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8.4 Potential Energy Diagrams and Stability - University Physics Volume 1 | OpenStax

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Often, you can get a good deal of useful information about the dynamical behavior of a mechanical system just by interpreting a graph of its potential energy as a function of position, called a potential energy diagram. This is most easily accomplished for a one-dimensional system, whose potential energy can be plotted in one two-dimensional graph—for example, U(x) versus x—on a piece of paper or a computer program. For systems whose motion is in more than one dimension, the motion needs to be studied in three-dimensional space. We will simplify our procedure for one-dimensional motion only. First, let’s look at an object, freely falling vertically, near the surface of Earth, in the absence of air resistance. The mechanical energy of the object is conserved, 𝐸=𝐾+𝑈, 𝐸 = 𝐾 + 𝑈 , and the potential energy, with respect to zero at ground level, is 𝑈(𝑦)=𝑚𝑔𝑦, 𝑈 ( 𝑦 ) = 𝑚 𝑔 𝑦 , which is a straight line through the origin with slope 𝑚𝑔 𝑚 𝑔 . In the graph shown in Figure

8.4 Potential Energy Diagrams and Stability - University Physics Volume 1 | OpenStax Skip to Content Go to accessibility page Keyboard shortcuts menu University Physics Volume 1 8.4 Potential Energy Diagrams and Stability University Physics Volume 1 8.4 Potential Energy Diagrams and Stability Contents Highlights Print Close 8.4 Potential Energy Diagrams and Stability By the end of this section, you will be able to: Create and interpret graphs of potential energy Explain the connection between stability and potential energy Often, you can get a good deal of useful information about the dynamica

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