Work Energy Theorem Formula Derivation

The net work w done on a particle during a given time interval by the net force acting on the particle is equal to the change in the particle s kinetic energy during. The work energy theorem is useful however for solving problems in which the net work is done on a particle by external forces is easily computed and in which we are interested in finding the particles speed at certain positions of even more significance is the work energy theorem as a starting point for a broad generalization of the concept. The work w done by the net force on a particle equals the change in the particle s kinetic energy ke.

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A constant force is rare in the everyday world.

Work energy theorem formula derivation.

The force that we come across everyday is usually variable forces. Starting with the work energy theorem and then adding newton s second law of motion we can say that. Work kinetic energy theorem for a system of particles. Proving the work energy theorem for a variable force is a little tricky.

The work kinetic energy theorem for a single particle. The kinetic energy derivation using only algebra is one of the best ways to understand the formula in depth. This explanation can be extended to rigid bodies by describing the work of rotational kinetic energy and torque. A variable force is what we encounter in our daily life.

Thus we can say that the work done on an object is equal to the change in the kinetic energy of the object. The work energy theorem also known as the principle of work and kinetic energy states that the total work done by the sum of all the forces acting on a particle is equal to the change in the kinetic energy of that particle. Latex text w delta text ke frac 1 2 text mv text f 2 frac 1 2 text mv text i 2 latex where v i and v f are the speeds of the particle before and after the application of force and m is the particle s mass. Deriving the work energy formula for variable force is a bit hectic.

To develop a mathematical expression that relates work to the kinetic energy we ll assume that all of the work done on a system gives the system kinetic energy only. This is the derivation of work energy theorem. Work energy theorem for variable force. The derivation of the work energy theorem is provided here.

We will start with the definition of work and then apply newton s second law. Workdone under a variable force. For the sake of simplicity we will consider the. Derivation of the mathematical expression for work kinetic energy theorem.

For any net force acting on a particle moving along any curvilinear path it can be demonstrated that its work equals the change in the kinetic energy of the particle by a simple derivation analogous to the equation above. The work done on an object is equal to the change in its kinetic energy. Therefore we have proved the work energy theorem. General derivation of the work energy theorem for a particle.

Derivation of the work kinetic energy theorem for a single particle.