Does Water Depth Affect the Force Needed to Hold an Apple Submerged?

In summary, the conversation discusses the concept of buoyancy and how it applies to an object submerged in water. The question asks whether the force needed to hold the object at a deeper point in the water is larger, the same, smaller, or impossible to determine compared to holding it just below the surface. The correct answer is that the force remains the same, as explained by Archimedes' principle, which states that the buoyant force on an object always equals the weight of the fluid displaced. The question also mentions the possibility of the object and water being compressible, which could affect the buoyant force, but it ultimately depends on whether the shrinking in volume of the object or the increase in density of the liquid has a greater impact.
  • #1
Ethan Godden
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It should be noted that this is not homework but rather practice for an exam. Is this the place I should be asking these types of questions?

Homework Statement


An apple is held completely submerged just below the surface of the water in a container. The apple is then moved to a deeper point in the water. Compared with the force needed to hold the apple just below the surface, what is the force needed to hold it at a deeper point? (a) larger (b) the same (c) smaller (d) impossible to determine

Homework Equations


P=Po+ρgh

The Attempt at a Solution


I thought since we know pressure increases with depth that the answer would be (a), but apparently it is (b). I do realize it is in a container, but shouldn't the pressure inside the container vary with depth?

A good explanation would be greatly appreciated.
 
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  • #2
Ethan Godden said:
It should be noted that this is not homework but rather practice for an exam. Is this the place I should be asking these types of questions?

Homework Statement


An apple is held completely submerged just below the surface of the water in a container. The apple is then moved to a deeper point in the water. Compared with the force needed to hold the apple just below the surface, what is the force needed to hold it at a deeper point? (a) larger (b) the same (c) smaller (d) impossible to determine

Homework Equations


P=Po+ρgh

The Attempt at a Solution


I thought since we know pressure increases with depth that the answer would be (a), but apparently it is (b). I do realize it is in a container, but shouldn't the pressure inside the container vary with depth?

A good explanation would be greatly appreciated.
Once the object is fully submerged, pressure acts all around it. It acts more at the bottom than at the top because the pressure is greater there, and this provides the buoyancy. But if you increase the pressure, e.g. by taking the object to greater depth, you increase the pressure equally all round it, so there is no net change to the buoyancy.
Stick to Archimedes' principle. What does that tell you here?

But it is not clear from the question whether we should consider the apple and water as incompressible. Or if they are compressible, which is more readily compressed. How would that change your answer?
 
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  • #3
Archimedes law, which is derived based on integrating the pressure force distribution over the surface of a submerged object, indicates that the buoyant force on the object is equal to the weight of the displaced volume of fluid. This doesn't change with depth.
 
  • #4
Thank you, I think I understand now.

Archimedes principle tells us that the magnitude of the buoyant force on an object always equals the weight of the fluid displaced. I think the reason for this is even though the pressure on the top of the container and apple is less than the pressure at the bottom or the container and apple, they both increase by the same amount as the depth increases.

I would assume both are incompressible as that's what most other questions in my textbook assume. If they were compressible, however, the total volume displaced would shrink, and by Archimedes principle, the buoyant force would decrease meaning the force required to hold the container would decrease. Am I correct in my thinking?
 
  • #5
Not exactly. If the liquid got compressed, more mass of liquid could fit into the displaced space, and this would tend to increase the buoyant force. So you would have to determine whether the shrinking in volume of the object wins out over the increase in density of the liquid.

Chet
 
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FAQ: Does Water Depth Affect the Force Needed to Hold an Apple Submerged?

1. What is pressure variance with depth?

Pressure variance with depth is the change in pressure as one moves deeper into a fluid or gas. It is a result of the weight of the fluid or gas above pushing down and compressing the molecules below.

2. How does pressure vary with depth in a fluid?

In a fluid, pressure varies with depth according to the equation P = ρgh, where P is pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth. This means that as depth increases, pressure also increases due to the weight of the fluid above.

3. What factors can affect pressure variance with depth?

The density of the fluid, the acceleration due to gravity, and the depth are the main factors that can affect pressure variance with depth. Additionally, temperature and the compressibility of the fluid can also play a role.

4. How does pressure variance with depth impact marine life?

Pressure variance with depth can have a significant impact on marine life. As depth increases, the pressure also increases, which can affect the physiology and behavior of marine organisms. Some organisms have adapted to live at specific depths where the pressure is optimal for their survival.

5. What is the practical application of understanding pressure variance with depth?

Understanding pressure variance with depth is important for a variety of applications, such as deep-sea diving, underwater construction, and oil drilling. It is also crucial for understanding the behavior of fluids in pipes and containers, as well as the functioning of hydraulic systems.

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