8.4:
Work Done on a System by External Force
Consider a person moving a box in a warehouse.
If there is no frictional force, the work done by the applied force on the box would be the change in the kinetic energy of the box.
In real life, a frictional force acts on the box. So, the difference between the applied force and the frictional force magnitudes decides the acceleration of the box.
As the forces are constant, the box has a constant acceleration. The final velocity can then be written in terms of the box's initial velocity, acceleration, and displacement.
The acceleration is made the subject, and its expression is substituted into the force equation and further simplified.
As there is no change in potential energy, the difference in kinetic energy can be written as the change in the mechanical energy of the box.
The second term represents the increase in thermal energy due to friction between the box and the floor.
In summary, the work done by external forces equals the energy transferred to or from the system.
8.4:
Work Done on a System by External Force
The work done by an external force on a particle changes its kinetic energy. However, internal forces must also be considered for a system of interacting particles. The potential energy formulation helps formulate the effect of internal forces. The net work done by an external force can be written in terms of the total change of mechanical energy, which includes both kinetic and potential energies.
In the presence of a non-conservative opposing force, like friction, some part of the work done by an external force is lost as thermal energy. As layers of the object on which the force acts and layers of the opposing ground collide, the molecules along the colliding layers interact via electromagnetic forces, and the layers heat up. Eventually, some part of the work done by the external force goes on to heat the layers and is lost as irreversible thermal energy. The total work is obtained if this lost thermal energy is added to the change in kinetic and potential energies.
Suggested Reading
- Halliday, Resnick and Walker (2014), Fundamentals of Physics, 10th Edition, Wiley and Sons Inc.: section 8.4; pages 192–194.