Physical Science

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Physical Science

• Work and Energy
• Slides subject to change

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Work and Energy

• Work refers to an activity involving force and
  motion.
• The force is in the direction of the motion.

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What Is Work?

• Work done by a constant force F equals the
  product of the force and parallel distance d
  through which the object moves while the force is
  applied.
• Units are N-m or joules (J).

force
distance
W Fd
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Example

• Given Formula
• F1 800 N W Fd
• d 20 m

F1
d 20 meters
0
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Example

• Given Formula
• F1 800 N W Fd
• d 20 m
• W (800)(20) 16,000 J

F1
d 20 meters
0
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Luggage

• Given Formula
• F2 400 N W Fd
• Motion in direction of F2 0 m.
• d0.

luggage F2
0
20 meters
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Luggage

• Given Formula
• F2 400 N W Fd
• Motion in direction of F2 0 m.
• d0.
• W (400)(0) 0 J

• F2 (luggage weight) does NO work.

0
20 meters
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Weightlifting

• Lift m 23 kg, d 2 meters.
• F mg 23(9.8) 225 N
• W Fd (225)(2) 450 J

• Hold it there for 300 seconds.
• How much additional work does it take?
• d 0
• W (1000)(0) 0 J

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Kinetic Energy

• Energy associated with motion.
• Motion Gr. kinesis
• KE ½ mv2
• Energy units in SI system are joules (J)

v
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Kinetic Energy

• Energy associated with motion.
• Given Formula
• m 1,000 kg KE ½ mv2
• v 13 m/s
• KE (½)(1000)(13)2 84,500 J

Energy associated with motion
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Kinetic Energy
Mass Speed KE ½ mv2
1,000 kg 13 m/s 84,500 J
1,000 kg 26 m/s 338,000 J

• As speed goes up, the kinetic energy goes up as
  the speed squared!
• Double the speed from 13 m/s to 26 m/s, energy
  increases four-fold.

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Energy

• When positive work is done, there is an increase
  of kinetic energy.
• When negative work is done, there is an decrease
  of kinetic energy.
• ?W ?KE , or amount of work done equals the
  change in kinetic energy.

? means change in
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Kingda Ka

• How much work does is take to accelerate Kingda
  Ka from 0 to 128 mi/h (57 m/s)? Assume that all
  work goes into kinetic energy.

• Calculate how much kinetic energy it gains.

Mass Speed KE ½ mv2
Initial 9,000 kg 0 m/s 0 J
Final 9,000 kg 57 m/s 14.6x106 J
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Kingda Ka

• Initial KE is 0 J.
• Final KE is 14.6x106 J.
• ?E KEf - KEi 14.6x106 - 0
• 14.6x106 J
• Since W ?KE, it must take 14.6x106 J of
• work to accelerate the Kingda Ka car.

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Potential Energy

• Work can also be done to change the position of
  an object and create potential energy (PE).
• Example work done against gravity to lift an
  object and give it potential energy.
• Gravitational potential energy
• mg weight of an object
• h height raised

PE mgh
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Other PE Examples

• Springs
• Archery Bow

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Potential Energy

• Gravitational PE comes from raising the height of
  mass m.
• Given Formula
• m 80 kg PE mgh
• h 50 m
• PE mg h
• (80)(9.8)(50)
• 38,200 J

70
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Kingda Ka
139

• How much gravitational potential energy does
  Kingda Ka gain by climbing from from 0 m to 139
  m? (h 139 m)

Mass Height PE mgh
9,000 kg 139 m 12.3x106 J
0
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Mechanical Energy

• Total mechanical energy E is the total of kinetic
  energy and potential energy.
• E KE PE

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Conservation of Energy

• The total mechanical energy of an isolated system
  remains constant.
• Initial total energy equals final total energy.
• Ebefore Eafter
• (KE PE)before (KE PE)after
• Isolated means no work is done from the outside
  that affects the system.

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An Example

• Slowly lift a 10-kg anvil to h 5 meters and
  hold it there. What is its total energy at h?
• Initally
• KE 0
• PE mgh 10(9.8)(5) 490 J
• Einitial KE PE 0 490 490 J

5 m
0 m
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An Example

• Release it, it falls to h 0. Without your hands
  in the way, the anvil and gravity form an
  isolated system.
• Finally
• KE ½ mv2
• PE 0
• Efinal (KE PE)final ½ mv2

5 m
0 m
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An Example

• As it falls, by conservation of energy,
• Ebefore Eafter
• (KE PE)before (KE PE)after
• (490) (½ mv2)
• Solve for v,
• v2 2(490)/10 98
• v 9.9 m/s

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A Pendulum

• At h 3 m above equilibrium (the lowest point),
  and at rest.
• m 5 kg
• KE 0
• PE mgh 5(9.8)(3) 147 J
• Einitial 147 J

3 m
0 m
Equilibrium
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A Pendulum

• At lowest point h 0 m
• m 5 kg
• KE ½ mv2
• PE mgh 0 J
• Efinal
• ½ (5)v2 2.5v2

• Conservation of Energy Einitial Efinal
• 147 2.5 v2
• v 6.8 m/s

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Look at Energy

• Total is always the same

KE 147 J
PE 147 J
PE
PE
KE
KE
KE 0
PE 0
in-between, a mix of both
initial
final
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Power

• WORK Done on an object, and results in a
  transfer of energy.
• W Fd
• POWER The rate of this energy transfer.
• P W/t

• Example A 60 watt light bulb transforms 60
  joules of electric energy into thermal energy and
  light in 1 second.

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Power Units

• MKS unit for power is watt (W).
• 1 joule per second 1 watt (W)
• In the U.S. system, also measure power in
  horsepower (hp).
• 1 hp 746 W

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Example

• A 0.0020 N force pushes a piece of broccoli 2.1
  cm in a time of 0.40 seconds. Calculate the power
  output.
• F 0.0020 N
• d 2.1 cm or 0.021 m
• Work Fd (0.0020)(0.021) 4.2x105 J
• P Work/?t 4.2x105 /0.40 1.1x104 W

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Example

• John runs up 20 stairs in 5.0 seconds. He has a
  mass of 80 kg. What amount of power has John
  generated? Each step is 19 cm.
• Step height 19 cm, or 0.19 meter.
• Height raised h 20 (0.19) 3.8 m
• Work Fd mg ?h 80(9.8)(3.8) 3,000 J
• P Work/?t 3,000/5.0 600 watts

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Kingda Ka

• Recall work to accelerate Kingda Ka from 0 to 128
  mi/h (57 m/s)
• Work ?KE 14.6x106 joules
• Recall, it does this in t 3.5 seconds.
• What is the minimum power required of the
  hydraulic motors?
• P Work/t 14.6x106 J/3.5 s (at least).
• 4.9x106 watts

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Kinda Ka

• Convert 4.9x106 W to horsepower (hp).
• 1 hp 746 W
• P 6,500 hp

• Kinda Kas hydraulic motors are actually rated at
  7,400 hp.

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Top Fuel Dragster

• Mass 1,000 kg, v 148 m/s in 4.5 s
• ½ mv2 ½ (1000)(148)2 11.0 x 106 J
• Work ?KE 11.0 x 106 joules
• P Work/t 11.0 x 106/4.5 2.43 x 106 W
• Convert to hp
• 3,300 hp

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Energy Delivered

• Power P W/t
• Rearrange
• W P t
• The energy delivered, or work done P t

• How much work or energy (in joules) is sent to a
  light bulb in 60 seconds?
• W P t (100)(60) 6,000 J

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Measure Energy Delivered

• Power companies bill customers according to
  energy or work done in kilowatt-hours.
• Price in LA County about 17 /kW-hr (1 kW (1,000
  watts) consumed over 1 hour).
• Units are kW and hours.

power
time
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Measure Energy Delivered

• In Power Company units
• How much energy is sent to a 1,300-W hair dryer
  in 15 minutes? In kW-hrs.
• P 1,300 W 1.3 kW
• t 15 min 0.25 hr
• W P t (1300)(0.25) 0.325 kW-hr
• At 17 / kW-hr, what is the cost?
• Cost (0.325 kW-hr)(17/kW-hr) 6

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Measure Energy Delivered

• Power of 100-W bulb 100 W 0.10 kW
• In one hour it uses
• W Pt (0.10)(1) 0.10 kW-hr
• In 24 hours it uses
• W Pt (0.10)(24) 2.4 kW-hr
• _at_17 / kW-hr 41
• In one month (30 days) 12.30

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U.S. Sources of Energy

• US DOE, 2009

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Utility-Scale Energy Sources

• Fossil energy - burn fossil fuels, heat water,
  and create steam, turn turbine.
• Nuclear heat water, create steam, turn turbine.
• Geothermal steam from deep in Earth (6000 feet
  Hawaii), turn turbine.
• Gas turbine hot gases direct into turbine.
• Wind wind turns turbine.
• Hydroelectric water pressure turns turbine.

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Coal Power

• Longwall Coal Mining

NPR Visualizing the U.S. Grid
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Longwall Issues
Longwall
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Gas Power
NPR Visualizing the U.S. Grid
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Nuclear Power
NPR Visualizing the U.S. Grid
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Hydroelectric Power
NPR Visualizing the U.S. Grid
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Solar Power
NPR Visualizing the U.S. Grid
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Historical View
Energy Information Administration / Annual Energy
Review 2007
http//www.eia.doe.gov/cneaf/electricity/epa/epa_s
um.html