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Potential energy is defined...

Potential energy is defined

A

Only in conservative fields

B

As the negative work done by conservative forces

C

As the negative of work done by external forces when `DeltaK=0`

D

All of these

Text Solution

AI Generated Solution

The correct Answer is:
To define potential energy, we can follow these steps: ### Step 1: Understanding Potential Energy Potential energy is the energy stored in an object due to its position in a force field, typically a gravitational or electric field. It is a form of mechanical energy. **Hint:** Think about how energy can be stored based on an object's position relative to other objects or fields. ### Step 2: Conservative Forces Potential energy is associated with conservative forces. A conservative force is one where the work done by the force on an object moving between two points is independent of the path taken. The work done by a conservative force can be expressed in terms of potential energy. **Hint:** Consider how the work done by a force relates to energy changes in a system. ### Step 3: Mathematical Representation The relationship between force (F) and potential energy (V) can be expressed mathematically as: \[ F = -\frac{dV}{dx} \] This equation indicates that the force is the negative gradient of the potential energy. **Hint:** Remember that the negative sign indicates that the force acts in the direction of decreasing potential energy. ### Step 4: Work Done by Conservative Forces The work done by conservative forces can be defined as the negative change in potential energy: \[ W = -\Delta V \] This means that when work is done by conservative forces, potential energy decreases. **Hint:** Think about how energy is transferred when work is done on or by an object. ### Step 5: Non-Conservative Forces In contrast, non-conservative forces (like friction) do not have a potential energy associated with them, and the work done depends on the path taken. **Hint:** Consider examples of forces that do not conserve mechanical energy. ### Conclusion Based on the definitions and properties discussed, potential energy is specifically defined in the context of conservative fields. Therefore, the correct answer to the question is that potential energy is defined as existing only in conservative fields. **Final Answer:** The correct option is A: only in conservative field.
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