Energy Diagrams: Difference between revisions

Latest revision as of 14:11, 29 November 2015

Claimed by Julianne Oliver

What is an Energy Diagram?

Energy Diagrams are extremely useful for analyzing the interactions between two different objects. These diagrams can also be confusing if not properly understood. How do all of the different pieces of an energy diagram fit together? This page serves as a resource on how to construct and interpret energy diagrams. Let's get started!

The Basics

Energy diagrams are very useful for understanding different repulsive and attractive situations. These diagrams consist of three main components: kinetic energy, potential energy, and kinetic plus potential energy. These three energies are plotted as a function of energy versus separation between two objects.

Let's review:

Kinetic Energy: the energy that a moving object has in addition to its rest energy. Kinetic energy is K on an energy graph.

Potential Energy: the energy associated with multiparticle systems. This is the energy between interacting objects, and this energy can be either attractive or repulsive. Potential energy is U on an energy graph.

What is the sum? Simply the sum of the potential and kinetic energies displayed on the graphs. We will discuss how to plot this value momentarily. K+U symbolizes the sum of the potential and kinetic energies.

Positive or Negative?

Kinetic energy can NEVER be negative! Potential energy is negative if the interaction is attractive and positive if the interaction is repulsive. The sum of the potential and kinetic energies depends on a few factors. If an object can "escape" from an attractive interaction, and, after having escaped, come to rest, then K+U is equal to zero. If however the object can escape with some final velocity, some final speed and motion, then K+U is greater than zero. Lastly, in a bound state, an object cannot escape the interaction it is involved in, and K+U is less than zero.

More Important Tidbits

K (kinetic energy) is zero or nonzero depending on the motion of the objects. At rest, kinetic energy is zero. In motion, kinetic energy is greater than zero. In an attractive interaction, U (potential energy) increases (becomes less negative) and K decreases as two objects move farther away from one another. In a repulsive interaction, U(potential energy) decreases and K increases as the two objects move farther away from one another. The x-axis is separation, denoted r, and the y-axis is energy.

=How to construct an energy diagram

Now that you know the basics, practicing constructing and analyzing energy graphs is the best way to learn!

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

See end for solutions to all examples.

Beginner

Label K, U, and K+U on the energy diagrams for the following situations:

Example 1: Two electrons are held at rest some finite distance apart, and they move away from each other after they are released. Their initial velocities are zero.

Example 2: A proton and an electron start out far apart. Their initial velocities are nonzero, and their energy is repulsive.

Example 3: An daughter has just enough energy to escape from her controlling mother (they have an attractive relationship).

Intermediate

Label K, U, and K+U on the following energy diagrams. THEN, label the following three energy graphs 1, 2, or 3 based on the following scenarios:

1: One of the components of this energy diagram is incorrect.

2: A proton and a electron are at rest, and they start out infinitely far apart.

3: An astronaut orbits the moon.

Advanced

Create an energy graph for each of the following situations.

Situation 1: A spacecraft is orbiting a moon. The spacecraft is given an initial velocity that allows the spacecraft to leave the moon's orbit with a final velocity greater than zero.

Situation 2: A boy jumps onto a merry-go-round and is attracted to the merry-go-round's axle. The boy's initial velocity is not high enough for him to escape the merry-go-round, so he continues to "orbit" the merry-go-round.

Situation 3: Two people are repulsed by on another and are trying to fight. They are held at rest by two of their friends a finite distant apart, and they of course move away from one another as soon as they are released, since their friends will not let them approach one another.

Solutions to Beginner Examples

Example 1: Example 2: Example 3:

Solutions to Intermediate Examples

Example 1: K+U is incorrect! Example 2: Example 3:

Solutions to Advanced Examples

Situation 1: Situation 2: Situation 3:

Connectedness

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

History

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

@@ Line 1: / Line 1: @@
 Claimed by Julianne Oliver
-==The Main Idea==
+==What is an Energy Diagram?==
+[[File:Mainideapic.JPG|center|300px|Example 2]]
+Energy Diagrams are extremely useful for analyzing the interactions between two different objects. These diagrams can also be confusing if not properly understood. How do all of the different pieces of an energy diagram fit together? This page serves as a resource on how to construct and interpret energy diagrams. Let's get started!
-Energy Diagrams are extremely useful for analyzing the interactions between two different objects. These diagrams can also be confusing if not properly understood. This page serves as a resource on how to construct and interpret energy diagrams. Let's get started!
+===The Basics===
+Energy diagrams are very useful for understanding different repulsive and attractive situations. These diagrams consist of three main components: kinetic energy, potential energy, and kinetic plus potential energy. These three energies are plotted as a function of energy versus separation between two objects.
-===A Mathematical Model===
+Let's review:
+'''Kinetic Energy:''' the energy that a moving object has in addition to its rest energy. Kinetic energy is '''K''' on an energy graph.
+'''Potential Energy:''' the energy associated with multiparticle systems. This is the energy between interacting objects, and this energy can be either attractive or repulsive. Potential energy is '''U''' on an energy graph.
+'''What is the sum?''' Simply the sum of the potential and kinetic energies displayed on the graphs. We will discuss how to plot this value momentarily. '''K+U''' symbolizes the sum of the potential and kinetic energies.
+===Positive or Negative?===
+Kinetic energy can NEVER be negative!
+Potential energy is negative if the interaction is attractive and positive if the interaction is repulsive.
+The sum of the potential and kinetic energies depends on a few factors. If an object can "escape" from an attractive interaction, and, after having escaped, come to rest, then K+U is equal to zero. If however the object can escape with some final velocity, some final speed and motion, then K+U is greater than zero. Lastly, in a '''bound state,''' an object cannot escape the interaction it is involved in, and K+U is less than zero.
+===More Important Tidbits===
+K (kinetic energy) is zero or nonzero depending on the motion of the objects. At rest, kinetic energy is zero. In motion, kinetic energy is greater than zero.
+In an '''attractive''' interaction, U (potential energy) increases (becomes less negative) and K decreases as two objects move farther away from one another.
+In a '''repulsive''' interaction, U(potential energy) decreases and K increases as the two objects move farther away from one another.
+The '''x-axis''' is separation, denoted r, and the '''y-axis''' is energy.
+===How to construct an energy diagram==
+Now that you know the basics, practicing constructing and analyzing energy graphs is the best way to learn!
 ===A Computational Model===
-How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]
+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==
+'''See end for solutions to all examples.
+'''
+===Beginner===
+Label K, U, and K+U on the energy diagrams for the following situations:
+Example 1:
+Two electrons are held at rest some finite distance apart, and they move away from each other after they are released. Their initial velocities are zero.
+[[File:109.jpg|300px|Example 1]]
+Example 2:
+A proton and an electron start out far apart. Their initial velocities are nonzero, and their energy is repulsive.
+[[File:111.jpg|300px|Example 2]]
+Example 3:
+An daughter has just enough energy to escape from her controlling mother (they have an attractive relationship).
+[[File:JDO78.JPG|300px|Example 3]]
+===Intermediate===
+Label K, U, and K+U on the following energy diagrams. THEN, label the following three energy graphs 1, 2, or 3 based on the following scenarios:
+: One of the components of this energy diagram is incorrect.
+: A proton and a electron are at rest, and they start out infinitely far apart.
+: An astronaut orbits the moon.
+[[File:JDO78.JPG|300px|Example 1]]
+[[File:JDO100.JPG|300px|Example 2]]
+[[File:Jdo77.jpg|300px|Example 3]]
+===Advanced===
+Create an energy graph for each of the following situations.
+Situation 1: A spacecraft is orbiting a moon. The spacecraft is given an initial velocity that allows the spacecraft to leave the moon's orbit with a final velocity greater than zero.
+Situation 2: A boy jumps onto a merry-go-round and is attracted to the merry-go-round's axle. The boy's initial velocity is not high enough for him to escape the merry-go-round, so he continues to "orbit" the merry-go-round.
+Situation 3: Two people are repulsed by on another and are trying to fight. They are held at rest by two of their friends a finite distant apart, and they of course move away from one another as soon as they are released, since their friends will not let them approach one another.
+===Solutions to Beginner Examples===
+Example 1: [[File:Simpleex1solution.JPG|300px|Example 1]]
+Example 2: [[File:Simpleex2solution.JPG|300px|Example 2]]
+Example 3: [[File:Simpleex3solution.JPG|300px|Example 3]]
+===Solutions to Intermediate Examples===
+Example 1: K+U is incorrect![[File:Intermediateex1solution.JPG|300px|Example 1]]
+Example 2:[[File:Intermediateex2solution.JPG|300px|Example 2]]
+Example 3:[[File:Intermediateex3solution.JPG|300px|Example 3]]
-Be sure to show all steps in your solution and include diagrams whenever possible
+===Solutions to Advanced Examples===
-===Simple===
+Situation 1:  [[File:Simpleex2solution.JPG|300px|Situation 1]]
-labeling K, U, and K+U for varying situations
+Situation 2: [[File:Advancedex2solution.JPG|300px|Situation 2]]
-===Middling===
+Situation 3:[[File:Simpleex1solution.JPG|300px|Situation 3]]
-matching energy graphs to different situations
-===Difficult===
-creating energy graphs for different situations
 ==Connectedness==