquid that it displaces. Since weight is directly proportional to mass (Weight = Mass × gravity), when weights are equal, masses must also be equal. Thus, Mass_object = Mass_{displaced liquid}.

• Condition for Flotation: Floating occurs because the object has a lower average density than the liquid it is in. An object with a higher density than the liquid will sink.
  (Reference 2: "This can happen if the object has a lower average density (or lower density), than liquid.")

Calculating Density of a Floating Object

To apply the fundamental density formula (Mass/Volume) to a floating object, based on the principles provided:

1. Determine the Mass of the Object: According to the Principle of Flotation (Reference 1), this mass is equal to the mass of the volume of liquid the object displaces while floating freely.
2. Determine the Total Volume of the Object: This step involves finding the volume of the entire object, not just the portion submerged in the liquid.
3. Calculate the Density: Apply the fundamental density formula by dividing the object's mass (determined in step 1) by its total volume (determined in step 2).

Density_object = Mass_object / Total Volume_object

In summary, while the principles of flotation explain the relationship between the object and the displaced liquid (References 1 & 2) and why floating occurs, finding the object's density requires applying the fundamental definition of density (Reference 3) using the object's mass and its total volume.