Теорема о работе и энергии

The work-energy theorem states that the total work done by all the forces on an object is equal to the change in kinetic energy of that object, where m is the mass and v₁ and v₂ are the initial and final velocities of the object.

For instance, when a force is applied to a box, the velocity of the box increases, which increases its kinetic energy. Hence, the work done by the force contributes to a change in the kinetic energy of the box.

According to Newton's second law of motion, force is equal to mass times acceleration.

Consider a case where the box is moving with an acceleration a along a straight line. From the third equation of motion, the relationship between velocity and acceleration can be rearranged to obtain the displacement covered by the box.

By substituting the force and displacement terms in the work formula, a relationship between work done and change in kinetic energy is obtained. This expression is called the work-energy theorem.

According to this theorem, when an applied force increases the velocity of an object, the work done is positive. If the applied force causes no change in the velocity of the object or its kinetic energy, the work done is said to be zero.

If the net force applied is used to stop the moving object, the kinetic energy decreases, and hence the work done is negative.