The Volume of Water Displaced

Oct 13, 2025 by talynt.org 132 views

Introduction

When a person stands on a raft, the raft displaces a certain volume of water. This displacement is directly related to the mass of the person standing on the raft. In this article, we will explore the relationship between the mass of the person and the volume of water displaced by the raft. We will use the principles of buoyancy and density to solve this problem.

The Principle of Buoyancy

The principle of buoyancy states that an object will experience an upward force equal to the weight of the fluid it displaces. This force is known as the buoyant force. The magnitude of the buoyant force is equal to the weight of the fluid displaced, which is given by the product of the density of the fluid and the volume of the fluid displaced.

The Density of Water

The density of water is given as 1,000 kg/m^3. This means that 1 cubic meter of water has a mass of 1,000 kilograms.

The Volume of Water Displaced

The raft displaces a volume of 0.224 m^3 of water when a person stands on it.

The Mass of the Person

Let's assume that the mass of the person is x kg. The weight of the person is equal to their mass multiplied by the acceleration due to gravity (g). The weight of the person is given by:

Weight of person = x * g

The buoyant force exerted on the raft is equal to the weight of the water displaced. The weight of the water displaced is given by:

Weight of water displaced = ρ * V * g

where ρ is the density of water, V is the volume of water displaced, and g is the acceleration due to gravity.

Since the buoyant force is equal to the weight of the person, we can set up the following equation:

x * g = ρ * V * g

Simplifying the equation, we get:

x = ρ * V

Substituting the values given in the problem, we get:

x = 1,000 kg/m^3 * 0.224 m^3

x = 224 kg

Therefore, the mass of the person is 224 kg.

Conclusion

In this article, we used the principles of buoyancy and density to solve the problem of finding the mass of a person standing on a raft. We assumed that the mass of the person is x kg and used the equation x = ρ * V to find the value of x. The result was that the mass of the person is 224 kg.

Discussion

This problem is a classic example of the principle of buoyancy in action. The buoyant force exerted on the raft is equal to the weight of the water displaced, which is a direct result of the density of water and the volume of water displaced. The mass of the person is directly proportional to the volume of water displaced, which is a fundamental concept in physics.

Limitations

This problem assumes that the raft is fully submerged in water and that the person is standing on the raft. In reality, the raft may not be fully submerged, and the person may not be standing on the raft. These factors would affect the calculation of the mass of the person.

Future Work

This problem can be extended to include other factors such as the density of the person and the raft, as well as the effects of air resistance. These factors would add complexity to the calculation but would provide a more accurate representation of the real-world scenario.

References

[1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics. John Wiley & Sons.
[2] Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers. Cengage Learning.

Appendix

The following is a list of the equations used in this article:

Weight of person = x * g
Weight of water displaced = ρ * V * g
x = ρ * V

Introduction

In our previous article, we explored the relationship between the mass of a person standing on a raft and the volume of water displaced by the raft. We used the principles of buoyancy and density to solve the problem and found that the mass of the person is directly proportional to the volume of water displaced. In this article, we will answer some of the most frequently asked questions about this problem.

Q: What is the principle of buoyancy?

A: The principle of buoyancy states that an object will experience an upward force equal to the weight of the fluid it displaces. This force is known as the buoyant force.

Q: What is the density of water?

A: The density of water is given as 1,000 kg/m^3. This means that 1 cubic meter of water has a mass of 1,000 kilograms.

Q: How does the volume of water displaced relate to the mass of the person?

A: The volume of water displaced is directly proportional to the mass of the person. This means that if the volume of water displaced increases, the mass of the person also increases.

Q: What are some of the limitations of this problem?

A: Some of the limitations of this problem include the assumption that the raft is fully submerged in water and that the person is standing on the raft. In reality, the raft may not be fully submerged, and the person may not be standing on the raft. These factors would affect the calculation of the mass of the person.

Q: Can this problem be extended to include other factors?

A: Yes, this problem can be extended to include other factors such as the density of the person and the raft, as well as the effects of air resistance. These factors would add complexity to the calculation but would provide a more accurate representation of the real-world scenario.

Q: What are some of the real-world applications of this problem?

A: Some of the real-world applications of this problem include the design of boats and ships, the calculation of the weight of cargo, and the determination of the buoyancy of objects in water.

Q: How can this problem be used to teach physics?

A: This problem can be used to teach physics by illustrating the principles of buoyancy and density. It can also be used to introduce students to the concept of proportionality and the relationship between variables.

Q: What are some of the common misconceptions about this problem?

A: Some of the common misconceptions about this problem include the assumption that the buoyant force is equal to the weight of the person, rather than the weight of the water displaced. Another misconception is that the volume of water displaced is directly proportional to the mass of the person, rather than the weight of the person.

Conclusion

In this article, we have answered some of the most frequently asked questions about the problem of finding the mass of a person standing on a raft. We have discussed the principle of buoyancy, the density of water, and the relationship between the volume of water displaced and the mass of the person. We have also highlighted some of the limitations and real-world applications of this problem.

Discussion

References

[1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics. John Wiley & Sons.
[2] Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers. Cengage Learning.

Appendix

The following is a list of the equations used in this article:

Weight of person = x * g
Weight of water displaced = ρ * V * g
x = ρ * V

These equations are fundamental to the solution of the problem and provide a clear understanding of the principles involved.