We continue our investigation of energy by allowing interactions to be part of the system, rather than external forces. You will learn that interactions can store energy within the system. Further, this interaction energy can be transformed—via the interaction forces—into kinetic energy.

Interaction energy is usually called potential energy. There are many kinds of potential energy, each associated with position.

• Gravitational potential energy changes with height.

• Elastic potential energy changes with stretching.

《 LOOKING BACK Section 9.1 Energy overview

• If a system is isolated, its total energy is conserved.

• If a system both is isolated and has no dissipative forces, its mechanical energy, $K+U$, is conserved.

Energy bar charts are a tool for visualizing energy conservation.

An energy diagram is a graphical representation of how the energy of a particle changes as it moves. Turning points occur where the total energy line crosses the potential-energy curve. And potential-energy minima are points of stable equilibrium.

Only certain types of forces, called conservative forces, are associated with a potential energy. For these forces,

• The work done changes the potential energy by $\text{Δ}U=-W$.

• Force is the negative of the slope of the potential-energy curve.

Energy is a big topic, not one that can be presented in a single chapter. Chapters 9 and 10 are primarily about mechanical energy and the mechanical transfer of energy via work. And we’ve touched on thermal energy because it’s unavoidable in realistic mechanical systems with friction. These are related by the energy principle:

Part V of this book, Thermodynamics, will expand our energy ideas to include heat and a deeper understanding of thermal energy. Then we’ll add another form of energy—electric energy—in Part VI.