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The last question emphasizes two very important points.

• The zero of the potential energy is arbitrary. Only change in potential energies matter.
• Potential energy can be negative unlike kinetic energy.

In a system with no friction and no external forces, the energy of the system can only change form between kinetic and potential.

The pendulum is a great example of the back and forth between gravity and potential.

Energy Bar Charts

The idea behind the bar charts is to think in terms of bank accounts as energy going from one form to the other. These diagrams are much more useful than you may think and are really worth the extra couple seconds that it requires to draw them when solving problems.

Look at the following simulation "Energy skate park". Turn on the bar graphs and put the skateboarder on the ramp!