Buoyant Force Problem: Equilibrium and Submerged Objects Explained

[PsychonautQQ]

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?

 

[voko]

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.

 

[haruspex]

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.)

 

[Enigman]

Equilibrium doesn't just depend on force...

 

[Nickie]

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