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How Can we Analyze the Total Energy in a System?
By Laura Zinszer 2011Columbia Public Schools & Physics First
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All Energy is measured in a unit called a Joule. This unit is usedwith all types of energy. It is abbreviated with a J.
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To understand total energy in a system, we must calculate both the potential energy and the kinetic energy.
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We will then add the Eg and Ek together.
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The formula for Total Energy becomes…
TE = Eg + Ek
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Let’s start with
Gravitational Potential
Energy (Eg)
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Gravitational Potential Energy (Eg)
To determine the Eg use the formula…
Eg = m * g * hWhere m = mass g = 9.8 h = height
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For example, a 1.5 kg ball held at a vertical position of 20 m above the ground has gravitational potential energy.
Gravitational Potential Energy (Eg)
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Gravitational Potential Energy (Eg)
.
Eg = m * g * h
Eg = 1.5kg * 9.8 * 20m
Eg = 294 J
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Why would a ball on the ground, have no gravitational potential energy?
Gravitational Potential Energy (Eg).
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TBI for Gravitational Potential Energy (Eg)
The higher that an object is elevated, the greater the Eg…
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What is Kinetic Energy?
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Kinetic Energy is the energy of motion. The amount of Ek depends on the mass and velocity of the object.
Kinetic Energy (Ek)
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Kinetic Energy (Ek)To calculate the kinetic
energy, use the formula…
Ek= ½ m * V2
m = mass V = velocity of the object.
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If the car has a mass of 1000 kg, and travels at a velocity of 20 m/s, then the Kinetic Energy equals…
Kinetic Energy (Ek)
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Kinetic Energy (Ek)Ek= ½ m * V2
Ek= ½ 1000kg * (20 m/s)2
Ek= 500 kg * 400 m2/s2
Ek= 200,000 J
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The greater the velocity or speed of an object, then the greater the Ek!
TBI for Kinetic Energy (Ek)
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How do Eg and Ek relate in an energy system?
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As the car moves down the track, what happens to the Eg?
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As the height is lower, the Eg becomes less.
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As the car moves down the track, what happens to the Ek?
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The car speeds up, so Ek increases!!!
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What is the car’s position on the track when the Eg = Ek?
One-half of the distance down the track.
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What happens to the Total Mechanical Energy (TME)?
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Total Mechanical Energy (TME) TME = Eg + Ek
The TME will always remain constant!!
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As the pendulum swings, the Eg is transformed into Ek…
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but the Total Mechanical Energy (TME) remains constant.
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What is the position of the pendulum when all energy is Eg?
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The pendulum is at the top and not moving.
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What is the position of the pendulum when Ek is the greatest?
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The pendulum is at the bottom of the swing and fastest!!
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What is the position of the pendulum when Eg = Ek?
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The pendulum is ½ way through the drop.
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As the coaster travels on the track, the Eg is exchanged for the Ek.
but the Total Energy (TME) remains constant.
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The BIG IDEA for energy is Total Mechanical Energy in the system is equal to the Eg + Ek….
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The Total Energy in the system will always remain constant.
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TBI - Energy can not be created or destroyed;
it can only be transformed from one type of energy
form to another.
Conservation of Energy!
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Reflection: What are 2 things you figured out about energy from this PPT??
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Now, Let’s Look at some Energy Graphs
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As the swinging pendulum falls…
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Eg Ek TE
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Eg Ek TE
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Eg Ek TE
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The Eg is transformed into Ek
Eg Ek TE
Eg Ek TE
Eg Ek TE
Eg Ek TE
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Eg Ek TE
Eg Ek TE
Eg Ek TE
Eg Ek TE
but the Total Energyin the system at each position remains constant.
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Eg Ek TE
Eg Ek TE
Eg Ek TE
Eg Ek TE
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As the kids on the sled go down the hill… the energy graph would look like
this…
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Eg Ek TE
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Eg Ek TE
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Eg Ek TE
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Eg Ek TE
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Eg Ek TE
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But the Total Energy in this system remains constant as the sled goes down the hill!
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A car at the top of a track had a beginning Eg of 32 J.
Eg of 32 J.
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The car traveled down the track and hit a rubberband
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Eg of 28 J
After it hit the car only bounced part of the way up and had only 28 J of Eg.
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Eg of 32 J
Eg of 28 J
What happened to the 4J of missing Eg if energy cannot be lost or destroyed??
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Eg of 32 J
Eg of 28 J
Of course, it must have been transformed into thermal energy into the rubberband!!
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Eg of 32 J
Eg of 28 J
How can we determine the efficiency of this energy system?
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Energy Efficiency=87.5%Original Eg 28 J Final Eg 32 J
Eg of 32 J
Eg of 28 J
= .875 x 100
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Energy Efficiency
Eg of 32 J
Eg of 28 J
This system is 87.5% efficient. This means 87% of the original Eg was in the final Eg.
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Energy Efficiency
Eg of 32 J
Eg of 28 J
What happened to 12.5% of the energy that “disappeared”?
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Energy Efficiency
Eg of 32 J
Eg of 28 J
12.5% became thermal energy due to the friction when the car hit the rubberband.