Conservation of Energy
Potential Energy and Conservation of Energy
Goals
- Know the sources of potential energy.
- Understand how potential energy and kinetic energy move back and
forth.
- Apply the law of conservation of energy to solve problems.
Definitions
Potential Energy
Energy which is stored in various forms. This can
be changed into kinetic energy.
Gravitational Potential Energy (Close to the Earth)
Gravitational potential energy comes from moving an object farther away from
a source of a gravitational field. For instance, if you lift up a book, you
are giving the book potential energy. If you let the book go, gravity
does work on the book and it accelerates toward the floor: potential energy
is converted to kinetic energy. The gravitational potential energy of an object is given by:
Ug = mgy
where m is the mass, g is the gravitational
constant and y is the height of the object.
Please note that this is only valid when the object is very near to the
surface of the earth. Longer distances require a more complex formula which
we will discuss later in the semester.
Elastic Potential Energy
Elastic potential energy is energy that is stored in anything that is
flexible, such as a spring or a rubber band. When you pull back on a
slingshot, you are creating a source of potential energy. When you release
the elastic, it accelerates a pellet at a target. The elastic potential
energy of a spring can be calculated with:
where k is the spring constant of proportionality and
x is the distance that the spring is stretched or compressed
from its relaxed length.
The following diagram illustrates elastic potential energy.
Conservation of Mechanical Energy
The total amount of mechanical energy in a system is the sum of the kinetic
energy of the system and the potential energy of the system. If the total
energy in a system is constant it is said to be a conservative
system. We can write it mathematically as:
This equation only applies if there is only potential and kinetic energy in
the system.
If there is some place that the energy may be lost, such as work done to
offset friction, then we must use this equation:
In this equation the Wother stands for any work not
accounted for in the potential and kinetic energy functions that we know.
Summary of Energy Forms
| Energy Type |
Formula |
| Kinetic |
 |
| Gravitational |
Ug = mgy |
| Elastic |
|
Example 1
You are standing on the edge of a cliff and decide to push a rock that has a
mass of 2kg off the edge with your foot. Using conservation of mechanical
energy, determine how fast the rock is going just before it impacts the
ground 75m below. Assume that there is no air resistance. If you dropped a
20kg rock from the same spot would the velocity be the same?
Example 2
A 4kg block slides across a frictionless table with a velocity of 5m/s into
a spring with a stiffness of 2500N/m. How far does the spring compress?
Solutions