How Does a Submerged Stone Affect Balance Scale Readings?

In summary: The scale supports all the water in the beaker, right? (I don't know why you would consider just that column of water.)In summary, the conversation discusses the balance reading when a cord is tied to a stone and soaked in water without touching the bottom of the beaker. It is determined that the balance reads an increase in weight due to the upward buoyant force on the stone. The stone must exert an equal downward force on the water, and the scale must support the weight of the water and the downward force on it. The weight of the entire column of water is considered, rather than just the water above the stone.
  • #1
vinirn
13
0

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.
 
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  • #2
vinirn said:
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.
 
  • #3
Doc Al said:
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.
 
  • #4
vinirn said:
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.
 
  • #5
Doc Al said:
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 :smile:. But how this downward force on the water is reflected in the measure of the balance?
 
  • #6
vinirn said:
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.
 
  • #7
Doc Al said:
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.
 
  • #8
vinirn said:
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.)
 

1. How does buoyancy work?

Buoyancy is the upward force exerted by a fluid (such as water) on an object immersed in it. This force is equal to the weight of the fluid that the object displaces. When the buoyant force is greater than the weight of the object, the object will float. This is because the object is less dense than the fluid, causing it to displace a larger volume and therefore experience a greater upward force.

2. What is the difference between buoyancy and weight?

Buoyancy is the upward force exerted by a fluid on an object, while weight is the downward force due to gravity on an object. Buoyancy is dependent on the density of the fluid and the volume of the object, while weight is dependent on the mass of the object. In order for an object to float, the buoyant force must be greater than the weight of the object.

3. How do you calculate the buoyant force?

The buoyant force can be calculated using Archimedes' Principle, which states that the buoyant force is equal to the weight of the fluid that the object displaces. This can be expressed as Fb = ρVg, where Fb is the buoyant force, ρ is the density of the fluid, V is the volume of the object, and g is the acceleration due to gravity.

4. What is a balance scale and how does it relate to buoyancy?

A balance scale is a type of weighing scale that uses two pans suspended from a lever to compare the weight of two objects. In terms of buoyancy, a balance scale can be used to determine if an object will float or sink in a fluid. If the weight of the object is less than the weight of the fluid it displaces, the object will float. If the weight of the object is greater, it will sink.

5. How does the concept of buoyancy apply to ships and boats?

Buoyancy is a crucial concept in the design and operation of ships and boats. The shape and size of a ship's hull is designed to displace a large volume of water, creating a greater buoyant force and allowing the ship to float. The weight of the ship is also carefully calculated to ensure that it does not exceed the buoyant force, which would cause it to sink. In addition, ballast can be used to adjust the weight and buoyancy of a ship for stability and control.

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