How to Create and Interpret Energy Diagrams: Difference between revisions

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


1) Determine if the potential energy is attractive or repulsive  
# Determine if the potential energy is attractive or repulsive  
  a. For example, gravitational potential energy is attractive since it draws objects to the surface of the Earth (Ug<0). Electric potential  
#* For example, gravitational potential energy is attractive since it draws objects to the surface of the Earth <math>\left(U_g < 0\right)</math>.
      energy for charges with the same sign is repulsive, since like charges repel (Ue>0).
#* Electric potential energy for charges with the same sign is repulsive, since like charges repel <math>\left(U_e > 0\right)</math>.
2) Analyze whether the system is bound, unbound, or at escape speed to determine the location of the total energy line
# Analyze whether the system is bound, unbound, or at escape speed to determine the location of the total energy line  
  a. Bound System: A system in which the total energy is negative
#* Bound System: A system in which the total energy is negative
      i. E = K + U < 0; horizontal line below the x-axis
#** <math>E = K + U < 0</math>; horizontal line below the x-axis  
      ii. The distance between the objects in the system is limited and quantifiable
 
  b. Unbound System: A system in which the total energy is positive
 
      i. E = K + U > 0; horizontal line is above the x-axis
      ii. If r approaches ∞, the distance between the objects in the system is infinite and unquantifiable; the kinetic energy cannot equal 0
  c. System at Escape Speed: A system in which the total energy is equal to 0
      i. E = K + U = 0; horizontal line is at the x-axis
3) Draw the kinetic energy line/curve – this is always positive!


===A Mathematical Model===
===A Mathematical Model===

Revision as of 22:05, 2 December 2023

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 below the x-axis


A Mathematical Model

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

Simple

Intermediate

Difficult

creating energy graphs for different situations

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