Law of Conservation of Energy

The total energy of all the participants in any process remains unchanged through that process. That is, energy cannot be created or destroyed.

Energy can be transformed (changed from one form to another).

Energy can be transferred (moved),

...but the total amount always remains the same.

Work-energy principle

Where does work (= Force $\times$ distance) fit in?

Work is an energy transfer.


  • reduces the energy of the system doing the work and
  • increases the energy of the system on which work is done, both by an amount equal to the work done.

Energy is forever?

In this picture, what happened to the kinetic energy when the book hit the floor?

Energy diagrams

If energy is really conserved, we might picture it as a river, whose flow is diverted into different channels, but never lost.

Our dropping book at three points in time:

  1. Raised above the floor, but not moving
  2. Just before impact,
  3. Just after impact.

Diagram with human's energy

  1. Before pushing car.
  2. After it's been accelerated to its fastest speed.
  3. After it slows down to speed=0 again.

Energy efficiency

energy efficiency = "useful" output energy / total input energy

For animals and humans, this peaks at about 25% (periods of sustained exercise). Though if we include sleep, it's lower

For internal combustion engines, about 25%.

Diagram of a car

How might you diagram a car at these three points: a.) at rest, b.) after accelerating to 30 mph, c.) after going up a hill?

Thermal energy

Is energy conserved when thermal energy is involved?

James Prescott Joule used the apparatus pictured, along with ridiculously precise thermometers to find that the temperature increase of a given amount of water was reproducibly proportional to the amount of mechanical work done (by the falling weight).


image credits

Daniel James