Potential Energy and Conservation of Energy

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CHAPTER-8

• Potential Energy and Conservation of Energy

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8-1 Potential Energy

• Potential Energy U energy associated with the
  configuration of a system of objects that exerts
  force on one another.
• Gravitational Potential Energy Ug energy
  associated with the separation between two
  objects that attracts each other by
  gravitational force.
• Elastic Potential Energy Us energy associated
  with the compression or extension of an elastic
  object.

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Ch 8-2 Work and Potential Energy

• Kinetic (K) and Gravitational Potential energy
  (Ug) of tomato-earth system
• Negative work Wg done by gravitational force in
  the rise of tomato in transferring K (decreasing)
  into Ug (increasing) of tomato
• Positive work Wg done by gravitational force in
  the fall of tomato in transferring Ug
  (decreasing) into K (increasing) of tomato.
• ? Ug - Wg or -? Ug Wg

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Ch 8-2 Work and Potential Energy

• Kinetic (K) and Elastic Potential energy (Us ) of
  block-spring system
• Negative work Ws done by spring force in the
  rightward motion transferring K (decreasing) of
  block into Us (increasing) of spring
• Positive work Ws done by spring force in the
  leftward motion transferring Us (decreasing) of
  spring into K (increasing) of block.
• ? Us - Ws or -? Us Ws

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Ch 8-2 Conservative and NonconservativeForces

• System contains two or more objects including a
  point-like objects (tomato or block)
• A force acts between point-like object and rest
  of the system
• When the configuration change force does work W1,
  changing kinetic energy K of the object and other
  type of energy of the system
• When the configuration change reversed, force
  reverse the energy transfer and does work W2
• Conservative Force W1-W2
• Nonconservative Force W1?-W2

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Ch 8-3 Path Independence of Conservative Forces

• The net work done by a conservative force on a
  particle moving around any closed path is zero.
• ?U-W0
• UiUf (cylic process)
• The work done by a conservative force on a
  paticle moving between two points does not
  depends on the path
• Wab1Wab

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Ch 8 Check Point 1

• The figure below show three paths connecting
  points a and b. A single force F does the
  indicated work on a particle moving along each
  path in the he indicated direction. On the basis
  of this information is the force conservative?

• Non-conservative force

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Ch 8-4 Determining Potential Energy Values

• Work done by a conservative force F
• W?xixfF (x) dx but ?U - W , then
• ?U - W - ?xixfF (x) dx
• Gravitational Potential Energy Ug
• ?Ug-?yiyf-mg dy mg(yf-yi) Ug(y) mgy
• Elastic Potential Energy Us
• ?US-?yiyf-kx dx k(xf2-xi2)/2 Us(y)(kx2)/2

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Ch 8 Check Point 2

• A particle to move along an x-axis from x0 to
  xx1., while a conservative force , directed
  along the x-axis, acts on the particle. The
  figure shows three situations , in which the x
  component of that force varies with x. The force
  has same maximum magnitude F1 in all three
  situations. Rank the the situation according to
  the change in the associated potential energy
  during the particle motion , most positive first

?U -?Fxdx Calculate area under the curve 1)
?U-(Fi X1)/2 2) ?U-(Fi X1) 3) ?U--(Fi X1)/2
FiX1/2 Ans 3, 1, 2
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Ch 8-5 Conservation of Mechanical Energy

• Mechanical energy Emec EmecKU
• In an isolated system where only conservatives
  forces cause energy change Emec is conserved
• ?KW ?U -W then ?K-?U
• Kf-Ki-(Uf-Ui)Ui Uf
• KfUf KiUi
• Emec-f Emec-i
• ?Emec0

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Ch 8-7 Work Done on a System by an External force

• Work Wa is energy transfer to or from a system by
  means of an external force acting on that system
• Work done on a system , no friction involved
  (Ball Earth system)
• Wa?K?U ?Emec

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Ch 8-7 Work done on a system by an external force

• Work done on a system , friction involved
  (Blockfloor system)
• F-fkma
• v2v022ad a(v2-v02)/2d
• Ffkma fkm(v2-v02)/2d
• Wa Fdfkdm(v2-v02)/2
• Wa fkd ?K ?Eth ?Emec
• ?Ethfkd
• Wa?K?U ?Emec

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Ch 8-8 Conservation of energy

• Total energy E EmecEthEint
• The total energy E of a system can change only by
  amounts of energy W that are transferred to or
  from the system
• W?E ? Emec ? Eth ? Eint , W is work done on
  the system.
• Isolated System The total energy E of an
  isolated system cannot be changed then
• ?E ? Emec ? Eth ? Eint0
• Emec-f-Emec-i ? Eth ? Eint0
• Emec-f Emec-i -? Eth- ? Eint