183_notes:force_and_pe

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183_notes:force_and_pe [2021/04/01 12:47] – [Force and Potential Energy] stumptyl183_notes:force_and_pe [2021/04/01 12:49] – [Force is the Negative Gradient of Potential Energy] stumptyl
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 ==== Force is the Negative Gradient of Potential Energy ==== ==== Force is the Negative Gradient of Potential Energy ====
  
-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.
  
 $$\Delta U = -W_{int} = -\int_i^f\vec{F}\cdot d\vec{r}$$ $$\Delta U = -W_{int} = -\int_i^f\vec{F}\cdot d\vec{r}$$
  
-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,
  
 $$\Delta U = -\int_{x_i}^{x_f} F_x dx$$ $$\Delta U = -\int_{x_i}^{x_f} F_x dx$$
  • 183_notes/force_and_pe.txt
  • Last modified: 2023/11/30 20:35
  • by hallstein