Potential and Kinetic Energy

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Potential and Kinetic Energy

• Demo bouncing ball

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What will happen to the kinetic energy in this
demo?

• It will increase linearly with time (the graph of
  energy as a function of time will form a straight
  line)
• The increase will be quadratic with time (the
  graph of energy as a function of time will form a
  parabola)
• It will decrease linearly with time (the graph of
  energy as a function of time will form a straight
  line)
• The decrease will be quadratic with time (the
  graph of energy as a function of time will form a
  parabola)
• It will remain constant

3
What will happen to the potential energy in this
demo?

• It will increase linearly with time (the graph of
  energy as a function of time will form a straight
  line)
• The increase will be quadratic with time (the
  graph of energy as a function of time will form a
  parabola)
• It will decrease linearly with time (the graph of
  energy as a function of time will form a straight
  line)
• The decrease will be quadratic with time (the
  graph of energy as a function of time will form a
  parabola)
• It will remain constant

4
What will happen to the total mechanical energy
in this demo?

• It will increase linearly with time (the graph of
  energy as a function of time will form a straight
  line)
• The increase will be quadratic with time (the
  graph of energy as a function of time will form a
  parabola)
• It will decrease linearly with time (the graph of
  energy as a function of time will form a straight
  line)
• The decrease will be quadratic with time (the
  graph of energy as a function of time will form a
  parabola)
• It will remain constant

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Units of Energy

• U mgh
• kg(m/s2) m kgm2/s2 J
• Unit of energy Joule J
• K mv2/2
• kg(m/s)2 kgm2/s2 J

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Conservation of Energy

• Example heavy ball, small speed we can neglect
  air resistance
• EKU
• U mgh0 mg (h-1/2 gt2) mgh mg2t2/2
• kg(m2/s4) s2 kgm2/s2 J
• K mv2/2 m(gt)2/2 mg2t2/2
• E K U mgh0

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Energy Diagrams
Energy
Total Energy TE
TE KE PE
KE and PE change as the particle moves from h1 to
h2, but their sum is always the same.
height
h1
h2
KE
PE
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• We need certain energy to lift the heavy object
  to some height.
• Why some people can do it faster than others?
• The once who can do it faster are
• more powerful
• Power energy per unit time

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Snowboard Manhttp//phet.colorado.edu/new/simulat
ions/sims.php?simEnergy_Skate_Park
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What if we repeat the experiment with a very
light object like a coffee filter?
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What will happen to the total mechanical energy
in this demo?

• It will increase linearly with time (the graph of
  energy as a function of time will form a straight
  line)
• The energy will increase all the way to the
  bottom.
• It will decrease linearly with time (the graph of
  energy as a function of time will form a straight
  line)
• The energy will decrease all the way to the
  bottom.
• It will remain constant

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Lets talk about money first

• Cash flow
• Income
• Spending
• Steady state

Household Dad Mom Kids
Spending
Income
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Basic energy model of a system interacting with
the environment
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Dropping the light object

• Dynamic equilibrium resulting in constant
  velocity
• Equilibrium parameter (velocity)
• Negative feedback
• Double the weight all other things the same

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Dynamic equilibrium

• Equilibrium of what
• Forces!
• In spite of the fact that there are forces acting
  on the object the velocity remains constant. (We
  will discuss dynamics later).
• Equilibrium parameter the quantity, which
  remain constant. In this case velocity
• Feedback Increasing velocity increases the drag
  force, which in term slows the object down. It is
  called negative feedback resulting in dynamic
  equilibrium

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Pump, water fountain system

• Dynamic equilibrium
• Equilibrium parameter (water level)
• Feedback?
• Limits?

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Dynamic equilibrium

• Equilibrium of what
• Flow in equals flow out
• In spite of the fact that there is water flowing
  in the level remains constant
• Equilibrium parameter the quantity, which
  remain constant. In this water level
• Feedback Increasing level increases the pressure
  at each hole, which in term speeds up the flow
  out. It is again a negative feedback resulting in
  dynamic equilibrium

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Heating of the house problem

• Why do we want to solve this problem?
• Practical application in energy consumption
• How much energy and money can we save for each
  degree that we lower the temperature in our
  homes?
• What does this correspond to in greenhouse gas
  emissions?
• We have to learn a lot before attacking it!