8.01 Lecture Notes - Lecture 1: Potential Energy, Mechanical Energy, Kinetic Energy
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Document Summary
In one dimension, the potential energy difference is de nite as. This is just the interrogation of newton"s second law in the x-direction. The x-component of the force is the negative derivative of the potential energy. Consider the potential energy associated wit a spring u(x) = kx where is the displacement of the spring from its equilibrium. The negative slope of the plot of u(x) vs. x is the x-component of the force and is given by. Mechanical energy is represented by a horizontal line since it is constant. E = k(x) + u(x) = mv + kx. Kinetic energy is difference between mechanical energy and potential energy. The gure above shows a graph of potential energy u(x) verses position for a particle executing one dimensional motion along the x- axis. The total mechanical energy of the system is indicated by the dashed line. At t =0 the particle is somewhere between points a and g.