Work in general transfers energy from one place to another or one form to another, and the following is an explanation of the work-energy principle as it applies to particle dynamics. It should be noted that in more general systems, work can change the potential energy of a mechanical device, the heat energy in a thermal system, or the electrical energy in an electrical device.
The Work-Energy Theorem
The principle of work and kinetic energy (also known as the work-energy theorem) states that the work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle (Figure 1). This definition can be extended to rigid bodies by defining the work of the torque and rotational kinetic energy.
The work W done by the resultant (net) force on a particle equals the change in the particle's kinetic energy Ek:
where vi and vf are the speeds of the particle before and after the change and m is the particle's mass.
For the sake of simplicity, we will consider the case in which the resultant force F is constant in both magnitude and direction and is parallel to the velocity of the particle. The particle is moving with constant acceleration a along a straight line. The relationship between the net force and the acceleration is given by the equation F = ma (Newton's second law), and the particle's displacement d can be expressed by the equation:
which follows from the following kinematic equation:
The work of the net force is calculated as the product of its magnitude and the particle's displacement. Substituting the above equations yields: