Conservative and non-conservative systems

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In summary, conservative systems maintain a constant total mechanical energy, while non-conservative systems can lose energy due to external forces. A system can be determined as conservative if there is no work done by external forces, otherwise it is considered non-conservative. Real-life examples include a pendulum as a conservative system and a car as a non-conservative system. It is not possible for a non-conservative system to become conservative. Understanding these concepts is important for predicting the behavior and energy conservation in various fields such as physics, engineering, and environmental sciences.
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Homework Statement



The potential energy (V) of a conservative system is a function of position (q) only. Thus, V = V(q) for any conservative system.

When a conservative system interacts with radiation (spectroscopy), then the PE of the system depends explicitly on time (t) also: V = V(q,t).

Is the latter system a non-conservative system? Is V = V(q,t) characteristic of a non-conservative system, just like V = V(q) is characteristic of a conservative system?

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The Attempt at a Solution


 
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Do you know what a hamiltonian is and what the hamiltonian equations of motion are?
 

FAQ: Conservative and non-conservative systems

What is the difference between conservative and non-conservative systems?

In a conservative system, the total mechanical energy (kinetic and potential) of the system remains constant over time. In a non-conservative system, energy can be lost due to external forces, such as friction or air resistance.

How can you determine if a system is conservative or non-conservative?

A system is considered conservative if the work done by external forces is zero, meaning that energy is conserved. If work is being done by external forces, the system is considered non-conservative.

What are some real-life examples of conservative and non-conservative systems?

An example of a conservative system is a pendulum swinging back and forth, where the total mechanical energy (kinetic and potential) remains constant. An example of a non-conservative system is a car moving on a road, where energy is lost due to friction and air resistance.

Can a non-conservative system become conservative?

No, a non-conservative system cannot become conservative. Energy can only be conserved in a closed system where no external forces are acting.

Why is it important to understand the concept of conservative and non-conservative systems?

Understanding conservative and non-conservative systems allows us to predict the behavior of a system and how energy is conserved or lost. This can be applied to various fields such as physics, engineering, and environmental sciences.

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