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 interact…
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.
View the full transcript and gain access to JoVE Core videos
Q1: How does work done by an external force relate to changes in kinetic energy?
Work done by an external force directly changes an object's kinetic energy. When no friction acts on the object, all work transfers to kinetic energy change. However, in real situations with friction present, the applied force must overcome both resistance and accelerate the object, making the relationship more complex.
Q2: What happens to work when friction acts on a moving object?
When friction acts on an object, part of the work done by the external force converts to thermal energy rather than kinetic energy. Molecules along colliding layers interact via electromagnetic forces, causing the layers to heat up. This irreversible thermal energy loss means not all external work increases the object's mechanical energy.
Q3: How does mechanical energy change when external forces do work on a system?
The net work done by external forces equals the total change in mechanical energy, which includes both kinetic and potential energy changes. In systems with non-conservative forces like friction, some work is lost as thermal energy. The total work can be calculated by adding the change in mechanical energy to the thermal energy generated.
Q4: Why is potential energy important when analyzing work done on a system?
Potential energy formulation helps account for internal forces within a system of interacting particles. When external forces act on a system, potential energy changes reflect how internal forces affect the system's state. This allows complete analysis of energy transfer beyond just kinetic energy changes alone.
Q5: What is the relationship between external work and total energy change in a system?
Work done by external forces equals the total energy transferred to or from the system. This total includes changes in kinetic energy, potential energy, and thermal energy from friction. Understanding this relationship is essential for applying conservation of energy principles to real-world scenarios with non-conservative forces.
Q6: How do you calculate the work done when both applied and frictional forces act on an object?
The net force determines acceleration, which relates to the change in kinetic energy through kinematics. The difference between applied force and frictional force magnitudes produces constant acceleration. Work done by the applied force distributes between increasing kinetic energy and generating thermal energy through friction.
Q7: What role do non-conservative forces play in work-energy analysis?
Non-conservative forces like friction dissipate mechanical energy as irreversible thermal energy. When these forces oppose motion, they reduce the portion of external work that increases kinetic or potential energy. Accounting for this energy loss is crucial for accurately determining how much work actually changes the system's mechanical energy.