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183_notes:potential_energy [2014/10/10 14:47] – [Potential Energy Depends on Separation NOT Location] caballero | 183_notes:potential_energy [2021/03/12 02:43] (current) – [What is 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 " | + | 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 " |
+ | ** | ||
+ | ==== Lecture Video ==== | ||
+ | {{youtube> | ||
==== What is potential energy? ==== | ==== What is potential energy? ==== | ||
- | Potential energy is energy associated with pairs of objects that interact with each other within | + | __**Potential energy |
==== Formal definition of Potential Energy ==== | ==== Formal definition of Potential Energy ==== | ||
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==== Energy in a multi-particle system ==== | ==== 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, |
$$E_{sys} = \left(K_1 + K_2 + K_3 + \dots\right) + \left(U_{1, | $$E_{sys} = \left(K_1 + K_2 + K_3 + \dots\right) + \left(U_{1, | ||
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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. | 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> | ||
==== Potential Energy Depends on Separation NOT Location ==== | ==== Potential Energy Depends on Separation NOT Location ==== | ||
[{{ 183_notes: | [{{ 183_notes: | ||
- | As you will read, there is potential energy associated with the gravitational interaction between two objects ([[183_notes: | + | As you will read, there is potential energy associated with the gravitational interaction between two objects ([[183_notes: |
It might appear that the location of the " | It might appear that the location of the " | ||
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$$\Delta U = -\vec{f}_{2, | $$\Delta U = -\vec{f}_{2, | ||
- | 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 | + | 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 |
- | $$\Delta\vec{r}_2 - \Delta\vec{r}_1 = \left(\vec{r}_{2, | + | $$\Delta\vec{r}_2 - \Delta\vec{r}_1 = \left(\vec{r}_{2, |
+ | $$\Delta\vec{r}_2 - \Delta\vec{r}_1 = \left(\vec{r}_{2, | ||
- | This is precisely the vector that tracks the separation between the two objects. | + | This is precisely the vector that tracks the change in separation between the two objects, $\Delta \vec{r}$. |
- | $$\Delta U = -\vec{f}_{2, | + | $$\Delta U = -\vec{f}_{2, |
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. |