How Does a Submerged Stone Affect Balance Scale Readings?

[vinirn]

Homework Statement

A beaker with water is in equilibrium with a certain weight in a balance. Then we tie a cord to a stone, and soak the stone in water, without touching the bottom. What will the balance read and why?

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The Attempt at a Solution

The experience shows that the balance reads a increase of beaker's weight. I can't see how to employ the Arquimedes principle to solve the problem.

 

[Doc Al]

The experience shows that the balance reads a increase of beaker's weight. I can't see how to employ the Arquimedes principle to solve the problem.

Use Archimedes's principle to determine the force that the water exerts on the stone. Then consider Newton's 3rd law.

 

[vinirn]

Use Archimedes's principle to determine the force that the water exerts on the stone. Then consider Newton's 3rd law.

I can see three forces: the tension exerted by the cord, the buoyancy and the weight of the stone. The buoyancy is smaler than the weight of the stone, resulting in a downward net force. But this net force has the same intensity of the cord's tension, right? I know that the net force resulting from the three forces is zero, since the stone doesn't move.

 

[Doc Al]

I can see three forces: the tension exerted by the cord, the buoyancy and the weight of the stone. The buoyancy is smaler than the weight of the stone, resulting in a downward net force. But this net force has the same intensity of the cord's tension, right? I know that the net force resulting from the three forces is zero, since the stone doesn't move.

OK. The bottom line is that the water exerts an upward buoyant force on the stone, and thus the stone must exert an equal downward force on the water.

 

[vinirn]

OK. The bottom line is that the water exerts an upward buoyant force on the stone, and thus the stone must exert an equal downward force on the water.

Yah, I understood . But how this downward force on the water is reflected in the measure of the balance?

 

[Doc Al]

But how this downward force on the water is reflected in the measure of the balance?

The scale must now support the weight of the water plus the downward force on it.

Think of the water as something that must be in equilibrium. The forces on it are its weight, the upward force from the scale (which is what you're trying to determine), and the downward force from the stone.

 

[vinirn]

The scale must now support the weight of the water plus the downward force on it.

We consider the weight of the entire column of water from the bottom to the surface, or only the water beneath the stone? (considering only the column occupied by the stone)
The stone is now supporting the weight of the water above itself.

 

[Doc Al]

We consider the weight of the entire column of water from the bottom to the surface, or only the water above the stone? (considering only the column occupied by the stone)

The scale supports all the water in the beaker, right? (I don't know why you would consider just that column of water.)