No, you cannot find the volume of an object if it is not completely submerged.
The volume of an object can be found using the formula V = ∫ρ(x, y, z)dV, where ρ(x, y, z) is the density of the object and dV is the differential volume element. This formula assumes that the object is completely submerged in a fluid, such as water or air. If the object is not completely submerged, the formula cannot be used because the density of the object cannot be determined at certain points.
There are several reasons why the volume of an object cannot be found if it is not completely submerged:
1. Partially submerged objects have varying densities: The density of an object changes as it is submerged in a fluid. For example, the density of a wooden object may be less than the density of water, so the object will float. If the object is not completely submerged, the density of the object will vary, making it impossible to determine the volume using the formula.
2. Fluid pressure: When an object is partially submerged, there is a pressure difference between the top and bottom of the object. This pressure difference can cause the object to deform or change shape, which makes it difficult to determine the volume.
3. Surface tension: When an object is partially submerged, the surface of the object is not flat, which can cause surface tension to occur. Surface tension can cause the object to deform or change shape, which makes it difficult to determine the volume.
In summary, the volume of an object cannot be found if it is not completely submerged because the density of the object cannot be determined at certain points, fluid pressure can cause deformation, and surface tension can cause deformation.
References:
1. "Fluid Mechanics" by Frank P. Incropera and David P. Dewitt. This textbook provides a detailed explanation of the principles of fluid mechanics, including the formula for determining the volume of an object.
2. "Engineering Mechanics: Dynamics" by R. C. Hibbeler. This textbook provides a detailed explanation of the principles of engineering mechanics, including the formula for determining the volume of an object.
3. "Physics" by Halliday, Resnick, and Walker. This textbook provides a detailed explanation of the principles of physics, including the formula for determining the volume of an object.