A Basketball Floats In A Bathtub Of Water. The Ball Has A Mass Of 0.5 Kg And A Diameter Of 22 Cm.What Is The:(a) Upthrust Or Buoyant Force? (b) Volume Of Water Displaced By The Ball?

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A Basketball in a Bathtub: Exploring the Principles of Buoyancy

When a basketball is placed in a bathtub filled with water, it appears to float effortlessly on the surface. This phenomenon is a result of the fundamental principles of buoyancy, which is a crucial concept in physics. In this article, we will delve into the world of buoyancy and explore the upthrust or buoyant force acting on the basketball, as well as the volume of water displaced by the ball.

Buoyancy is the upward force exerted by a fluid (such as water or air) on an object 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, the fluid exerts an upward force on the object, known as the buoyant force. The magnitude of the buoyant force depends on the density of the fluid, the volume of the fluid displaced by the object, and the acceleration due to gravity.

Calculating the Upthrust or Buoyant Force

To calculate the upthrust or buoyant force acting on the basketball, we need to use the formula:

F_b = ρ * V * g

where:

  • F_b is the buoyant force
  • ρ is the density of the fluid (water in this case)
  • V is the volume of the fluid displaced by the object
  • g is the acceleration due to gravity (approximately 9.8 m/s^2)

The density of water is approximately 1000 kg/m^3. To calculate the volume of the fluid displaced by the basketball, we need to know the volume of the ball.

Calculating the Volume of the Basketball

The volume of a sphere (such as a basketball) can be calculated using the formula:

V = (4/3) * π * r^3

where:

  • V is the volume of the sphere
  • r is the radius of the sphere

The diameter of the basketball is given as 22 cm, so the radius is half of that, which is 11 cm or 0.11 m.

Volume of the Basketball

Substituting the value of the radius into the formula, we get:

V = (4/3) * π * (0.11)^3 V ≈ 0.0013 m^3

Upthrust or Buoyant Force

Now that we have the volume of the fluid displaced by the basketball, we can calculate the upthrust or buoyant force using the formula:

F_b = ρ * V * g F_b = 1000 kg/m^3 * 0.0013 m^3 * 9.8 m/s^2 F_b ≈ 12.6 N

The upthrust or buoyant force acting on the basketball is approximately 12.6 N. This force is what allows the basketball to float effortlessly on the surface of the water. The volume of the fluid displaced by the basketball is approximately 0.0013 m^3.

In conclusion, the principles of buoyancy are a fascinating aspect of physics that can be observed in everyday life. The upthrust or buoyant force acting on the basketball is a result of the difference in pressure between the top and bottom of the object, and the volume of the fluid displaced by the object. By understanding these principles, we can gain a deeper appreciation for the natural world and the forces that shape our surroundings.

  • Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics. John Wiley & Sons.
  • Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers. Cengage Learning.
  • Buoyancy and Archimedes' Principle: A detailed explanation of the principles of buoyancy and Archimedes' principle.
  • Density and Buoyancy: An exploration of the relationship between density and buoyancy.
  • Fluid Dynamics: A comprehensive overview of the principles of fluid dynamics, including buoyancy and fluid flow.
    A Basketball in a Bathtub: Exploring the Principles of Buoyancy - Q&A

In our previous article, we explored the principles of buoyancy and calculated the upthrust or buoyant force acting on a basketball submerged in a bathtub of water. In this article, we will answer some frequently asked questions related to buoyancy and provide additional insights into this fascinating topic.

Q: What is the difference between upthrust and buoyant force? A: The terms "upthrust" and "buoyant force" are often used interchangeably, but technically, "upthrust" refers to the upward force exerted by a fluid on an object, while "buoyant force" is the specific force that causes an object to float or rise in a fluid.

Q: Why does the buoyant force depend on the density of the fluid? A: The buoyant force depends on the density of the fluid because the pressure exerted by the fluid on the object increases with depth. In a denser fluid, the pressure is greater, resulting in a greater buoyant force.

Q: Can an object be denser than the fluid it is submerged in? A: Yes, an object can be denser than the fluid it is submerged in. In such cases, the object will sink to the bottom of the fluid, as the weight of the object exceeds the buoyant force.

Q: What is the relationship between the volume of the fluid displaced and the buoyant force? A: The volume of the fluid displaced by an object is directly proportional to the buoyant force. The more fluid an object displaces, the greater the buoyant force.

Q: Can the buoyant force be greater than the weight of the object? A: Yes, the buoyant force can be greater than the weight of the object, resulting in the object floating or rising in the fluid.

Q: What is the significance of Archimedes' Principle in buoyancy? A: Archimedes' Principle states that the buoyant force on an object is equal to the weight of the fluid displaced by the object. This principle is a fundamental concept in buoyancy and is used to calculate the buoyant force on an object.

Q: Can the buoyant force be affected by the shape of the object? A: Yes, the buoyant force can be affected by the shape of the object. A more streamlined object will displace less fluid and experience a smaller buoyant force, while a more irregularly shaped object will displace more fluid and experience a greater buoyant force.

Q: What are some real-world applications of buoyancy? A: Buoyancy has numerous real-world applications, including:

  • Shipbuilding: The design of ships takes into account the buoyant force to ensure that they can float and remain stable in the water.
  • Submarines: Submarines use buoyancy to control their depth and remain submerged.
  • Diving: Divers use buoyancy to control their descent and ascent in the water.
  • Hydroelectric power plants: The buoyant force is used to generate electricity in hydroelectric power plants.

In conclusion, buoyancy is a fascinating topic that has numerous real-world applications. By understanding the principles of buoyancy, we can gain a deeper appreciation for the natural world and the forces that shape our surroundings.

  • Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics. John Wiley & Sons.
  • Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers. Cengage Learning.
  • Buoyancy and Archimedes' Principle: A detailed explanation of the principles of buoyancy and Archimedes' principle.
  • Density and Buoyancy: An exploration of the relationship between density and buoyancy.
  • Fluid Dynamics: A comprehensive overview of the principles of fluid dynamics, including buoyancy and fluid flow.