7.4: Conservation of Energy

The Law of Conservation of Energy states that the total energy in any process is constant. Energy can be transformed between different forms, and energy can be transferred between objects. However, energy cannot be created or destroyed. This is a broader law than the conservation of mechanical energy because this applies to all energy, not just energy when only conservative forces are applied.

We can write the Law of Conservation of Energy as $KE + PE + OE = \mathrm{Constant}$ or as $KE_{i} + PE_{i} + OE_{i} = KE_{f} + PE_{f} + OE_{f}$

In the second equation, the $KE_{i}$, $PE_{i}$, and $OE_{i}$ are initial conditions and $KE_{f}$, $PE_{f}$, and $OE_{f}$ are final conditions. The new term, $OE$, is other energy. This is a collected term for all forms of energy that are not kinetic energy or potential energy. Other forms of energy include: thermal energy (heat), nuclear energy (used in nuclear power plants), electrical energy (used to power electronics), radiant energy (light), and chemical energy (energy from chemical reactions).

When solving Conservation of Energy problems, it is important to identify the system of interest, and all forms of energy that can occur in the system. To do this, we need to first identify all forces acting on the system. Then, we can plug equations for different types of energy into the Law of Conservation of Energy equation to solve for the unknown in the problem.