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Equilibrium and Potential Energy DiagramsPotential energy is associated only with conservative forces. Recall the definition of a conservative force from the discussion of friction (not a conservative force): A force
For any conservative force, the connection between the force and its potential energy function is
One problem that seldom comes up on the AP free-response section but puts in frequent appearances on the multiple-choice section has to do with potential energy diagrams. These are plots of There are two basic things to know about potential energy diagrams: equilibrium points and accessibility. A local maximum is said to be a point of unstable equilibrium, because an object placed at such a point will not return to its equilibrium position after being displaced slightly. Points Although it’s not a rigorous treatment, when presented with a potential energy diagram, you can think about points of equilibrium in terms of what would happen to a small marble placed at a given point. If it’s placed at a local maximum and displaced slightly, it will roll down—unstable equilibrium. Placed at a local minimum, upon displacement it will return to the local minimum—stable equilibrium. Finally, a marble on a saddle point will stay wherever you displace it to—neutral equilibrium. The cones below provide another example of the three types of equilibrium.
The other issue with potential energy diagrams is that of accessibility. If an object has a particular initial kinetic energy |