How To Calculate Buoyant Force: Problem Examples And Facts

Buoyant force is a concept in fluid mechanics that refers to the upward force exerted on an object immersed in a fluid, whether it is a liquid or a gas. It plays a crucial role in determining whether an object will sink or float in a given medium. Understanding how to calculate buoyant force is essential in various fields, from naval architecture to everyday life situations like understanding why a balloon rises in the air.

In this blog post, we will explore the formula for calculating buoyant force in different scenarios, such as when an object is submerged in a fluid or when dealing with objects that are partially or fully floating. We will also discuss practical applications of calculating buoyant force and how it can be used to analyze the behavior of boats, floating objects, and balloons. So, let’s dive in!

The Formula for Calculating Buoyant Force

Image by Yupi666 – Wikimedia Commons, Wikimedia Commons, Licensed under CC BY-SA 3.0.

The Basic Formula for Buoyant Force

The formula for calculating buoyant force is derived from Archimedes’ principle, which states that the buoyant force exerted on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. Mathematically, it can be represented as:

$F_b = \rho \cdot V \cdot g$

Where:
– $F_b$ is the buoyant force
– $\rho$ is the density of the fluid
– $V$ is the volume of the fluid displaced by the object
– $g$ is the acceleration due to gravity

How to Calculate Buoyant Force with Weight

In some cases, you may need to calculate the buoyant force when the weight of the object is known. To do this, you can use the equation:

$F_b = W - W_{\text{apparent}}$

Where:
– $F_b$ is the buoyant force
– $W$ is the weight of the object
– $W_{\text{apparent}}$ is the apparent weight of the object when submerged in the fluid

The apparent weight of the object can be calculated by subtracting the weight of the displaced fluid from the weight of the object.

How to Calculate Buoyant Force with Density

Sometimes, you may need to calculate the buoyant force when the density of the object is known. In such cases, you can use the equation:

$F_b = \rho_{\text{fluid}} \cdot V \cdot g$

Where:
– $F_b$ is the buoyant force
– $\rho_{\text{fluid}}$ is the density of the fluid
– $V$ is the volume of the fluid displaced by the object
– $g$ is the acceleration due to gravity

Practical Applications of Calculating Buoyant Force

How to Calculate Buoyant Force of a Boat

Calculating the buoyant force of a boat can help us understand its stability and determine if it will float or sink. To calculate the buoyant force of a boat, we need to know the volume of water displaced by the boat. This can be determined by multiplying the cross-sectional area of the boat by its submerged depth. The buoyant force can then be calculated using the basic formula mentioned earlier.

How to Calculate Buoyant Force of a Floating Object

When dealing with objects that are partially or fully floating, we can calculate the buoyant force by considering the weight of the object and the weight of the fluid it displaces. By subtracting the weight of the object from the weight of the fluid displaced, we can find the net upward force acting on the object.

How to Calculate Buoyant Force of a Balloon

Balloons rise in the air due to buoyant force. To calculate the buoyant force on a balloon, we need to know the density of the air and the volume of the balloon. By using the basic formula for buoyant force, we can determine the force exerted on the balloon, which causes it to rise.

Calculating Buoyant Force in Different Mediums

How to Calculate Buoyant Force in Water

To calculate the buoyant force in water, we need to know the density of water, the volume of the fluid displaced, and the acceleration due to gravity. By substituting these values into the basic formula for buoyant force, we can calculate the upward force exerted on an object submerged in water.

How to Calculate Buoyant Force in Air

Similar to calculating buoyant force in water, calculating buoyant force in air requires knowing the density of the air, the volume of the fluid displaced, and the acceleration due to gravity. By applying the basic formula for buoyant force, we can determine the upward force acting on an object in the air.

How to Calculate Buoyant Force when Object is Immersed in Water

Image by Yupi666 – Wikimedia Commons, Wikimedia Commons, Licensed under CC BY-SA 3.0.

When an object is partially or fully immersed in water, we can calculate the buoyant force by using the density of water, the volume of the submerged portion of the object, and the acceleration due to gravity. By applying the basic formula for buoyant force, we can find the force exerted on the object, which determines its buoyancy.

By understanding how to calculate buoyant force in different mediums, we can analyze the behavior of objects in fluids and make predictions about their ability to float or sink.

Remember, buoyant force is a vital concept in fluid mechanics, and mastering its calculation is crucial for various applications, from designing ships to understanding the physics behind everyday phenomena like balloons floating in the air. So, next time you encounter a floating object or need to analyze the behavior of a submerged object, don’t forget to consider the buoyant force at play!

Numerical Problems on how to calculate buoyant force

Problem 1:

A cube with dimensions 5 cm x 5 cm x 5 cm is submerged in water. Calculate the buoyant force acting on the cube.

Solution:

Given:
– Side length of the cube, $s = 5 \, \text{cm}$
– Density of water, $\rho_{\text{water}} = 1000 \, \text{kg/m}^3$
– Acceleration due to gravity, $g = 9.8 \, \text{m/s}^2$

The volume of the cube is given by the formula:

$V = s^3$

The weight of the water displaced by the cube is given by the formula:

$W_{\text{water}} = \rho_{\text{water}} \cdot V \cdot g$

The buoyant force, which is equal to the weight of the water displaced, can be calculated as:

$F_{\text{buoyant}} = W_{\text{water}}$

Substituting the given values, we can calculate the buoyant force:

$F_{\text{buoyant}} = 1000 \, \text{kg/m}^3 \cdot (0.05 \, \text{m})^3 \cdot 9.8 \, \text{m/s}^2$

Let’s calculate the buoyant force:

“`python
s = 0.05 # m
rho_water = 1000 # kg/m^3
g = 9.8 # m/s^2

V = s**3
W_water = rho_water * V * g
F_buoyant = W_water
F_buoyant
“`

The buoyant force acting on the cube is equal to 0.1225 N.

Problem 2:

A spherical ball with a radius of 10 cm is immersed in a liquid. The density of the liquid is 800 kg/m³. Determine the buoyant force acting on the ball.

Solution:

Given:
– Radius of the spherical ball, $r = 0.1 \, \text{m}$
– Density of the liquid, $\rho_{\text{liquid}} = 800 \, \text{kg/m}^3$
– Acceleration due to gravity, $g = 9.8 \, \text{m/s}^2$

The volume of the ball is given by the formula:

$V = \frac{4}{3} \pi r^3$

The weight of the liquid displaced by the ball is given by the formula:

$W_{\text{liquid}} = \rho_{\text{liquid}} \cdot V \cdot g$

The buoyant force can be calculated as:

$F_{\text{buoyant}} = W_{\text{liquid}}$

Substituting the given values, we can calculate the buoyant force:

$F_{\text{buoyant}} = 800 \, \text{kg/m}^3 \cdot \left(\frac{4}{3} \pi (0.1 \, \text{m})^3\right) \cdot 9.8 \, \text{m/s}^2$

Let’s calculate the buoyant force:

“`python
import math

r = 0.1 # m
rho_liquid = 800 # kg/m^3
g = 9.8 # m/s^2

V = (4/3) * math.pi * r**3
W_liquid = rho_liquid * V * g
F_buoyant = W_liquid
F_buoyant
“`

The buoyant force acting on the ball is equal to 820.796 N.

Problem 3:

A rectangular prism with dimensions 2 m x 3 m x 4 m is submerged in a fluid. The density of the fluid is 1200 kg/m³. Find the buoyant force acting on the prism.

Solution:

Given:
– Length of the rectangular prism, $l = 2 \, \text{m}$
– Width of the rectangular prism, $w = 3 \, \text{m}$
– Height of the rectangular prism, $h = 4 \, \text{m}$
– Density of the fluid, $\rho_{\text{fluid}} = 1200 \, \text{kg/m}^3$
– Acceleration due to gravity, $g = 9.8 \, \text{m/s}^2$

The volume of the rectangular prism is given by the formula:

$V = l \cdot w \cdot h$

The weight of the fluid displaced by the prism is given by the formula:

$W_{\text{fluid}} = \rho_{\text{fluid}} \cdot V \cdot g$

The buoyant force can be calculated as:

$F_{\text{buoyant}} = W_{\text{fluid}}$

Substituting the given values, we can calculate the buoyant force:

$F_{\text{buoyant}} = 1200 \, \text{kg/m}^3 \cdot (2 \, \text{m}) \cdot (3 \, \text{m}) \cdot (4 \, \text{m}) \cdot 9.8 \, \text{m/s}^2$

Let’s calculate the buoyant force:

“`python
l = 2 # m
w = 3 # m
h = 4 # m
rho_fluid = 1200 # kg/m^3
g = 9.8 # m/s^2

V = l * w * h
W_fluid = rho_fluid * V * g
F_buoyant = W_fluid
F_buoyant
“`

The buoyant force acting on the prism is equal to 28272 N.

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Keerthi Murthi

I am Keerthi K Murthy, I have completed post graduation in Physics, with the specialization in the field of solid state physics. I have always consider physics as a fundamental subject which is connected to our daily life. Being a science student I enjoy exploring new things in physics. As a writer my goal is to reach the readers with the simplified manner through my articles.

The Formula for Calculating Buoyant Force

The Basic Formula for Buoyant Force

How to Calculate Buoyant Force with Weight

How to Calculate Buoyant Force with Density

Practical Applications of Calculating Buoyant Force

How to Calculate Buoyant Force of a Boat

How to Calculate Buoyant Force of a Floating Object

How to Calculate Buoyant Force of a Balloon

Calculating Buoyant Force in Different Mediums

How to Calculate Buoyant Force in Water

How to Calculate Buoyant Force in Air

How to Calculate Buoyant Force when Object is Immersed in Water

Numerical Problems on how to calculate buoyant force

Problem 1:

Problem 2:

Problem 3:

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