How to Create and Interpret Energy Diagrams: Difference between revisions
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#** <math>E = K + U > 0</math>; horizontal line is above the x-axis | #** <math>E = K + U > 0</math>; horizontal line is above the x-axis | ||
#** If <math>r</math> approaches <math>\infty</math>, the distance between the objects in the system is infinite and unquantifiable; the kinetic energy cannot equal 0 | #** If <math>r</math> approaches <math>\infty</math>, the distance between the objects in the system is infinite and unquantifiable; the kinetic energy cannot equal 0 | ||
#*System at Escape Speed: A system in which the total energy is equal to 0 | |||
#** <math>E = K + U = 0</math>; horizontal line is on the x-axis | |||
# Draw the kinetic energy line/curve – this is always positive! | |||
#* his is usually the reverse of the potential energy curve because <math>K + U = E</math> | |||
Revision as of 22:13, 2 December 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:
- 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].
- 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 [math]\displaystyle{ r }[/math] approaches [math]\displaystyle{ \infty }[/math], the distance between the objects in the system is infinite and unquantifiable; the kinetic energy cannot equal 0
- System at Escape Speed: A system in which the total energy is equal to 0
- [math]\displaystyle{ E = K + U = 0 }[/math]; horizontal line is on the x-axis
- Bound System: A system in which the total energy is negative
- Draw the kinetic energy line/curve – this is always positive!
- his is usually the reverse of the potential energy curve because [math]\displaystyle{ K + U = E }[/math]
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
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Intermediate
Difficult
creating energy graphs for different situations
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