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.
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Kinetic Energy
A force does work on the block. The kinetic energy of the block increases as a result by the amount of work. This relationship is generalized in the work-energy theorem.
The work W done by the net force on a particle equals the change in the particle's kinetic energy KE:
where vi and vf are the speeds of the particle before and after the application of force, and m is the particle's mass.
Derivation
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 determined from the equation:
obtaining,
The work of the net force is calculated as the product of its magnitude (F=ma) and the particle's displacement. Substituting the above equations yields: