Overview: Mechanical energy

Prerequisites

Balanced rock, Arches National Park
Thomas Wolf, www.foto-tw.de /
Wikimedia Commons/ CC BY-SA 3.0

The concept of energy is an abstract one. Our direct experience with the concept of energy is more indirect than it is with the concept of force. We can see an avalanche of snow moving fast down a mountain as "having a lot of energy", or a balanced rock as potentially "having a lot of energy" it is were to unbalance and fall.

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A crouching tiger, ready to pounce looks like it potentially has a lot of energy, and the buzzing wings of a hummingbird looks like it has a lot of energy of motion. And we have a personal feel for when we're tired and when "we have a lot of energy".  

To quantify these senses of energy, we can build on our well established framework for the quantification of motion: Newton's laws.  

To build a strong grounding of the necessary energy-related concepts in our kinesthetic experience, let's ask the question:

Newton's second law tells us how forces change velocity. Can it also tell us how forces change speed?

Picking out the part of the force working with or against an object's velocity leads us to a scalar (non-vector) variation on Newton's second law: the work-energy theorem. Work is what forces do to change an object's speed as measured by its kinetic energy. We can then see that the work done by some of our forces (the non-resistive ones), can be reformulated as potential energies, leading to a powerful theorem: the conservation of mechanical energy when there are no resistive forces.

When there are resistive forces, our understanding of the kinetic and potential energies of macroscopic objects helps us to build it helps us to build a picture of the transformation of energy from the kinetic energy of macroscopic objects to the (hidden) thermal energy of the atoms and molecules of which the objects are made. In the next chapter (Chemical energy - An essential energy for life) we will further extend our concept of energy to the internal energy of the molecules themselves. 

Here are the links to the discussions of the most important principles and foothold ideas.

  • Kinetic energy and the work-energy theorem — Picking out the part of Newton's 2nd law that affects an object's speed leads to a definition of work and kinetic energy.
  • Energy of place -- potential energy — For non-resistive (conservative) forces, the work done by the forces can be reformulated as a potential (stored) energy.
  • The conservation of mechanical energy — When resistive forces can be ignored, the work-energy theorem with potential energy leads to a powerful and useful conservation law.
  • Energy in fluid flow — The application of the work-energy theorem to fluids unifies three critical principles of fluids and helps us understand when each one applies: Archimedes' principle, Bernoulli's principle, and the Hagen-Poiseuille equation.

Joe Redish 7/19/19