The negative of the work done by the conserative internal forces on a system equals the change iln

Options

A. total energy
B. kinetic energy
C. potential energy
D. none of these

Answer

To solve the question "The negative of the work done by the conservative internal forces on a system equals the change in...", we will analyze the relationship between work done by conservative forces and potential energy.

### Step-by-Step Solution:

1. **Understanding Work Done by Conservative Forces**:
- Conservative forces, such as gravitational force, are forces for which the work done is independent of the path taken and depends only on the initial and final positions.
- The work done by a conservative force can be expressed as the change in potential energy associated with that force.

2. **Defining Work Done**:
- When a conservative internal force does work on a system, it can either add energy to the system or take energy away from it.
- If we lift an object against gravity, we are doing work on the object, which increases its potential energy.

3. **Relating Work Done to Energy Change**:
- The work done \( W \) by a conservative force is related to the change in potential energy \( \Delta U \) of the system:
\[ W = -\Delta U \]
- Here, \( \Delta U \) is the change in potential energy, which is defined as the final potential energy minus the initial potential energy.

4. **Interpreting the Negative Sign**:
- The negative sign indicates that when work is done against the conservative force (like lifting an object), the potential energy of the system increases.
- Thus, the negative of the work done by the conservative internal forces is equal to the increase in potential energy.

5. **Conclusion**:
- Therefore, the negative of the work done by the conservative internal forces on a system equals the change in potential energy.
- The final answer is:
\[ \text{The negative of the work done by the conservative internal forces equals the change in potential energy.} \]

### Final Answer:
The negative of the work done by the conservative internal forces on a system equals the change in potential energy.

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