Energy

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Energy
Energy is Conserved
?KE W
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Energy
Energy is Conserved
?KE W
Work-Energy Theorem
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Motion Newtons Laws
Special Case Friction Example A force is
applied to an object, causing the object to slide
on a table (with friction) at a constant
velocity. The speed is 2 m/sec. If the force
is removed, how far will the block slide before
it stops? The coefficient of kinetic friction is
0.8 and g 10 m/s2.
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Motion Newtons Laws
Special Case Friction Example A force is
applied to an object, causing the object to slide
on a table (with friction) at a constant
velocity. The speed is 2 m/sec. If the force
is removed, how far will the block slide before
it stops? The coefficient of kinetic friction is
0.8 and g 10 m/s2. NOTE We already solved
this problem in our discussions about Newtons
second Law. John E. Erdei, SCI190 Lecture
Slides Newtons Second Law, Slide 18,
University of Dayton (Unpublished) .
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Motion Newtons Laws
Special Case Friction Example A force is
applied to an object, causing the object to slide
on a table (with friction) at a constant
velocity. The speed is 2 m/sec. If the force
is removed, how far will the block slide before
it stops? The coefficient of kinetic friction is
0.8 and g 10 m/s2. ?KE W F d µk m g d ½
m v2 µk m g d v2 2 µk g d d v2 / ( 2 µk g)
0.25 m
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Motion Newtons Laws
Special Case Friction Example A force is
applied to an object, causing the object to slide
on a table (with friction) at a constant
velocity. The speed is 2 m/sec. If the force
is removed, how far will the block slide before
it stops? The coefficient of kinetic friction is
0.8 and g 10 m/s2. Note This is the same
result that we got using the constant
acceleration equations d ½ a t2 ?v a t
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Energy
Potential Energy
Potential energy comes in a variety of forms.
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Motion Newtons Laws
MEarth
Earth
m
REarth
r
gsurface G Mearth / R2 earth
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Motion Newtons Laws
MEarth
Earth
m
REarth
r
g G Mearth / r2
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Energy
Potential Energy
Gravitational Potential Energy of a mass m at a
distance r from the Center of the Earth
PEGRAV mgr G Mearth m / r
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Energy
Potential Energy
More commonly written Gravitational Potential
Energy of a mass m at a distance h from the
Surface of the Earth
PEGRAV mg ( REarth h)
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Energy
Potential Energy
Change in Gravitational Potential Energy of a
mass m at a distance h from the Surface of the
Earth h ltlt Rearth
Earth
h
?PEGRAV mgh
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Energy
Potential Energy
Gravitational Potential Energy often written as
PEGRAV mgh Where h is measured from the surface
of the earth
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Energy
Potential Energy
Football coach Jones becomes angry with a player,
and in order to get the players attention, coach
Jones makes the player go from playing field
level up to the top row of seats in the stadium.
Will the player do more work if he walks to the
top row or runs to the top row? Assume the
player starts from rest and stops when he reaches
the top.
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Energy
Potential Energy
Football coach Jones becomes angry with a player,
and in order to get the players attention, coach
Jones makes the player go from playing field
level up to the top row of seats in the statium.
Will the player do more work if he walks to the
top row or runs to the top row? Assume the
player starts from rest and stops when he reaches
the top. There is actually not enough information
to determine the work from first principles.
However, since the change in kinetic energy is 0,
the work done by the player must be used to
increase his potential energy (Conservation of
Energy). The amount of potential energy (PE
mgh) is the same, independent of running or
walking, and therefore the amount of work done by
the player is the same if he runs or walks!
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Energy
Potential Energy
Football coach Jones becomes angry with a player,
and in order to get the players attention, coach
Jones makes the player go from playing field
level up to the top row of seats in the stadium.
Will the player do more work if he walks to the
top row or runs to the top row? Assume the
player starts from rest and stops when he reaches
the top. If this is true, why do they make you
run as punishment, ie, why not punish the player
by making him walk at a leisurely pace to the top
of the stadium????
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Energy
Potential Energy
Football coach Jones becomes angry with a player,
and in order to get the players attention, coach
Jones makes the player go from playing field
level up to the top row of seats in the stadium.
Will the player do more work if he walks to the
top row or runs to the top row? Assume the
player starts from rest and stops when he reaches
the top. The punishment is related to Power, and
not directly to work. Since P W / t Walking
will result in the work to be expended over a
longer time period, therefore requiring less
power. Running expends the work over a shorter
time period, therefore requiring more power.