Contents

Conservation of energy¶

Conservation of energy states, that the energy in any isolated system is constant, no matter what happens within a system.

  • isolated system is a system that has no interactions with its surroundings

This states that energy can be transformed but cannot be created or destroyed. The total energy of a mechanical system at the end \((f)\) at any process equals the total mechanical energy at the beginning \((i)\) plus the work \(W_{\text{other}}\) done by the forces other than gravity and elastic forces.

\[\begin{split} K_f + U_f = K_i + U_i + W_{\text{other}} \\ U = U_{\text{grav}} + U_{\text{el}} \end{split}\]

Conservative force¶

If a force performs two-way conversion between kinetic and potential energies, it is called conservative force. (Always reversible). Work done by conservative force has the following properties:

  1. It can be always expressed as the difference between the initial and the final values of potential energy-function.

  2. It is reversible

  3. It is independent of the path the object and depends only on the starting and ending points

  4. When the starting and ending points are the same, the total work is zero

If All the work done by the object is by conservative forces the total mechanical energy is

\[ E=K+U \]

Is CONSTANT.

Non conservative forces¶

Example: friction always acts opposite to motion, thus its work is always negative. Energy therefore cannot be recovered by reversing motion, it is non conservative.

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