How to Create and Interpret Energy Diagrams

Roshni Desai, Fall 2023

The Main Idea

Energy diagrams are tools used to analyze a system's energy and motion with respect to a scalar variable like position or time. They are typically used to represent the kinetic and potential energy within a system, in addition to a horizontal line that depicts the total mechanical energy of the system.

To draw the energy graph of a system, the following method should be used:

1. Determine if the potential energy is attractive or repulsive
   • For example, gravitational potential energy is attractive since it draws objects to the surface of the Earth [math]\displaystyle{ \left(U_g \lt 0\right) }[/math].
   • Electric potential energy for charges with the same sign is repulsive, since like charges repel [math]\displaystyle{ \left(U_e \gt 0\right) }[/math].
2. Analyze whether the system is bound, unbound, or at escape speed to determine the location of the total energy line
   • Bound System: A system in which the total energy is negative
     • [math]\displaystyle{ E = K + U \lt 0 }[/math]; horizontal line is below the x-axis
     • The distance between the objects in the system is limited and quantifiable
   • Unbound System: A system in which the total energy is positive
     • [math]\displaystyle{ E = K + U \gt 0 }[/math]; horizontal line is above the x-axis
     • If r approaches ∞, the distance between the objects in the system is infinite and unquantifiable; the kinetic energy cannot equal 0

A Computational Model

Vpython is great for modeling this concept. Using vpython, we can model many different systems that have kinetic and potential energy. We can model a spacecraft orbiting the Earth, and we can create graphs to display the kinetic, potential, and kinetic+potential energies of this system. See this code for how to do this!

[Sample Vpython code:https://trinket.io/glowscript/4010e21bc3]

Examples

Difficult

creating energy graphs for different situations

Connectedness

1. How is this topic connected to something that you are interested in?
2. How is it connected to your major?
3. Is there an interesting industrial application?

History

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

See also

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

Further reading

Books, Articles or other print media on this topic

External links

Internet resources on this topic

References

This section contains the the references you used while writing this page