Lecture notes for Lecture #3, October7th, 2010
On the first day of class we briefly talked about mechanical energies, but today we
introduced the concept of mechanical energy more formally. We identified Kinetic
Energy and Potential Energy as the 2 types of mechanical energy systems, and we also
used the law of conservation of energy to help us predict final outcomes of a simple
mechanical energy system, such as tossing an object upward.
Using the law of
conservation of energy we were able to find expressions that related maximum heights
and initial speeds. The process to predict these outcomes is identical to what we used
when we were trying to determine the final or equilibrium temperatures for substances in
thermal contact with each other.
Shortly we will see how these processes are similar. For
now, let’s take a moment and make sure we have some of the definitions clearly
understood.
Definitions
Kinetic Energy
: This is the energy due to a body’s motion.
When the body is idealized
as a point mass, then the only motion that is possible is translational motion. In this case
then we can write the Kinetic Energy in equation form as KE = ½ mv
2
Potential Energy
: This is the energy due to a body’s position.
And since potential energy
is a result of energy due to position, we must specify the reference frame, or coordinate
system i.e. where y=0, from which we are
measuring the body’s position.
There are two
types of potential energy that we will discuss in this class.
1) In the case of a body’s potential
energy due to its position in a gravitational
field we can write the Potential Energy in equation form as PE = mgh where h is
the height or distance away from the reference frame that has been defined, or the
place where we are setting y equal to zero.
2
) In the case of a body’s potential energy due to its varying position
at the end of
a stretched or compressed spring we can write the Potential Energy in equation
form as PE = ½ kx
2
where k is the spring constant and x is the distance the spring
is stretched or compressed away from its equilibrium
position
Units
Kinetic and potential energies are measured in joules. For kinetic energy we have KE = ½
mv
2
. We can write the units for this quantity as: [kg*meters
2
/(sec
2
)], and since [kg
meter/sec
2
] is an equivalent expression for a Newton we can rearrange to find:
[kg*meters
2
/(sec
2
)] = [kgmeter/sec
2
]*meter = Newtonmeter = joule
We can do a similar analysis for deriving the units for potential energy as follows: Units
for PE are [kg*(meter/sec
2
)*meter], since the g=meters/sec
2
, giving:
[kg*(meter/sec
2
)*meter] = [kgmeter/sec
2
]*meter = Newtonmeter = joule
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 Fall '08
 PARDINI
 Physics, Energy, Kinetic Energy, Potential Energy

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