Weight of the object equals the weight of the displaced water

In summary, the conversation discusses the concept of buoyant force and the confusion surrounding it. The weight of the fluid displaced is not equal to the weight of the displaced object, it is equal to the buoyant force on the object. This means that when finding the buoyant force, one must consider the volume and density of the displaced water. It is important to draw a free body diagram and identify all the forces involved in order to correctly solve the problem.
  • #1
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On my book, it says the weight of the object equals the weight of the displaced water. Here is a question: A 70-kg ancient statue lies at the bottom of the sea. Its volume is 3.0*10^4 cm3. How much force is needed to lift it?

Now, Ignore how much force is needed, just focus on the buoyant force. My book says:Fb=m(water)*g=p(water)Vg. Why should we use volume to solve the problem if the weight of the statue equals to the weight of the object? so we can just do:Fb=m(water)g=m(statue)g=70*10=700N. However, this answer is different from the "correct" one. So I am confused at the concept of equal weight of the fluid and the object.

THanks for help.
 
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  • #2
The weight of the fluid displaced is not equal to the weight of the displaced object. It is equal to the buoyant force on the object. Since the object is not floating, the bouyant force must be less than the weight of the statue. Therefore, the weight of the displaced water is less than the weight of the statue.

So, when finding the bouyant force, you are going to have to work with the volume and density of the displaced water.

HINT: Start by drawing a free body diagram. What forces are involved?
 
  • #3


I can explain the concept of buoyant force and why we use volume to solve this problem. The buoyant force is the upward force exerted by a fluid on an object that is partially or fully submerged in it. This force is equal to the weight of the fluid that is displaced by the object. In other words, the weight of the object is equal to the weight of the displaced fluid.

In the given scenario, the ancient statue has a weight of 70 kg and a volume of 3.0*10^4 cm3. This means that when the statue is submerged in water, it will displace 3.0*10^4 cm3 of water. According to Archimedes' Principle, the buoyant force acting on the statue will be equal to the weight of this displaced water, which is p(water)Vg.

Now, the weight of the statue is equal to its mass (70 kg) multiplied by the acceleration due to gravity (10 m/s^2). This gives us a weight of 700 N, as you correctly calculated. However, this is not the buoyant force acting on the statue. To find the buoyant force, we need to use the weight of the displaced water, which is p(water)Vg. Using the density of water (1000 kg/m^3), we can convert the volume of water displaced (3.0*10^4 cm3) to its equivalent volume in cubic meters (0.03 m^3). Multiplying this by the acceleration due to gravity (10 m/s^2) gives us a buoyant force of 300 N.

Therefore, the correct answer is not 700 N, but 300 N. This shows that the buoyant force acting on the statue is less than its weight, which is why the statue sinks to the bottom of the sea. I hope this explanation helps clarify the concept of buoyant force and why we use volume to solve this problem.
 

1. What does the phrase "weight of the object equals the weight of the displaced water" mean?

This phrase is known as Archimedes' principle, which states that the buoyant force experienced by an object immersed in a fluid is equal to the weight of the fluid that the object displaces. In simpler terms, it means that the weight of an object floating in water is equal to the weight of the water that it pushes out of the way.

2. Why is it important to understand this principle?

Understanding Archimedes' principle is important in various fields such as engineering, physics, and oceanography. It helps in designing and constructing floating structures, determining the stability of ships, and predicting the behavior of objects in fluids.

3. How can we apply this principle in real-life situations?

This principle can be applied in various real-life situations, such as determining the weight of a sunken ship, designing submarines and ships that can float and navigate in water, and predicting the ability of objects to float or sink in different fluids.

4. Does this principle only apply to water or can it be applied to other fluids as well?

Archimedes' principle is not limited to water and can be applied to any fluid, including gases. It depends on the density of the fluid and the density of the object in question.

5. What are the implications of this principle in terms of buoyancy and density?

This principle helps us understand the relationship between buoyancy and density. An object with a higher density than the fluid it is immersed in will sink, while an object with a lower density will float. It also explains why some objects float while others sink in water.

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