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 . 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: