Peoples Physics Concepts

17.1. Buoyancy http://www.ck12.org

17.1 Buoyancy

• Define the Buoyant force and calculate problems involving buoyancy and Archimedes principle.

Students will learn about the Buoyant force, how to calculate problems involving buoyancy and Archimedes

principle.

Key Equations

Fbuoy=ρwatergVdisplaced Archimedes’ principle

Guidance

Archimedes’ Principlestates that the upward buoyant force on an object in the water is equal to the weight of the

displaced volume of water. The reason for this upward force is that the bottom of the object is at lower depth, and

therefore higher pressure, than the top. If an object has a higher density than the density of water, the weight of the

displaced volume will be less than the object’s weight, and the object will sink. Otherwise, the object will float. The

ratio of an object or substance’s density to the density of water is called it’s specific gravity.

Example 1

A simple boat (really a metal box with an open top) is floating at rest in a pond. The boat is 3 m long, 2 m wide,
and has walls 1.5 m high and has an empty mass of 500 kg. If you begin filling the boat with gravel of density 1922
kg/m^3 at a constant rate of .1 m^3 /s, how long will it be before your boat sinks?

Solution

To solve this problem, we’re going to start out by determining the maximum mass that the boat can support. The

weight of the maximum mass is equal to the buoyant force when the boat is submerged all the way up the the edge

of the side wall.

mg=Fbuoy

mg=ρwatergV

m=ρwaterV

m=1000 kg/m^3 ∗3 m∗2 m∗ 1 .5 m

m=9000 kg

Now we need to convert the rate at which sand is being added from m^3 /s to kg/s.