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lecturenotes_oct7th2010_correctedenergyineractiondiagram_

# lecturenotes_oct7th2010_correctedenergyineractiondiagram_ -...

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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 )] = [kg-meter/sec 2 ]*meter = Newton-meter = 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] = [kg-meter/sec 2 ]*meter = Newton-meter = joule

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