--- ## The basics - A graph showing a system's potential energy and total energy as a function of the object or system's **position is known as an energy diagram**. - If the system that the diagram depicts is **isolated** then the total energy line will always stay constant. ==This line is colloquially referred to as the "E line". - Usually either the gravitational or elastic potential energy of an object/system will change as a function of that object/system's position. This is because those two type of potential energy are **directly related to the objects position relative to some other object *(like the equilibrium position of a spring or the ground)***. >[!quote] >##### *Reading an energy diagram* >![[energydiagram.png|850]] >##### *Kinetic energy and energy diagrams* >![[KEandenergydiagrams.png|850]] ## Understanding energy diagrams #### *Energy diagrams and kinetic energy* - If the potential energy is changing but the total energy is staying constant we **can make assumptions about how the kinetic energy of that object is changing in response.** *Note this only works for potential energy vs position graphs.* - For example if the object's potential energy is getting closer to its total energy line that indicates that the kinetic energy of the object is decreased and thus **the object is slowing down.** - On the other hand if the object's potential energy is getting closer towards the axis **or zero** that indicates that the object's kinetic energy is increasing and therefore the object **is speeding up**. - ==*You can think of the space above the PE curve and below the E line as the amount of KE that object has. If there is more space between the two lines the object has a higher KE, if there is less space the object has a lower KE.*== #### *Energy diagrams and force* - If an energy diagram depicts the **potential energy of an object as a function of that object's position** we can make the following KEY observation: - **==If the derivative/slope of the potential energy line is negative, the force on the particle at that point is positive. On the other hand if the derivative is positive the force will be negative==**. #### *Turning points* - Places where the kinetic energy of an object is 0 are places where the object is either stopped or **switching directions**. On an energy curve **these are places where the PE curve is at the E line. - We an object switches directions it **momentarily must stop and therefore will momentarily have 0 kinetic energy which means that the potential energy will constitute *all* of the objects energy**, which is why the PE curve is equal to A at the locations. #### *Equilibrium positions* - Places where the potential energy line of an object have **local maxima's and minimums are special**. At these positions we can assume the object/system is in **equilibrium** because the [[Derivative]] of the line here is 0 indicating that the potential energy is un-changing. - ==**A stable equilibrium position**== is one where the potential energy curve slopes upwards around it. **in other words they are any place where the PE line has a local minima.** On the other hand **unstable equilibrium points** are places where the PE line has a local maxima. >[!check] >##### *Energy diagram tips:* >- At any position, the distance from the axis to the PE curve is the object’s potential energy. The distance from the PE curve to the E line is its kinetic energy. >- The object cannot be at a position where the PE curve is above the E line. > - A position where the E line crosses the PE curve is a turning point where the object reverses direction. > - A position where the slope of the PE curve changes signs is a point where the object reverses direction >- If the E line crosses the PE curve at two positions, the object will oscillate between those two positions. Its speed will be maximum at the position where the PE curve is a minimum. --- #mainpage