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# Section 7.1: Classical Energy Diagrams

Please wait for the animation to completely load.

A large k = 2-N/m spring is shown attached to a 1-kg red ball that is initially displaced 5 m (position is given in meters, time is given in seconds, and energy on the bar graph is given in joules).  The total energy and the potential energy are shown in the graph. Two bar graphs that depict the kinetic (blue) and potential (green) energies are also shown. Finally, the values of the energy are shown in the table.   Restart.

The energy diagram is an important diagram for both classical and quantum mechanics because it depicts the potential energy function, often just called the potential. The potential energy function is plotted vs. position, and therefore it tells you the potential energy of an object if you know its position. The potential energy function for a mass on a spring is just V(x) = 0.5 kx2, and therefore V(x) = x2.

Because of the form of this potential energy function, it is easy to get confused as to what it is actually showing and what it represents. If you have not done so already, run the animation. The red dot on the potential energy curve does NOT represent the actual motion of a particle on a bowl or roller coaster. In other words, it does NOT represent the two-dimensional motion of an object. It represents the one-dimensional motion of an object, here the one-dimensional motion of a mass attached to a spring. The motion of the red mass is limited to between the turning points represented by where the total energy is equal to the potential energy.

Now select the also show the kinetic energy on the graph animation. Watch the kinetic and potential energies change as the mass moves and the spring ceases to be stretched and then gets compressed. Notice that the potential energy and the kinetic energy is always equal to the total energy. Therefore, if you know the total energy and the potential energy function, you know the kinetic energy of the object at any position in its motion.

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