# Buoyant Force Problem: Equilibrium and Submerged Objects Explained

• PsychonautQQ
In summary, the conversation discusses the disturbance of equilibrium when a system of two objects, suspended from strings on opposite sides of a beam with a fulcrum halfway between, is submerged underwater. While one person argues that equilibrium will not be disturbed due to equal buoyant forces on each side, the other person presents a scenario where the masses of the objects are not equal and each loses a different amount of mass, leading to a disturbance in equilibrium. The conversation also touches on the concept of weight reduction and the importance of considering both force and weight in determining equilibrium.

## Homework Statement

If two objects are suspended from strings on opposite side of a beam with a fulcrum halfway between and has reached equilibrium, if the entire system is submerged underwater will equilibrium be disturbed?
The volumes are identical. The mass's are not equal but it is in equilibrium because one is closer to the center of mass than the other.

## The Attempt at a Solution

I said it won't be because each side will have an equal buoyant force due to identical volumes so the equilibrium will not be upset. However chegg.com says equilibrium will be upset.

originally
m1gL1 = m2gL2
m1L1 = m2L2
m1/m2 = L2/L1

Then it says something I'm having a hard time making sense of.
It says let the mass of reduction of each mass by c1 and c2 where c1≠c2
(m1 - c1)/(m2 - c2) ≠ m1/m2
therefore equilibrium will be disturbed.

I don't get it. c1 and c2 is the mass each loses? mass reduction wutt?? wouldn't the mass of reduction be the same since they displace and equal volume of water?

PsychonautQQ said:
it is in equilibrium because one is closer to the center of mass than the other

I said it won't be because each side will have an equal buoyant force due to identical volumes so the equilibrium will not be upset.

Think.

1 person
PsychonautQQ said:
It says let the mass of reduction of each mass by c1 and c2 where c1≠c2
(m1 - c1)/(m2 - c2) ≠ m1/m2
therefore equilibrium will be disturbed.
I don't like calling it mass reduction. Weight reduction perhaps, but I prefer to think of it as adding a buoyant force to each. Now, are you sure it says c1 ≠ c2? From the rest of the question, I would say you have c1 = c2 but m1 ≠ m2. Does it make sense to you then? ( It's also strange that at first you say the fulcrum is half way, but then later it clearly is not.)

Equilibrium doesn't just depend on force...

I would like to provide some clarification on this topic. The concept of buoyancy and equilibrium is often misunderstood, so it is important to approach it with a clear understanding of the principles involved.

First, let's define what we mean by equilibrium. In this context, equilibrium refers to a state where the forces acting on an object are balanced and there is no net force causing it to move. In other words, the object is in a stable position and will not move unless acted upon by an external force.

Now, let's consider the situation described in the problem. We have two objects, suspended from strings on opposite sides of a beam with a fulcrum in the middle. We are told that the objects have different masses, but the same volume. In this scenario, the objects are in equilibrium because the force of gravity pulling them down is balanced by the tension in the strings pulling them up.

Now, if we submerge the entire system underwater, the objects will displace water and experience a buoyant force. This buoyant force is equal to the weight of the water displaced by the objects. Since the objects have the same volume, they will displace the same amount of water and therefore experience the same buoyant force.

However, the objects still have different masses. This means that their weights are different and therefore the forces acting on them are not balanced. This will cause the objects to move, disrupting the equilibrium of the system.

To further explain this, let's look at the equations you provided. The first equation, m1gL1 = m2gL2, represents the forces acting on the objects in the original scenario (before submerging). The second equation, m1L1 = m2L2, represents the relationship between the masses and distances from the fulcrum that result in equilibrium.

Now, when we introduce the concept of mass reduction, we are essentially changing the masses in the equations. This is represented by the terms c1 and c2, which are the amounts by which each object's mass is reduced. Since the masses are now different, the equation m1/m2 = L2/L1 is no longer valid. This means that the objects will not be in equilibrium when submerged, as the forces acting on them will not be balanced.

In conclusion, the equilibrium of the system will be disturbed when submerged because the objects have different masses, even though they have the same volume. It is important to remember that equilibrium

## 1. What is buoyant force?

Buoyant force is the upward force exerted by a fluid on an object that is partially or fully submerged in the fluid. It is equal to the weight of the fluid that the object displaces.

## 2. How do you calculate buoyant force?

The buoyant force can be calculated using the formula Fb = ρVg, where ρ is the density of the fluid, V is the volume of the displaced fluid, and g is the acceleration due to gravity.

## 3. What factors affect buoyant force?

The buoyant force is affected by the density of the fluid, the volume of the displaced fluid, and the acceleration due to gravity. It is also influenced by the shape and size of the object submerged in the fluid.

## 4. How does buoyant force relate to Archimedes' principle?

Buoyant force is directly related to Archimedes' principle, which states that the buoyant force on an object is equal to the weight of the fluid that the object displaces. This principle helps explain why objects float or sink in a fluid.

## 5. How is buoyant force used in real life?

Buoyant force is used in various real-life applications, such as shipbuilding, designing submarines, and hot air balloons. It is also used in determining the densities of different materials by measuring their buoyant force in a fluid.