Mechanical equilibrium of the system in gravitational field

In summary, in this conversation the topic of a system contained in a tall vessel with a thermally heterogeneous distribution of material is discussed. It is mentioned that the system will eventually reach a state of uniform temperature, but not uniform pressure or density due to the influence of gravity. The question of whether the system is in mechanical equilibrium is brought up, with the understanding that although there is no macroscopic change in pressure, it is not spatially uniform. The concept of equilibrium is clarified to mean that the parameter does not change over time, but can still vary in space.
  • #1
misko
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Consider a system contained in a very tall adiabatically isolating vessel with rigid walls initially containing a thermally heterogeneous distribution of material, left for a long time under the influence of a steady gravitational field, along its tall dimension, due to an outside body such as the earth. It will settle to a state of uniform temperature throughout, though not of uniform pressure or density.

Pressure and density will be higher in the lower part of the vessel due to gravity. Is this system in mechanical equilibrium? I mean, we don't have macroscopic change of the pressure in the system once everything is settled down, but pressure is not spatially uniform and it depends on the height we measure it.
 
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  • #2
misko said:
Is this system in mechanical equilibrium?

Yes.
 
  • #3
Ok but what bothers me is that pressure is not spatially uniform. Since pressure is intensive parameter, shouldn't the system in equilibrium have intensive parameters same in all points?
 
  • #4
misko said:
Since pressure is intensive parameter, shouldn't the system in equilibrium have intensive parameters same in all points?
No. Equilibrium means that the parameter doesn't change with respect to time. It can still change with respect to space.
 
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1. What is mechanical equilibrium of a system in a gravitational field?

Mechanical equilibrium refers to a state in which the forces acting on a system are balanced, resulting in no net motion or acceleration. In a gravitational field, this means that the weight of the object is balanced by an equal and opposite force, such as a normal force or tension force.

2. How is mechanical equilibrium related to Newton's laws of motion?

Newton's first law states that an object in motion will remain in motion unless acted upon by an external force. In mechanical equilibrium, there is no net force acting on the object, so it will either remain at rest or continue moving at a constant velocity in a straight line, in accordance with Newton's first law. Additionally, Newton's third law states that for every action, there is an equal and opposite reaction. In a gravitational field, this means that the weight of an object is balanced by an equal and opposite force from the surface it is resting on, resulting in mechanical equilibrium.

3. What factors determine whether a system is in mechanical equilibrium in a gravitational field?

The primary factor that determines whether a system is in mechanical equilibrium in a gravitational field is the sum of all the forces acting on the system. If the sum of the forces is zero, then the system is in equilibrium. Additionally, the position and orientation of the object and the surface it is on can also affect whether the system is in equilibrium.

4. How can one calculate mechanical equilibrium in a gravitational field?

To calculate mechanical equilibrium in a gravitational field, one must first identify all the forces acting on the system. This may include weight, normal force, tension force, and frictional force. Then, the sum of all these forces must be calculated. If the sum is zero, then the system is in equilibrium.

5. What are some real-life examples of mechanical equilibrium in a gravitational field?

Some common examples of mechanical equilibrium in a gravitational field include a book resting on a table, a person standing on the ground, and a pendulum hanging at rest. In each of these cases, the weight of the object is balanced by an equal and opposite force, resulting in mechanical equilibrium.

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