183_notes:potential_energy

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183_notes:potential_energy [2015/10/06 11:02] – [What is potential energy?] caballero183_notes:potential_energy [2021/03/12 02:42] – [Potential Energy] stumptyl
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 +Section 6.7 in Matter and Interactions (4th edition)
 + 
 ===== Potential Energy ===== ===== 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 ==== ==== Lecture Video ====
  
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 [{{ 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.}}] [{{ 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.  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. 
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 $$\Delta\vec{r}_2 - \Delta\vec{r}_1 = \left(\vec{r}_{2,f} - \vec{r}_{1,f}\right)-\left(\vec{r}_{2,i} - \vec{r}_{1,i}\right)=\vec{r}_f-\vec{r}_i = \Delta \vec{r}$$ $$\Delta\vec{r}_2 - \Delta\vec{r}_1 = \left(\vec{r}_{2,f} - \vec{r}_{1,f}\right)-\left(\vec{r}_{2,i} - \vec{r}_{1,i}\right)=\vec{r}_f-\vec{r}_i = \Delta \vec{r}$$
  
-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. 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.
  • 183_notes/potential_energy.txt
  • Last modified: 2021/03/12 02:43
  • by stumptyl