Conservation of Energy Problem-Solving
The most general form of the Work-Energy Theorem is,
Reflective Mental Overseer Question:
To which system will I apply the conservation of work-energy?
* Select the system and consider the sources of any energy flow into or out of the system.
Is the system an isolated system ?
* An isolated system is one in which there is no energy exchange with its surroundings. If this is the case, then mechanical energy will be conserved.
* If the system is not isolated, then some energy (typically in the form of work) will flow into or out of the system. In this case you will have to use the generalized work-energy theorem to include the external force's work-energy contribution.
Will it be easier to solve the problem if I break the system up into two interacting subsystems ?
* You many have two or more systems exchanging energy with each other. One loses some energy while the other gains it.
What are the initial and final states of the system or systems ?
* Clarify in your mind the process described in the problem to determine the initial and final states of the system(s). A system's state includes both its spacial arrangement as well as its dynamic motion. For thermal problems this could include the initial and final temperature, pressure, or volume. For electrical problems this could include the initial and final amount of charge or voltage.
Are there any forces involved that do not have potential energy terms ?
* Determine which (if any) forces acting the system are nonconservative forces. For nonconservative forces you will have to determine their energy contribution by calculating the work they do directly from the definition of work. If you cannot calculate the work directly, then you will probably have to use the above work-energy relation to find their work contribution.
What type of energies are involved in the process described in the problem ?
* Determine the energy contribution for any conservative forces by calculating the change in potential energy associated with that type of force between the initial and final states of the system.
Where will I locate the zero of potential energy ?
* To calculate potential energy, select an origin for the zero energy level associated with the potential energy. For gravity near the surface of the Earth this can be any vertical location. For a spring force this has to be the equilibrium position of the system.
Which energy terms can I calculate and which terms are unknown ?
* If possible, determine the initial and final kinetic energy of the system, and the initial and final potential energy of each type of conservative force acting on the system.
* Apply the generalized work-energy equation. Examine the resulting equation and solve for any unknowns. If you have more than one unknown, then you will need to look at the problem again to see if it states or implies any additional relationships between the unknowns (such as a geometrical association or a that the kinetic energy is constant).