# 13.9 Potential energy

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Potential energy is associated with a system of objects - not with a single object.

Potential energy refers to the energy arising from the arrangement of a system of objects (particles), which interact with each other. Here, interaction means that objects apply force on each other. A change in the arrangement brings about a change in the forces interacting on the objects and the associated potential energy.

It is not very difficult to understand how energy can be associated with the arrangement of objects within a system. It is an unsaid rule, but it is a fact that objects (matter) always exist under the influence of different forces and as such objects interact with each other. One or combination of forces is actually the reason that we have a system of objects together. When the arrangement of the objects changes in the arrangement, there is change in the potential energy of the system . We facilitate the study of change in arrangement by an unique design. Generally, we isolate the object whose motion is to be studied from the rest of system that applies force on the object.

This definition of potential energy as quoted above is not definitive in the sense that the same can not be used for quantitative measurement. We shall formulate explicit mathematical expression in this module for potential energy for the general case. There are various forms of potential energy : gravitational, elastic, electromagnetic and such others potential energies. The meaning and definition of potential energy in the specific context is built upon this general definition.

Unlike kinetic energy, we do not refer or measure absolute value of potential energy. We generally work with the difference in potential energies between two states. Which of the configuration of particles can be considered to possess zero potential energy? One theoretical zero energy reference is the distribution of given particles at infinity. It is expected that no force operates on them and hence their potential energy is considered zero there. However, we can consider any other configuration as zero reference for our convenience. We consider, for example, ground level as zero potential reference in the case of gravitation. The main point is that measurement of change in potential energy does not change with the choice of reference.

From the discussion so far, we underline two characterizing aspects of potential energy :

• Potential energy is associated with a system of objects - not with a single object.
• Generally, potential energy of a particle at infinity is considered zero. In practice, we can refer measurement of potential energy with respect to certain datum.

Importantly, the above two features of potential energy is different to kinetic energy, which has an absolute value and is referred to a single object.

## Change in potential energy

In order to derive a general expression for change in potential energy, we refer to the vertical motion of a ball, projected upward. As the ball moves up, initial kinetic energy of the ball decreases by the amount of negative work done by the gravity. In the meantime, however, separation between Earth and ball also increases. Consequently, the potential energy of "Earth - ball" system increases by the same amount. In effect, gravity transfers energy "from" the kinetic energy of the ball "to" the potential energy of the "Earth - ball" system.

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