Problem Solving With the Conservation of Energy
To solve a conservation of energy problem determine the system of interest, apply law of conservation of energy, and solve for the unknown.
Learning Objective

Identify steps necessary to solve a conservation of energy problem
Key Points
 If you know the potential energies for the forces that enter into the problem, then forces are all conservative, and you can apply conservation of mechanical energy simply in terms of potential and kinetic energy. The equation expressing conservation of energy is: KE_{i}+PE_{i}=KE_{f}+PE_{f}.
 If you know the potential energy for only some of the forces, then the conservation of energy law in its most general form must be used: KE_{i}+PE_{i}+W_{nc}+OE_{i}=KE_{f}+PE_{f}+OE_{f}, where OE stands for all other energies.
 Once you have solved a problem, always check the answer to see if it is reasonable.
Terms

conservative force
A force with the property that the work done in moving a particle between two points is independent of the path taken.

potential energy
The energy an object has because of its position (in a gravitational or electric field) or its condition (as a stretched or compressed spring, as a chemical reactant, or by having rest mass)

kinetic energy
The energy possessed by an object because of its motion, equal to one half the mass of the body times the square of its velocity.
Full Text
Problemsolving Strategy
You should follow a series of steps whenever you are problem solving:
Step One
Determine the system of interest and identify what information is given and what quantity is to be calculated. For example, let's assume you have the problem with car on a roller coaster. You know that the cars of a roller coaster reach their maximum kinetic energy (
Determining Energy
The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path. When they start rising, the kinetic energy begins to be converted to gravitational potential energy. The sum of kinetic and potential energy in the system remains constant, ignoring losses to friction.
Step Two
Examine all the forces involved and determine whether you know or are given the potential energy from the work done by the forces. Then use step three or step four.
Step Three
If you know the potential energies (
Step Four
If you know the potential energy for only some of the forces, then the conservation of energy law in its most general form must be used:
where
Step Five
You have already identified the types of work and energy involved (in step two). Before solving for the unknown, eliminate terms wherever possible to simplify the algebra. For example, choose height
Step Six
Check the answer to see if it is reasonable. Once you have solved a problem, reexamine the forms of work and energy to see if you have set up the conservation of energy equation correctly. For example, work done against friction should be negative, potential energy at the bottom of a hill should be less than that at the top, and so on.
Key Term Reference
 Law
 Appears in these related concepts: TwoComponent Forces, Physics and Other Fields, and Models, Theories, and Laws
 conservation
 Appears in these related concepts: Conservation of Mechanical Energy, Museums and Private Collections, and Linear Momentum
 energy
 Appears in these related concepts: Surface Tension, Energy Transportation, and Introduction to Work and Energy
 equation
 Appears in these related concepts: Equations and Inequalities, Graphs of Equations as Graphs of Solutions, and What is an Equation?
 force
 Appears in these related concepts: Force of Muscle Contraction, Force, and First Condition
 friction
 Appears in these related concepts: ProblemSolving With Friction and Inclines, Inelastic Collisions in Multiple Dimensions, and The First Law: Inertia
 kinetic
 Appears in these related concepts: Friction: Static, The Kinetic Molecular Theory of Matter, and Postmodernist Sculpture
 potential
 Appears in these related concepts: What is Potential Energy?, Conservative and Nonconservative Forces, and Linear Expansion
 series
 Appears in these related concepts: Combination Circuits, Resisitors in Series, and The General Term of a Sequence
 work
 Appears in these related concepts: Heat and Work, Free Energy and Work, and The First Law of Thermodynamics
Sources
Boundless vets and curates highquality, openly licensed content from around the Internet. This particular resource used the following sources: