The Concept of Upthrust or Buoyant Force

Oct 13, 2025 by magicalceylontours.com 14 views

Introduction

When a basketball floats in a bathtub of water, it is a classic demonstration of the concept of upthrust or buoyant force. This phenomenon is a fundamental principle in physics, governed by Archimedes' Principle, which states that the buoyant force on an object is equal to the weight of the fluid it displaces. In this article, we will delve into the calculation of the upthrust or buoyant force and the volume of water displaced by the ball.

The Concept of Upthrust or Buoyant Force

The upthrust or buoyant force is the upward force exerted by a fluid (such as water) on an object that is partially or fully submerged in it. This force is a result of the difference in pressure between the top and bottom of the object. When an object is submerged in a fluid, it displaces a volume of fluid equal to its own volume. The weight of this displaced fluid is equal to the buoyant force exerted on the object.

Calculating the Upthrust or Buoyant Force

To calculate the upthrust or buoyant force, we need to know the mass of the fluid displaced and the acceleration due to gravity. The mass of the fluid displaced is equal to the volume of the fluid displaced multiplied by its density. The density of water is approximately 1000 kg/m³.

Given:

Mass of the ball (m) = 0.5 kg
Diameter of the ball (d) = 22 cm = 0.22 m
Density of water (ρ) = 1000 kg/m³
Acceleration due to gravity (g) = 9.8 m/s²

First, we need to calculate the volume of the ball. The volume of a sphere (V) is given by the formula:

V = (4/3) * π * r³

where r is the radius of the sphere. The radius of the ball is half of its diameter:

r = d/2 = 0.11 m

Now, we can calculate the volume of the ball:

V = (4/3) * π * (0.11)³ ≈ 0.0013 m³

The mass of the water displaced is equal to the volume of the water displaced multiplied by its density:

m_water = V * ρ ≈ 0.0013 m³ * 1000 kg/m³ ≈ 1.3 kg

The weight of the water displaced is equal to its mass multiplied by the acceleration due to gravity:

W_water = m_water * g ≈ 1.3 kg * 9.8 m/s² ≈ 12.74 N

The upthrust or buoyant force (F_buoyant) is equal to the weight of the water displaced:

F_buoyant = W_water ≈ 12.74 N

Calculating the Volume of Water Displaced by the Ball

The volume of water displaced by the ball is equal to the volume of the ball. We have already calculated the volume of the ball in the previous section:

V ≈ 0.0013 m³

Conclusion

In this article, we have calculated the upthrust or buoyant force and the volume of water displaced by a basketball floating in a bathtub of water. The upthrust or buoyant force is equal to the weight of the water displaced, which is approximately 12.74 N. The volume of water displaced by the ball is equal to the volume of the ball, which is approximately 0.0013 m³. This demonstrates the fundamental principle of Archimedes' Principle, which states that the buoyant force on an object is equal to the weight of the fluid it displaces.

References

Archimedes' Principle. (n.d.). In Encyclopedia Britannica.
Buoyancy. (n.d.). In Physics Classroom.
Density. (n.d.). In Physics Classroom.

Introduction

In our previous article, we explored the concept of upthrust or buoyant force and calculated the upthrust or buoyant force and the volume of water displaced by a basketball floating in a bathtub of water. In this article, we will address some common questions related to this topic.

Q&A

Q1: Why does the basketball float in the bathtub of water?

A1: The basketball floats in the bathtub of water because the weight of the water displaced by the ball is equal to or greater than the weight of the ball itself. This is a result of the principle of buoyancy, which states that the buoyant force on an object is equal to the weight of the fluid it displaces.

Q2: What is the relationship between the volume of the ball and the volume of water displaced?

A2: The volume of water displaced by the ball is equal to the volume of the ball. This is because the ball displaces a volume of water equal to its own volume when it is submerged in the water.

Q3: How does the density of the ball affect the upthrust or buoyant force?

A3: The density of the ball does not affect the upthrust or buoyant force. The upthrust or buoyant force is determined by the weight of the water displaced, which is equal to the volume of the water displaced multiplied by its density. The density of the ball is not a factor in this calculation.

Q4: Can the upthrust or buoyant force be greater than the weight of the ball?

A4: Yes, the upthrust or buoyant force can be greater than the weight of the ball. This occurs when the volume of water displaced by the ball is greater than the volume of the ball itself. In this case, the weight of the water displaced is greater than the weight of the ball, resulting in an upward force greater than the weight of the ball.

Q5: What is the significance of Archimedes' Principle in this scenario?

A5: Archimedes' Principle is a fundamental principle in physics that states that the buoyant force on an object is equal to the weight of the fluid it displaces. In this scenario, Archimedes' Principle is used to calculate the upthrust or buoyant force and the volume of water displaced by the ball.

Q6: Can the ball be submerged in the water if it is denser than water?

A6: No, the ball cannot be submerged in the water if it is denser than water. According to Archimedes' Principle, the buoyant force on an object is equal to the weight of the fluid it displaces. If the ball is denser than water, the weight of the ball will be greater than the weight of the water displaced, resulting in a net downward force.

Q7: What is the relationship between the upthrust or buoyant force and the acceleration due to gravity?

A7: The upthrust or buoyant force is directly proportional to the acceleration due to gravity. This is because the weight of the water displaced is equal to the mass of the water displaced multiplied by the acceleration due to gravity.

Q8: Can the upthrust or buoyant force be zero?

A8: No, the upthrust or buoyant force cannot be zero. According to Archimedes' Principle, the buoyant force on an object is equal to the weight of the fluid it displaces. Even if the object is not submerged in the fluid, there will still be a buoyant force acting on it.

Conclusion

In this article, we have addressed some common questions related to the concept of upthrust or buoyant force and the volume of water displaced by a basketball floating in a bathtub of water. We have also highlighted the significance of Archimedes' Principle in this scenario and the relationship between the upthrust or buoyant force and the acceleration due to gravity.

References

Archimedes' Principle. (n.d.). In Encyclopedia Britannica.
Buoyancy. (n.d.). In Physics Classroom.
Density. (n.d.). In Physics Classroom.