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--- 183_notes:potential_energy [2014/10/14 15:17] – [What is potential energy?] pwirving
+++ 183_notes:potential_energy [2021/03/12 02:43] (current) – [What is potential energy?] stumptyl
@@ Line 1: / Line 1: @@
+Section 6.7 in Matter and Interactions (4th edition)
 ===== Potential Energy =====
-For multi-particles systems, you will have to keep track of the energy changes associated with the internal forces. That is, the work done by objects in the system on other objects in the system. As you will read, we can often associate an energy with pairs of interacting of objects, which we call "potential energy." In these notes, you will read about potential energy, how it keeps track of the energy associated with interactions internal to the system, and some of its properties.
+For multi-particles systems, you will have to keep track of the energy changes associated with the internal forces. That is, the work done by objects in the system on other objects in the system. As you will read, we can often associate an energy with pairs of interacting of objects, which we call "potential energy." **In these notes, you will read about potential energy, how it keeps track of the energy associated with interactions internal to the system, and some of its properties.
+**
+==== Lecture Video ====
+{{youtube>yRqsEDsX3pQ?large}}
 ==== What is potential energy? ====
-Potential energy is energy associated with pairs of objects that interact with each other within a system. Because potential energy exists between pairs of objects, no single object can have potential energy, it is a multi-particle system that has potential energy. It's referred to as potential energy because it can be converted to other forms of energy. Common examples of systems with potential energy include stretched/compressed springs, galaxies of stars interacting gravitationally, atoms in which protons and electrons electrically, and TNT.
+__**Potential energy (J)**__ is energy associated with pairs of objects that interact with each other within a system. Because potential energy exists between pairs of objects, no single object can have potential energy, it is a multi-particle system that has potential energy. It's referred to as potential energy because it can be converted to other forms of energy. Common examples of systems with potential energy include stretched/compressed springs, galaxies of stars interacting gravitationally, atoms in which protons and electrons interact electrically, and TNT.
 ==== Formal definition of Potential Energy ====
@@ Line 40: / Line 45: @@
 ==== Energy in a multi-particle system ====
-The total energy of a multi-particle system where you have neglected the thermal energy of the objects in the system is given by the sum of the individual kinetic energies of the objects and potential energy between each pari of objects,
+The total energy of a multi-particle system where you have neglected the thermal energy of the objects in the system is given by the sum of the individual kinetic energies of the objects and potential energy between each pair of objects,
 $$E_{sys} = \left(K_1 + K_2 + K_3 + \dots\right) + \left(U_{1,2} + U_{1,3} + U_{2,3} + \dots\right)$$
@@ Line 48: / Line 53: @@
 Do not double count the energy. An object in the system does not do external work but it can  (with another object) share potential energy.
+==== Lecture Video ====
+{{youtube>IHYyQZN4vvg?large}}
 ==== Potential Energy Depends on Separation NOT Location ====
 [{{ 183_notes:potential_energy.002.png?400|Two objects that interact gravitationally move through different displacements. The potential energy change depends only on their separation.}}]
-As you will read, there is potential energy associated with the gravitational interaction between two objects ([[183_notes:grav_pe|local]] and Newtonian gravitation) and with the compression or extension of springs.
+As you will read, there is potential energy associated with the gravitational interaction between two objects ([[183_notes:grav_pe|local]] and [[183_notes:newton_grav_pe|Newtonian gravitation]]) and with [[183_notes:spring_pe|the compression or extension of springs]].
 It might appear that the location of the "smaller" object (either the falling or orbiting one) or the "moving" object (the mass attached to the end of the spring) is what matters for potential energy. But it is not the location of these objects that matter, but where these objects are relative to the objects with which they share the potential energy.
@@ Line 68: / Line 76: @@
 $$\Delta U = -\vec{f}_{2,1}\cdot \left(\Delta\vec{r}_2 - \Delta\vec{r}_1\right)$$
-So the change in potential energy depends on how the two objects change their positions relative to each other (i.e., their separation). You can make this more concrete by looking that the figure above and doing the vector subtraction. Here,
+So the change in potential energy depends on how the two objects change their positions relative to each other (i.e., their separation). You can make this more concrete by looking at the figure above and doing the vector subtraction. Here,
-$$\Delta\vec{r}_2 - \Delta\vec{r}_1 = \left(\vec{r}_{2,f} - \vec{r}_{2,i}\right)-\left(\vec{r}_{1,f} - \vec{r}_{1,i}\right)=\Delta \vec{r}$$
+$$\Delta\vec{r}_2 - \Delta\vec{r}_1 = \left(\vec{r}_{2,f} - \vec{r}_{2,i}\right)-\left(\vec{r}_{1,f} - \vec{r}_{1,i}\right)$$
+$$\Delta\vec{r}_2 - \Delta\vec{r}_1 = \left(\vec{r}_{2,f} - \vec{r}_{1,f}\right)-\left(\vec{r}_{2,i} - \vec{r}_{1,i}\right)=\vec{r}_f-\vec{r}_i = \Delta \vec{r}$$
-This is precisely the vector that tracks the separation between the two objects.
+This is precisely the vector that tracks the change in separation between the two objects, $\Delta \vec{r}$.
-$$\Delta U = -\vec{f}_{2,1}\cdot \underbrace{\Delta \vec{r}}_{\mathrm{separation}}$$
+$$\Delta U = -\vec{f}_{2,1}\cdot \Delta \vec{r}$$
 From this you can conclude that any change in potential energy is associated with a change in the shape of a system. For rigid systems, the potential energy is constant.