Water Displacement and Archimedes’ Principle in Physics Problems

By Consumer Dummies

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.

Practice questions

  1. 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?

  2. 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?

  3. 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?

Answers

The following are the answers to the practice questions:

  1. 7.75 kg

    Archimedes’ principle tells you that the weight of the water displaced is equal to the buoyancy force:

    image0.png

    To keep the wood afloat, the buoyancy force must have the same magnitude as the force of gravity on the block, so

    image1.png

    The volume of water displaced is

    image2.png

    So the mass of water displaced is

    image3.png

    Thus, the mass of the piece of wood is 7.75 kilograms.

  2. 35 N

    The buoyancy force is the mass of the water displaced multiplied by the acceleration due to gravity:

    image4.png

    The volume of water displaced is half the volume of the basketball:

    image5.png

    Here, r = 12 cm. In meters, the radius is

    image6.png

    Using the equation for density, the mass of water displaced is

    image7.png

    The buoyancy force is

    image8.png

  3. 0.14 m3

    The weight of the additional water displaced is equal to the combined weight of the two extra people who got into the boat:

    image9.png

    The mass of the water displaced is then

    image10.png

    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:

    image11.png