Conservative and Non-Conservative Forces

Conservative vs Non-Conservative Forces - Part 1

There are two types of work coming from different forces: conservative and nonconservative (nc).

• Conservative forces perform work that do not depend on the path taken (gravity, spring force). The energy is converted into potential energy.
• Nonconservative forces perform work that depend on the path (friction). The energy is dissipated as heat or sound. Any non-zero nonconservative work will change the mechanical energy.

Conservative Forces and Potential Energy

Work done by any conservative force is proportional to the change in the potential energy associated with that force:

• Potential energy is a type of energy which is stored inside the object and can be converted into other energies such as kinetic energy.
• Potential energy is usually shown by $U$, $PE$or $U_p$
• Gravitational Potential Energy (Earth): $$$\Delta{U_g} = mg\Delta{y}$ $$
• Gravitational Potential Energy (Any Planet): $\Delta{U_g} = -G\frac{m_1m_2}{r^2}$
• Spring Potential Energy: $U_s = \frac{1}{2}kx^2$

• A conservative force is always toward the points with lower potential energies.
• If work is done by only conservative forces, then the mechanical energy of the system is conserved.

• Potential energy can also be described as the negative integral of the dot product of conservative forces and distance as a mathematical expression:

• As a differential equation the above equation can be written as: