Potential energy is stored energy that depends on an object's position or state of deformation. There are different types of potential energy including gravitational potential energy due to height above a gravitational body, and elastic potential energy stored in deformed springs and elastic objects. An example problem calculates the elastic potential energy stored in a spring attached to a hanging mass that has stretched the spring from its relaxed length. The work-energy theorem states that changes in kinetic and potential energy are related, and mechanical energy is the total of an object's kinetic and potential energies. An example shows using this to calculate the speed of a child sliding from rest down a frictionless slide given her initial height and mass.

1. POTENTIAL ENERGY

2. Potential energy is stored
energy
 Potential energy is associated with an object that
has the potential to move because of its position
relative to some other location. Unlike kinetic
energy, potential energy depends not only on the
properties of an object but also on the object’s
interaction with its environment.

3. Gravitational Potential Energy
 The energy associated with an object due to the
object’s position relative to a gravitational source
is called gravitational potential energy

4. Elastic Potential Energy
 The energy available for use when a deformed
elastic object returns to its original configuration is
named elastic potential energy.

6. PROBLEM
 A spring with a force constant of 5.2 N/m has a
relaxed length of 2.45 m. When a mass is
attached to the end of the spring and allowed to
come to rest, the vertical length of the spring is
3.57 m. Calculate the elastic potential energy
stored in the spring.

7. Work-Potential Energy Theorem
 Work done on an object by the gravitational force
as it falls along vertical distance;

8. Mechanical Energy
 The sum of kinetic energy and all forms of
potential energy is called mechanical energy.

9. PROBLEM
 Starting from rest, a child zooms down a
frictionless slide from an initial height of 3 m.
What is her speed at the bottom of the slide?
Assume she has a mass of 25 kg.