Practice Applying Buoyancy Formulas

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  • 0:04 What Is Buoyant Force?
  • 1:25 Example 1: Calculating Volume
  • 2:13 Example 2: Calculating…
  • 3:10 Example 3: Will the…
  • 4:00 Example 4: Calculating…
  • 6:04 Lesson Summary
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Lesson Transcript
Instructor: Amanda Robb

Amanda holds a Masters in Science from Tufts Medical School in Cellular and Molecular Physiology. She has taught high school Biology and Physics for 8 years.

In this lesson, you'll learn how to apply the buoyancy formula. You'll practice calculating the volume of different shapes and buoyant force and evaluate problems to determine if an object will float.

What is Buoyant Force?

Have you ever seen barges floating down a river? These enormous ships carry giant loads of cargo, even heavy objects like cars. How do boats like these stay afloat when small stones sink in ponds?

The reason boats can float but not stones is due to the buoyant force. Buoyant force is the upward force that acts on an object in water. If the buoyant force is greater than the force pushing down on an object, or force due to gravity, then the object will float.

The likelihood of an object floating depends on the:

  • Density of the liquid, or how much mass there is per unit area
  • Volume of the liquid displaced by the object
  • Weight of the object

If a light object can displace a lot of fluid, it will have a greater buoyant force than the force due to gravity, so it will float, just like boats. Boats are filled with air. If a boat is large and flat, it displaces a lot of water, so the buoyant force is greater than the force due to gravity, and the boat floats.

The formula we use to calculate the buoyant force is the density of the liquid (p) multiplied by acceleration due to gravity (g) multiplied by the volume of the fluid displaced (Vfluid). In other words:

Fb = pgVfluid

Example 1: Calculating Volume

To start, let's practice calculating volume of the fluid displaced. To calculate volume, we need to know the shape of the object and certain characteristics about it. Let's start with a cylinder. The formula for the volume of a cylinder is:

volume formula

Imagine a child floating a cylindrical bucket in a pool. The bucket has a radius of 0.05m, and 0.1m of the bucket is submerged below the water. What's the volume of fluid displaced by the bucket?

Since we're trying to calculate the volume of a cylinder, we can use the formula that we just looked at:

example 1 math

Simple, right?

Example 2: Calculating Buoyant Force

Now that we know how to calculate volume, we can practice calculating the buoyant force. The density of any material is a known property, so you'll most likely not be asked to solve for density. For example, the density of water is 1,000kg/m2.

Knowing the density of water, what is the buoyant force acting on the bucket used in our first example?

Let's refer back to our density equation:

Fb = pgVfluid

The value for acceleration due to gravity (g) is always 10m/s2.

Fb = 1,000kg/m3 * 10m/s2 * 0.00078m3 = 7.8N

Remember to always include your units. Force is measured in Newtons (N), mass in kilograms (kg), and any length measurements in meters (m).

Example 3: Will the Object Float?

From personal experience, most of us know a plastic bucket will float in a pool, but can we prove this using the buoyancy formula? In order to decide if an object will float, you need to compare the buoyant force pushing it up to the gravitational force pushing it down.

Let's say the bucket has a mass of 0.25kg. We know the buoyant force from the previous problem: 7.8N. Now we need to calculate force due to gravity using Newton's third law:

Fg = mg

Fg = 0.25kg *10m/s2

Fg = 2.5N

So, will the bucket float? The answer is yes, because the buoyant force (7.8N) is greater than the force due to gravity (2.5N).

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