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| 183_notes:force_and_pe [2015/10/09 18:58] – [Equilibrium Points] caballero | 183_notes:force_and_pe [2021/04/01 12:49] – [Force is the Negative Gradient of Potential Energy] stumptyl |
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| ===== Force and Potential Energy ===== | ===== Force and Potential Energy ===== |
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| The [[183_notes:work_by_nc_forces|work done by a force is the integral of the force along the path]] that the force acts. This definition of the work gives rise to a relationship between the potential energy due to the interaction between the objects and the force responsible for that interaction. In these notes, you will read about the relationship between the force and the potential energy and how a graphical representation of the potential energy can also illustrate this force. | The [[183_notes:work_by_nc_forces|work done by a force is the integral of the force along the path]] that the force acts. This definition of the work gives rise to a relationship between the potential energy due to the interaction between the objects and the force responsible for that interaction.** In these notes, you will read about the relationship between the force and the potential energy and how a graphical representation of the potential energy can also illustrate this force.** |
| ==== Lecture Video ==== | ==== Lecture Video ==== |
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| ==== Force is the Negative Gradient of Potential Energy ==== | ==== Force is the Negative Gradient of Potential Energy ==== |
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| As [[183_notes:work_by_nc_forces|you have read]], the work done by a force is related to the integral along the path that the object takes. For forces where you can associate a potential energy, this integral is also related to the change in potential energy. | As [[183_notes:work_by_nc_forces|you have read]], the work (J) done by a force (N) is related to the integral along the path that the object takes. For forces where you can associate potential energy (J), this integral is also related to the change in potential energy. |
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| $$\Delta U = -W_{int} = -\int_i^f\vec{F}\cdot d\vec{r}$$ | $$\Delta U = -W_{int} = -\int_i^f\vec{F}\cdot d\vec{r}$$ |
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| The potential energy is the negative line integral of the force. In one-dimension this can be written as follows, | __**The potential energy is the negative line integral of the force.**__ In one-dimension this can be written as follows, |
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| $$\Delta U = -\int_{x_i}^{x_f} F_x dx$$ | $$\Delta U = -\int_{x_i}^{x_f} F_x dx$$ |