Water Displacement and Archimedes’ Principle in Physics Problems
Using Archimedes’ principle, you can calculate the volume of an object by determining how much water it displaces. For example, you can calculate the mass of a piece of wood based on how deeply it is submerged in water.
Here are some practice questions that you can try.
A block of wood with the dimensions 0.12 by 0.34 by 0.43 cubic meters floats along a river with the broadest face facing down. The wood is submerged to a height of 0.053 meters. What is the mass of the piece of wood?
You plunge a basketball beneath the surface of a swimming pool until half the volume of the basketball is submerged. If the basketball has a radius of 12 centimeters, what is the buoyancy force on the ball due to the water?
A 4,000-kilogram boat floats with one-third of its volume submerged. If two more people get into the boat, each of whom weighs 690 newtons, what additional volume of water is displaced?
The following are the answers to the practice questions:
Archimedes’ principle tells you that the weight of the water displaced is equal to the buoyancy force:
To keep the wood afloat, the buoyancy force must have the same magnitude as the force of gravity on the block, so
The volume of water displaced is
So the mass of water displaced is
Thus, the mass of the piece of wood is 7.75 kilograms.
The buoyancy force is the mass of the water displaced multiplied by the acceleration due to gravity:
The volume of water displaced is half the volume of the basketball:
Here, r = 12 cm. In meters, the radius is
Using the equation for density, the mass of water displaced is
The buoyancy force is
The weight of the additional water displaced is equal to the combined weight of the two extra people who got into the boat:
The mass of the water displaced is then
Solve the equation for density for the volume of water displaced and use this result for the mass of water displaced to find the answer: