Accounting for Energy II

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Accounting for Energy II

• Class 23.2

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Objectives

• Know that energy is conserved
• Understand state energies
• Kinetic, Potential, Internal
• Understand flow work
• Understand sequential energy conversion
• Be able to do calculations involving accounting
  for energy

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Recall Types of Energy(Table 22.1 - Foundations
Text)

• Energy is a conserved quantity, meaning the total
  energy of a system is constant.
• Energies that are net input are path quantities
  (depend on the path taken)
• Work, heat (discussed last time)
• Energies that can accumulate are state quantities
  (independent of path)
• Kinetic, potential, internal

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State Energies

• State energies dont depend on the path.
• Often specified by other state quantities.
• Three main types of state energy
• Kinetic
• Potential
• Internal

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Kinetic Energy

• The energy associated with mass in motion.
• Often mechanical energy is used to produce
  kinetic energy. For example, shaft work from a
  car engine produces the cars kinetic energy.

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Kinetic Energy

• Consider a rigid mass accelerated from an initial
  velocity v1 to a final velocity v2 as a result of
  an applied force, F.
• Thus, an input of mechanical work caused the
  object to change its kinetic energy, Ek

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Kinetic Energy

• From the UAE (w/ generation consumption 0 by
  conservation of energy)
• Energyfinal - Energyinitial Input - Output
• Thus, for a constant force F
• DEk Mech. Work Input FDx
• After applying Newtons Laws (see text for
  derivation) we get
• DEk ½ mv22 - ½ mv12

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Potential Energy

• The energy associated with the position of mass.
• Examples
• Gravitational Potential
• Spring Potential
• Others electrical (capacitors), magnetic
  (inductors), hydraulic (pumped storage), kinetic
  (flywheels), chemical (batteries),.

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Gravitational Potential

• Consider a rigid mass lifted vertically by a
  force F a distance Dx.
• Thus, an input of mechanical work caused the
  object to change its potential energy, Ep

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Gravitational Potential

• From the UAE
• Energyfinal - Energyinitial Input - Output
• Thus, for a constant force F
• DEp Mech. Work Input FDx
• By a force balance (in vertical (y) direction) we
  get F mg, so
• DEp mgDx

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Example

• A 4000 kg elevator starts from rest, accelerates
  uniformly to a constant speed of 1.8 m/s, and
  decelerates uniformly to a stop 20 m above its
  initial position. Neglecting friction and other
  losses, what work was done on the elevator?

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Example Solution

20m
M4000 Kg


Datum
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Example Solution( cont.)

• D EP mgDx
• (4000 Kg)(9.81 m/s2)(20 m)
• 784,000 (Kg.m.m)/(s2)
• 785 KN.m
• 785 KJ

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Spring Potential

• Consider a force F compressing a spring a
  distance of Dx.
• Thus, an input of mechanical work caused the
  springs potential energy to change.
• From the UAE
• Energyfinal - Energyinitial Input - Output, or
• DEp Mech. Work Input

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Spring Potential

• This time the force is not constant along x. By
  Hookes Law, the relationship is
• Fkx
• where k is the spring constant and x0 is the
  uncompressed (relaxed) state.
• Then we get

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Internal Energy

• The energy associated with translational,
  rotational, vibrational, and electronic potential
  energy of atoms and molecules.
• Loosely, it is the energy stored inside the
  medium.

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No Phase Change (Sensible Energy)

• When a path energy (heat, work) is added to a
  material (collection of atoms molecules), IF
  THERE IS NO PHASE CHANGE, temperature increases.
• This added energy changes the internal energy of
  the medium,
• Ufinal - Uinitial DU
• Path Energy Input - Path Energy Output

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Sensible Energies

• See your Foundations Text (sec. 22.3.3) for the
  derivation of
• Constant volume energy change
• DU mCv(T2 - T1)
• Constant pressure enthalpy change
• DH DU PDV mCp(T2 - T1)

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Phase Changes

• Energy can move across a medium with little
  temperature change if a phase change is taking
  place.
• For example, boiling water, thawing ice cubes in
  equilibrium with the liquid water.

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Total Energy Conservation

• For a closed system (no mass in or out)
• DEk DEp DU Win - Wout Qin - Qout
• For an open system, with M defined as energy
  entering or leaving the system with the mass
• DEk DEp DU Win - Wout Qin - Qout Min -
  Mout

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Flow Energies

• In open systems, energy is flowing, so we are
  looking at the rate of change of energy across
  the system boundary due to mass change.
• The mass flow rate is indicated by
• Potential
• Kinetic
• Etc.

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Exercise

• Individually, spend 15 minutes solving the
  problem outlined on the next slides
• Take care to document your steps
• Solution will be turned in

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Bungee Jumping Exercise

• Rock is going to bungee jump from a platform
  which is 195 meters above a river on a cord which
  has a taut length of 50.0 meters
• taut length of unstretched cord before this
  length, the cord exerts no force (i.e. freefall)

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Bungee Jumping Exercise - 2

• Using the following information for force in the
  bungee cord
• F(15 kg/s2)(X-Xtaut)
• Note, you may neglect the drag due to air in all
  the tasks listed.
• You may also assume that this is a one
  dimensional motion problem. That is, you may
  assume that Rock falls straight down and on the
  rebound follows the same path.

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Bungee Jumping Exercise - 3

• If Rock has a mass of 75 kg, determine his
  velocity at the instant the cord becomes taut.
• Determine if Rock will impact the river.
• Show computations to support Rock's lowest
  position from the platform.
• Determine the maximum mass of person that can
  jump from platform and NOT impact the river.
• HINT Newton may be useful

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15 minutes

• Be prepared to turn in your well documented
  solution 15 minutes from now.

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Exercise (10 minutes)

• As a team, compare answers, resolve differences
  prepare a solution to be submitted
• your submission should include the original
  solution from each member of your team

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Assignment 11

• Due3/20/03
• Individual Assignment
• Foundations 22.9, 22.10, 22.13