How do conservative forces conserve mechanical energy?

In summary, conservative forces do not actively conserve energy, but rather do not dissipate it. This is why potential energy is only defined for conservative forces, as it is a measure of the change in energy between two points that is independent of the path taken. The concept of potential energy is closely linked to the scalar potential, which is a powerful and widely used concept in physics.
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donaldparida
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How do conservative forces exactly conserve mechanical energy while non conservative forces do not. Also why is potential energy defined only for conservative forces?
 
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It's not so much that conservative forces do anything to conserve energy. It would be more accurate to say that a conservative force does nothing to dissipate energy. If a force field is conservative, the change in energy in moving from point A to point B is independent of the path taken. Potential energy is essentially a measure of this hypothetical change in moving from point A to point B. If the force was not conservative and the energy change was dependent on the path, then there would be no single-valued potential associated with moving from A to B since moving along different paths produces different answers, so the concept of potential energy doesn't really make sense anymore.

This is all intimately related to the scalar potential, which is a concept that pops up in many fields in physics and is quite powerful and interesting.
 
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1. What is a conservative force?

A conservative force is a type of force that does not dissipate or lose energy in a system. This means that the total mechanical energy (kinetic + potential) of the system remains constant, or is conserved, throughout the motion.

2. How do conservative forces conserve mechanical energy?

Conservative forces conserve mechanical energy by doing work on a system that can be fully recovered. For example, when a ball is thrown up in the air, gravity does work on it and converts its kinetic energy into potential energy. When the ball falls back down, the potential energy is converted back into kinetic energy, and the total mechanical energy remains constant.

3. What are some examples of conservative forces?

Some examples of conservative forces include gravity, electrostatic force, and spring force. These forces do not dissipate energy as they do work on a system, allowing for the conservation of mechanical energy.

4. How does the conservation of mechanical energy relate to the laws of thermodynamics?

The conservation of mechanical energy is related to the first law of thermodynamics, which states that energy cannot be created or destroyed, only transferred or transformed. The conservation of mechanical energy demonstrates this principle by showing that energy in a closed system remains constant.

5. What is the significance of conservative forces in physics?

Conservative forces play a crucial role in understanding and predicting the motion of objects in physics. By conserving mechanical energy, these forces allow us to make accurate calculations and predictions about the behavior of a system without having to consider energy loss due to friction or other non-conservative forces.

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