Download Potential Energy

Potential Energy
Height
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Work is a process.
When a box is lifted, work is done on the box.
At the end, the box is resting – no kinetic energy.
Where did the work go?
y2
F = -mg
h
y1
W  -mg( y2 - y1 )  -mgh
Path Dependence
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What happens to work as a
rollercoaster goes down hill
then up again?
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What if the roller coaster
took a less steep path?
Reversible Process
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If an object is acted on by a force has its path
reversed the work done is the opposite sign.
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This represents a reversible process.
y2
F = -mg
h
y1
 
W  F  d  -mg ( y2 - y1 )  -mgh
Closed Path
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If the work done by a force doesn’t depend on the
path it is a conservative force.
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Conservative forces do no work on a closed path.
From 1 to 2, the
path A or B
doesn’t matter
From 1 to 2 and
back to 1,
the path A then
the reverse path
B gives no work
Nonconservative Force
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Not all forces are conservative.
In particular, friction and drag are not conservative.
d
Negative work is
done by friction to
get here
F = -mFN
-d
F = mFN
Negative work is
also done returning
the box
Net Work
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The work-energy principle is DK = Wnet.
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The work can be divided into parts due to
conservative and non-conservative forces.
• Kinetic energy DK = Wcon + Wnon
d
Ff
Fg
Kinetic and Potential Energy
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Potential energy is the negative of the work done by
conservative forces.
• Potential energy DU = -Wcon
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The kinetic energy is related to the potential energy.
• Kinetic energy DK = -DU + Wnon
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The energy of velocity and position make up the
mechanical energy.
• Mechanical energy Emech = K + U
Conservation of Energy
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Certain problems assume only conservative forces.
• No friction, no air resistance
• The change in energy, DE = DK + DU = 0
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If the change is zero then the total is constant.
• Total energy, E = K + U = constant
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Energy is not created or destroyed – it is conserved.
Solving Problems
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There are some general techniques to solve energy
conservation problems.
• Make sure there are only conservative forces and kinetic
energy in the problem
• Identify all the potential and kinetic energy at the beginning
• Identify all the potential and kinetic energy at the end
• Set the initial and final energy equal to one another
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