The student is expected to investigate and calculate quantities using the work-energy theorem in various situations AND investigate examples of kinetic and potential energy and their transformations.
The work-energy theorem states that if one or more external forces acts upon a system, the net work done on the system equals the change in energy of the system. If the work is done on a single object, the net work done equals the change in kinetic energy of the object.
Work done on an object is equal to the product of the force on the object and the displacement of the point where the force is applied. Only forces that act in the direction of the displacement do work on an object. Without displacement there is no work.
Internal forces do not change the total energy of a system whereas external forces can change the total energy of a system.
Gravitational potential depends on an object’s position above a reference point; elastic potential energy depends on how much an object stretches and compresses.
The mechanical energy of a system is the sum of potential energy and kinetic energy. If no external forces act on a system, and if dissipative forces like friction can be ignored, then the mechanical energy of system does not change. For example, a truck at the top of a hill possesses potential energy. As it rolls to the bottom of the hill the potential energy becomes kinetic energy.
WORK-ENERGY THEOREM
Work (W) done on an object is equal to the product of force (F) on the object and the object’sdisplacement (S).
Formula for the work done on an object.
Diagram of work done on an object.
As shown above, work is done on the object only in the direction of displacement. Although the force “T” is also acting on the moving object, “T” is not in the direction of the displacement “S”. Hence, there is not work done by force “T”. In this case, force “F” is the only force that gives contribution to the total work as the direction of “F” is in the same direction with displacement.
No work is done without motion. The work done on an object by net forces is equal to the change in kinetic energy of the object. The quantities can be calculated using the equation for kinetic energy and the equation showing the relationship between force and work.
Formula for the change in energy of a system.
Formula showing the relationship between work and energy.
Energy is the food of industry. Energy is the ability to cause change or do work. The work-energy theorem involves a change in energy of a system due to the work done by all the forces, for example a sliding block comes to rest due to friction.
ENERGY TRANSFORMED
Energy can be transformed from one type to another. Mechanical energy is the ability to do work and is the sum of potential energy and kinetic energy. Potential energy is any stored energy and comes in several forms:
Gravitational potential energy
Elastic potential energy
Chemical potential energy
CONSERVATION OF ENERGY
A truck at the top of a hill possesses potential energy, and its kinetic energy at this moment is zero. As it rolls to the bottom of the hill the potential energy becomes kinetic energy. This transformation shows the conservation of energy according to the work-energy equation. During the entire process, the total amount of energy does not change.
Internal forces and external forces place different roles in the mechanical energy change. Internal forces do not change the total mechanical energy of a system whereas external forces do. Internal and external forces are relative concepts, and in this way it depends on which frame of reference you choose.