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 regarding the relationship between the work done by conservative internal forces and potential energy, we can follow these steps:

### Step-by-Step Solution

1. **Understanding Work Done by Conservative Forces**:
- Conservative forces, such as gravitational force or spring force, are forces for which the work done depends only on the initial and final positions, not on the path taken.
- The work done \( W \) by a conservative force when moving an object from point A to point B is related to the change in potential energy \( \Delta U \).

2. **Work-Energy Principle**:
- The work done by a conservative force is equal to the negative of the change in potential energy of the system:
\[ W = -\Delta U \]
- Here, \( \Delta U = U_f - U_i \), where \( U_f \) is the final potential energy and \( U_i \) is the initial potential energy.

3. **Rearranging the Equation**:
- From the equation \( W = -\Delta U \), we can express the change in potential energy in terms of work done:
\[ \Delta U = -W \]

4. **Conclusion**:
- Therefore, the negative of the work done by conservative internal forces on a system equals the change in potential energy:
\[ -W = \Delta U \]
- This means that as work is done by the conservative force, potential energy changes in the opposite direction.

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