Representation 4.13.1. Potential Energy Diagrams.
A potential energy diagram is a graph of the potential energy \(U(x)\) vs. \(x\) for some system of interest. It is also often useful to indicate the total energy of a system.
Section 4.13 Potential Energy Diagrams
Exercises Activity: Spring Potential Energy Diagram
A block on a frictionless, horizontal table is connected to a spring (the other end of the spring is fixed to a wall). The spring is initially compressed from its equilibrium position by a distance of \(x_i\text{.}\)
1.
Sketch and label a potential energy diagram for this system.
Hint.
Recall the definition of the spring potential energy from Definition 4.9.1.
2.
On your diagram, find the location(s) where the potential energy is (a) largest and (b) smallest. Explain how you can tell from the diagram.
Hint.
If you have not done so already, sketch the total energy on your diagram. How does the total energy change as the block moves?
3.
On your diagram, find the location(s) where the kinetic energy is (a) largest and (b) smallest. Explain how you can tell from the diagram.
4.
On your diagram, find the location(s) where the spring force is (a) largest and (b) smallest. Do you think there is a way to tell this from the diagram alone?
