The Potential Energy of a System Increases if Work is Done upon the System by a Conservative Force

Work and Potential Energy:
Work is defined as the transfer of energy from one object to another due to the application of a force over a distance. It can either be positive or negative depending on the direction of the force and the displacement of the object. On the other hand, potential energy is the energy possessed by an object due to its position or condition.

Conservative and Non-conservative Forces:
In physics, forces are classified into two main types: conservative forces and non-conservative forces. Conservative forces are those that do not dissipate energy and can be associated with a potential energy function. Examples of conservative forces include gravitational and elastic forces. Non-conservative forces, such as friction and air resistance, dissipate energy as they act on an object.

Potential Energy and Conservative Forces:
When a conservative force acts on a system, it can do work on the system, transferring energy to it. This work done by the conservative force increases the potential energy of the system. The potential energy associated with a conservative force is stored energy that can be converted into other forms, such as kinetic energy.

Example:
Let's consider a simple example of a ball being lifted against the force of gravity. When an external force is applied to lift the ball, work is done on the ball. In this case, the external force is a conservative force (gravity) because it can be associated with a potential energy function (gravitational potential energy). As the ball is lifted, the potential energy of the ball increases because work is done on it by the conservative force.

Conclusion:
In conclusion, the potential energy of a system increases when work is done upon the system by a conservative force. Conservative forces are associated with potential energy functions, and as work is done by these forces, the potential energy of the system increases. This relationship is fundamental in understanding the interplay between work, energy, and potential energy in various physical systems.