class notes; 4.26.11. Work and Horsepower NO Quiz TODAY

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class notes 4.26.11. Work and Horsepower NO
Quiz TODAY

• Personal Horsepower Lab
• Lab Due Wednesday
• Thursday More information coming tomorrow!!
• A couple more tickets available.------------------
  --
• Twins Physics Day
• Early bus stuff
• Dress for the weather
• Leave at 830

http//www.ftexploring.com/energy/energy-1.htm
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Lab is due tomorrowToday during work timeFind
out answers to questions

• Reading Notes (1 page )
• Gravitational Potential Energy
• Homework
• Physics Work (no angles)
• Check your understanding of Potential Energy

3
Mechanical Work Equals ZEROno change in speed?
no workno change in height ? no workForce is -
to motion ?no Work

• WFd 1 N m 1 Joule
• W 0! Carrying a weight corresponds to W 0.
• F is perpendicular to d, ? 90
• W 0. IF you are pushing against an immovable
  object, d 0 so W 0!!

90
F
d
d 0
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Gravitational Potential Energy

• Both blocks acquire the same gravitational
  potential energy, mgh.
• The same work is done on each block.  What
  matters is the final elevation, not thepath
  followed

5
Work F d Using the force and the distance
along the ramp

• The amount of work done by a force on any object
  is given by the equation
• Work F d cosT
• F is the Applied force,
• d is the displacement
• ? is the angle between the F d

6
Work and Potential Energy

•  The work done on the ball gives the ball
  gravitational potential energy.  Gravitational
  potential energy mgh

   
7
Which Path Requires the Most WORK?

• Suppose that a car traveled up three different
  roadways (each with varying incline angle or
  slope) from the base of a mountain

8
Vertical distance only affects the PE

• The PE at the top of each is 30 J,
• The work to move up each would be 30 J.
• How can this be????
• For Work use Force to displacement!!

Fg UP d
Fg UP d
Fg UP d
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Calculations
10
Watts and Horsepower

• James Watt patented the steam engine in 1769.
• To sell it, he needed to tell people how many
  horses it would replace.
• He measured how quickly farm horses could do
  work.
• There are few horses that actually produce
  exactly one horsepower of power.

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POWER
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Work, Power and Energy

• Notebooks 30 pts 5 EC for vertical loops
• More Equations and Notes today
• Tomorrow is the last day to bring in Valleyfair
  41.50 and permission slip.

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Work The Transfer of Mechanical Energy

• The baseball pitcher does work on the ball. The
  ball gains kinetic energy.
• To do the greatest possible amount of work, the
  greatest possible force
• the greatest possible distance

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Kinetic energy

• The amount of translational kinetic energy (from
  here on, the phrase kinetic energy will refer to
  translational kinetic energy) which an object has
  depends upon two variables the mass (m) of the
  object and the speed (v) of the object. The
  following equation is used to represent the
  kinetic energy (KE) of an object.
• where m mass of object
• v speed of object

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Units of work and energy

• Like work and potential energy, the standard
  metric units of measurement for kinetic energy is
  the Joule. As might be implied by the above
  equation, 1 Joule is equivalent to 1 kg(m/s)2.

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Analyze the animation and use the principles of
work and energy to answer the given questions.

• Use energy conservation principles to determine
  the speed of a 0.050-kg Hot Wheels car that
  descends from a height of 0.60-meters to a height
  of 0.00 meters. Assume negligible air resistance.
•  
• Use energy conservation principles to determine
  the speed of a 0.050-kg Hot Wheels car that
  descends halfway down a 0.60-meter high hill
  (i.e., to a height of 0.30 meters). Assume
  negligible air resistance.
•  
• If the mass of the Hot Wheels car was twice as
  great (0.100 kg), then what would be the speed at
  the bottom of the 0.60-meter high hill?
•  
• If the 0.050-kg Hot Wheels car is brought to a
  rest over a distance of 0.40 meters, then what is
  the magnitude of the frictional force acting upon
  the car?

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Which Path Requires the Most Energy?

• Suppose that a car traveled up three different
  roadways (each with varying incline angle or
  slope) from the base of a mountain

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Analyze the animation and use the principles of
work and energy to answer the given questions.

• Use energy conservation principles to determine
  the speed of a 0.050-kg Hot Wheels car that
  descends from a height of 0.60-meters to a height
  of 0.00 meters. Assume negligible air resistance.
•  
• Use energy conservation principles to determine
  the speed of a 0.050-kg Hot Wheels car that
  descends halfway down a 0.60-meter high hill
  (i.e., to a height of 0.30 meters). Assume
  negligible air resistance.
•  
• If the mass of the Hot Wheels car was twice as
  great (0.100 kg), then what would be the speed at
  the bottom of the 0.60-meter high hill?
•  
• If the 0.050-kg Hot Wheels car is brought to a
  rest over a distance of 0.40 meters, then what is
  the magnitude of the frictional force acting upon
  the car?

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Work 

• Work Force x DistanceF 500 pounds (2000
  N)D 8 feet (2.5 meters)----------------------
  -------------
• W 2000 N  x  2.5 m      5000
  N-m-----------------------------------Alternativ
  e unit  Joule1 N-m 1 joule (J)

   
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Work

• Work Force  x  DistanceIf the wall doesn't
  move,the prisoner does no work.

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 Energy

• Work is done on the bow.The work done is
  storedin the bow and string aselastic potential
  energy.After release, the arrow issaid to have
  kineticenergy, 1/2 mv2.
• Energy is measured in the same units (joules) as
  work.

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   Energy Transformation

• The work done in lifting the massgave the mass
  gravitationalpotential energy.Potential energy
  then becomeskinetic energy.
• Kinetic energy then does workto push stake into
  ground.

 
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Energy Transformation
 
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 Power

• Power Work/ Time1 joule / second 1 watt

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Total mechanical energy

• As discussed earlier, there are two forms of PE
  discussed in our course - gravitational potential
  energy and elastic potential energy. Given this
  fact, the above equation can be rewritten
• TME PEgrav PEspring KE

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TotalMechanical energy stays the same until it
hits the water.
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Work and EnergyHow High Will It Go?The motion
of the sled in the animation below is similar to
the motion of a roller coaster car on roller
coaster track.

• As on a roller coaster, energy is transformed
  from potential energy to kinetic energy and vice
  versa. Provided that external forces (such as
  friction forces and applied forces) do not do
  work, the total amount of mechanical energy will
  be held constant.

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Energy Conservation on an Incline

• If air resistance is neglected, then it would be
  expected that the total mechanical energy of the
  cart would be conserved. The animation below
  depicts this phenomenon (in the absence of air
  resistance).

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Total mechanical energy is constantconservative
force ? gravity transfers PE-KE

• The diagram below depicts the motion of Li Ping
  Phar (esteemed Chinese ski jumper) as she glides
  down the hill and makes one of her record-setting
  jumps.

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Measurement of Horsepower

• The maximum horsepower developed by a human being
  over a few seconds time can be measured by timing
  a volunteer running up the stairs in the lecture
  hall.
• If a person of weight W runs up height h in time
  t, then h.p. Wh/t X 1/550 ft-lbs/sec.
• A person in good shape can develop one to two
  horsepower. It will be entertaining to the
  students if the professor tries it too.
• Should the person be allowed a running start?

http//www.physics.ucla.edu/demoweb/demomanual/mec
hanics/energy/faith_in_physics_pendulum.html
http//www.physics.ucla.edu/demoweb/demomanual/mec
hanics/uniform_circular_motion/index.html
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Height at A 60m The car's mass is 500kg.

• A roller coaster with two loops and a small hill,
  see diagram below
• In the diagram A is the highest point of the
  coaster, B is 3/4 height of A, C is 1/2 of A, D
  is 1/4 of A, E is the ground level, and F is 1/8
  of A.

Point (A-F) Height (m) PE (J) KE (J) TME (J) Speed (m/s)
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• PE mgh
• Speed use KE ½ m v2 KE TME (previous) PE

HA 60m m 500kg
A toF h (m) PE (J) KE (J) TME (J) Speed (m/s)
A 60 (500(9.8)(60) 294,000-294,000 294,00
0 J 0 Joules 294,000J 0 m/s B
45 C 30 D 15 E 0 F 7.5
PE mgh
KE ½ m v2
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HA 60m m 500kg

• PE mgh
• Speed use KE ½ m v2 KE TME (previous) PE

A toF h (m) PE (J) KE (J) TME (J) Speed (m/s)
A 60 (500(9.8)(60) 294,000-294,000 294,00
0 J 0 Joules 294,000J 0 m/s B 45
(500(9.8)(45) 294,000-220,500
294,000J 220,500 J 73,500J
17.1 m/s
Equation KE ½ m v2
Substitute 73,500J ½ 500kg v2
X 2 / by 500take v .. v 17.1 m/s
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Mechanical Energy Equations
Page 7 section 3
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W1?Force of Gravity pulls down Mechanical Work ?
PE ? KE TME does not change
W1
W4
W2
W4
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The transfers of energy during the 1st Bounce
W1
W4
W2
W3
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W2?Force of Gravity pulls down Mechanical Work ?
PE ? KE TME does not change
W1
W4
W2
W3
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W3?ball compressed Mechanical Energy lost to
HEAT TME does change
W1
W4
W2
W3
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W4?Force of Gravity pulls down Mechanical Work ?
KE ? PE TME does not change
W1
W4
W2
W3
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Notice the speed change
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Missing mechanical energy??
Energyinitial Energyfinal Energylost
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Frictional Work

• According to the Cedar Point website the maximum
  speed of the Magnum XL-200 is 72 mph not 76 mph
  as we calculated above.
• The difference is due to frictional forces acting
  on the roller coaster cars.
• Assuming that the mass of a loaded roller coaster
  car is 600 kg what is the frictional
  (non-conservative) work done on the car by the
  track?

45
Analyze the transfers of energy during the 1st
Bounce
46
Work on incline

• Answer the following about the above picture
• Draw the three forces acting on the object.
• If the object slides down the incline, what work
  was done with gravity?
• What work is done against the motion?
• What is the net work done?
• Predict the final velocity of the object.

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Mechanical Energy
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Follow the bouncing ball
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Bouncing balls

• When a ball is dropped, it transfers its GPE to
  kinetic energy.  As the ball hits the floor, its
  kinetic energy is turned into elastic potential
  energy (and some heat, and noise).  High speed
  photography can show how the ball gets deformed.
• The elastic potential energy is transferred to
  kinetic energy as the ball bounces.  Some energy
  is lost as heat as the ball bounces, so it does
  not achieve the height from which it was dropped.

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Bouncing balls

• different types of balls at room temperature and
  when they are frozen.
• When a ball is dropped on a surface, molecules in
  the ball can deform or absorb the kinetic energy
  of the fall. If they return to their original
  shape they push the ball away from the surface.
  If the energy is absorbed, the ball does not
  bounce.

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Bouncing balls
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Bouncing balls
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Conservative and non-conservative work

• Forces can be categorized as internal forces or
  external forces. There are many sophisticated and
  worthy ways of explaining and distinguishing
  between internal and external forces. Many of
  these ways are commonly discussed at great length
  in physics textbooks. For our purposes, we will
  simply say that external forces include the
  applied force, normal force, tension force,
  friction force, and air resistance force. And for
  our purposes, the internal forces include the
  gravity forces, magnetic force, electrical force,
  and spring force.

Internal Forces External Forces
Fgrav Fspring Fapp Ffrict Fair Ftens Fnorm
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      In the following descriptions, the only
forces doing work upon the objects are internal
forces - gravitational and spring forces. Thus,
energy is transformed from KE to PE (or vice
versa) while the total amount of mechanical
energy is conserved. Read each description and
indicate whether energy is transformed from KE to
PE or from PE to KE.

• Description of Motion KE to PE or PE to
  KE? Explain.
• 1. A ball falls from a height of 2 meters in the
  absence of air resistance.
•  
• 2.A skier glides from location A to location B
  across a friction free ice.
•  
• 3.A baseball is traveling upward towards a man in
  the bleachers.
•  
• 4.A bungee cord begins to exert an upward force
  upon a falling bungee jumper.
•  
• 5.The spring of a dart gun exerts a force on a
  dart as it is launched from an initial rest
  position.

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The following descriptions involve external
forces (friction, applied, normal, air resistance
and tension forces) doing work upon an object.
Read the description and indicate whether the
object gained energy (positive work) or lost
energy (negative work). (NOTE If this is part is
difficult, review the section on work.) Then,
indicate whether the gain or loss of energy
resulted in a change in the object's kinetic
energy, potential energy, or both. Click the
buttons to view answers.Description or -
Work? Change PE or KE or Both?

• Megan drops the ball and hits an awesome
  forehand. The racket is moving horizontally as
  the strings apply a horizontal force while in
  contact with the ball.
• A tee ball player hits a long ball off the tee.
  During the contact time between ball and bat, the
  bat is moving at a 10 degree angle to the
  horizontal.
• Rusty Nales pounds a nail into a block of wood.
  The hammer head is moving horizontally when it
  applies force to the nail.
• The frictional force between highway and tires
  pushes backwards on the tires of a skidding car.
  
• A diver experiences a horizontal reaction force
  exerted by the blocks upon her feet at start of
  the race.
• A weightlifter applies a force to lift a barbell
  above his head at constant speed.

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Work out due to friction
63
Mechanical Energy Equations
6th section
64
A boulder resting at the top of a hill has
potential energy.
65
Potential energy changes to kinetic energy due to
work done by gravity
PE
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Roller coaster W/P/E

• The Work pulling the coaster to the top of the
  1st hill is the Potential Energy at the top of
  the hill and the Energy available for the entire
  ride.
• The total mechanical energy at any point of the
  roller coaster is the PE KE if there were no
  frictional forces

KEinitial PEinitial Wexternal KEfinal
PEfinal
67
Energy Transformation on a Roller CoasterA GIF
Animation
68
A roller coaster ride also illustrates the
work-energy theorem.

• The theorem is often stated in the form of the
  following mathematical equation.
• KEinitial PEinitial Wexternal KEfinal
  PEfinal
• The left side of the equation includes the total
  mechanical energy (KEinitial PEinitial) for the
  initial state of the object plus the work done on
  the object by external forces (Wexternal) while
  the right side of the equation includes the total
  mechanical energy (KEfinal PEfinal) for the
  final state of the object.

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A roller coaster ride also illustrates the
work-energy theorem.

• KEinitial PEinitial Wexternal KEfinal
  PEfinal

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Frictional Work

• Frictional Work
• According to the Cedar Point website the maximum
  speed of the Magnum XL-200 is 72 mph not 76 mph
  as we calculated above. The difference is due to
  frictional forces acting on the roller coaster
  cars. Assuming that the mass of a loaded roller
  coaster car is 600 kg what is the frictional
  (non-conservative) work done on the car by the
  track?

71

• Test Form A
• Mass 800 kg
• Test Form B
• 1. Find the Total Mechanical Energy at the end of
  the first horizontal platform.
• 2. Find the Acceleration on platform
• vf 2 vi 2 2 a d
• Then Find gs
• 6. radius 30 meters

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Height at A 60m

• a roller coaster with two loops and a small hill,
  see diagram below
• In the diagram A is the highest point of the
  coaster, B is 3/4 height of A, C is 1/2 of A, D
  is 1/4 of A, E is the ground level, and F is 1/8
  of A. The car's mass is 500kg.

Point Height(m) PE(J) KE(J) TME(J) Speed (m/s)
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coaster
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Roller coaster W/P/E

• The Work pulling the coaster to the top of the
  1st hill is the Potential Energy at the top of
  the hill and the Energy available for the entire
  ride.
• The Total Mechanical Energy at any point of the
  roller coaster is the PE KE if there were no
  frictional forces

KEinitial PEinitial Wexternal KEfinal
PEfinal
76
Energy Transformation on a Roller CoasterA GIF
Animation
77
Height at A 60m The car's mass is 500kg.

• A roller coaster with two loops and a small hill,
  see diagram below
• In the diagram A is the highest point of the
  coaster, B is 3/4 height of A, C is 1/2 of A, D
  is 1/4 of A, E is the ground level, and F is 1/8
  of A.

Point (A-F) Height (m) PE (J) KE (J) TME (J) Speed (m/s)
78

• PE mgh
• Speed use KE ½ m v2 KE TME (previous) PE

HA 60m m 500kg
A toF h (m) PE (J) KE (J) TME (J) Speed (m/s)
A 60 (500(9.8)(60) 294,000-294,000 294,00
0 J 0 Joules 294,000J 0 m/s B
45 C 30 D 15 E 0 F 7.5
PE mgh
KE ½ m v2
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HA 60m m 500kg

• PE mgh
• Speed use KE ½ m v2 KE TME (previous) PE

A toF h (m) PE (J) KE (J) TME (J) Speed (m/s)
A 60 (500(9.8)(60) 294,000-294,000 294,00
0 J 0 Joules 294,000J 0 m/s B 45
(500(9.8)(45) 294,000-220,500
294,000J 220,500 J 73,500J
17.1 m/s
Equation KE ½ m v2
Substitute 73,500J ½ 500kg v2
X 2 / by 500take v .. v 17.1 m/s
80
800 kg
TME KE PE
h (m) Speed m/s PE (J) KE (J) TME (J)
Top of 1st hill (Need to first find the TME
available)
80 m 10 m/s 800(9.8)(80) 627,200 J ½ (800)(10)2 40,000 J 667,200 J
PE mgh
KE ½ m v2
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800 kg
TME KE PE Stays same if no friction
h (m) Speed m/s PE (J) KE (J) TME (J)
Speed at the bottom of the 1st hill
0 m ?? 0 J 667,200 J 667,200 J
PE mgh
KE ½ m v2
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800 kg
TME KE PE
h (m) Speed m/s PE (J) KE (J) TME (J)
Speed at the bottom of the 1st hill
0 m 40.8 0 J 667,200 J 667,200 J
Equation KE ½ m v2
Substitute 667,200 J ½ 800kg v2
X 2 / by 800take v .. v 40.8 m/s
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Coaster gs Back side Save for tomorrow
84
Weight Equation
85
A boulder resting at the top of a hill has
potential energy.
86
Potential energy changes to kinetic energy due to
work done by gravity
PE
87
Use

• To convert from Newtons to kg
• And from kg to Newtons

88
The Total Mechanical Energy

• As already mentioned, the mechanical energy of an
  object can be the result of its motion (i.e.,
  kinetic energy) and/or the result of its stored
  energy of position (i.e., potential energy). The
  total amount of mechanical energy is merely the
  sum of the potential energy and the kinetic
  energy. This sum is simply referred to as the
  total mechanical energy (abbreviated TME).
• TME PE KE
• As discussed earlier, there are two forms of
  potential energy discussed in our course -
  gravitational potential energy and elastic
  potential energy. Given this fact, the above
  equation can be rewritten
• TME PEgrav PEspring KE

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Mechanical Energy as the Ability to Do Work
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Sample PE calculation
92
A boulder resting at the top of a hill has
potential energy.

• Gravitational Potential Energy is the energy
  stored due to height.
• Work can change the height of the Boulder
• Work can change the potential energy of the
  Boulder

93
Potential energy changes to kinetic energy due to
work done by gravity
PE
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4.17.09.notesWPE Introduction Equation sheet

• Hand in Valley Fair and slip
• Lab Question
• Who had the highest Horsepower??
• You may turn Lab in today or Monday.

1st 0.73 Mike 3rd 0.95 Joey 4th 0.88
Parker 5th 1.01 Chris 6th 0.91 Seth
95
WPE Introduction 4-17-09TODAY Notes and
Equation Sheet

• Valleyfair
• Friday, May15th --Passing by Friday 5pm
• Cash By 730 am Friday May 15th

Book notes Pg. 224-231 ½ page
96
New sheet Mechanical Work Equations in any
direction
Page 7 section 1
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To Do Work, Forces Must Cause Displacements

• To Do Work, Forces Must Cause Displacements
• Let's consider Scenario C above in more detail.
  Scenario C involves a situation similar to the
  waiter who carried a tray full of meals above his
  head by one arm straight across the room at
  constant speed. It was mentioned earlier that the
  waiter does not do work upon the tray as he
  carries it across the room. The force supplied by
  the waiter on the tray is an upward force and the
  displacement of the tray is a horizontal
  displacement. As such, the angle between the
  force and the displacement is 90 degrees.

99
Mechanical Work Equations
5th section
Page 7 section 2
100
Who or What is applying the Force??
101
Mechanical work and Energy work is done upon
an object whenever a force acts upon it and
changes the height or changes the speed
102
The amount of work done is dependent height
103
A boulder resting at the top of a hill has
potential energy.

• Gravitational Potential Energy is the energy
  stored due to height.
• Work can change the height of the Boulder
• Work can change the potential energy of the
  Boulder

104
Mechanical Energy Equations
Page 7 section 3
105
Horizontal displacement does not affect the
gravitational PE

• Knowing that the potential energy at the top of
  the tall pillar is 30 J, what is the potential
  energy at the other positions shown on the hill
  and the stairs.

106
Assignment4.17.09

• Lab report
• due MONDAY

NOTEBOOK Book notes Pg. 224-231 (½ page)
107
Work and Energy ProblemsWork and energy are
Scalar, so we do not use /- on numbers for
direction

• Potential energy
• (height)

Work
Kinetic energy (speed)
108
Work and Energy ProblemsWork and energy are
Scalar, so we do not use /- on numbers for
direction

• PE mgh

WFd
KE 1/2 mv2
109

• A ball starts from rest on top of a tall pillar
  and falls to the ground below. Assume the effect
  of air resistance is negligible.   
•  PEi KEf
• (Since initially at rest, KEi 0 and cancels.
  Since the final height is 0, PEf 0 and cancels.)

110
6. A 50-kg platform diver hits the water below
with a kinetic energy of 5000 Joules. The height
(relative to the water) from which the diver dove
was approximately ____ meters.the potential
energy change the work done.
Example from
5000 J
5000 J
111
Work and Energy ProblemsWork and energy are
Scalar, so we do not use /- on numbers for
direction

• PE mgh
• PE 5000J
• 5000J50(9.8)h
• h5000 /490
• h 10.2 m

• WFd
• W 5000 J transferring PE to KE

• KE 1/2 mv2
• KE 5000 J

112
Example from

• 7. Using 1000 J of work, a small object is
  lifted from the ground floor to the third floor
  of a tall building in 20 seconds. What power was
  required in this task?
• the potential energy change
• the work done
• the power delivered

113
Work and Energy ProblemsWork and energy are
Scalar, so we do not use /- on numbers for
direction

• PE mgh
• PE 1000J

• WFd
• W 1000 J transferred to PE

• KE 1/2 mv2

PW/t P1000J / 20sec50 Watts
114

• 4.20.09 notes
• Work, Potential Energy Problems

NOW. . . . . Hand in Personal Horsepower Lab by
215 Hand in Valleyfair and Slips together by
215 hOMEWORK Worksheet Work time
115
A boulder resting at the top of a hill has
potential energy.

• Gravitational Potential Energy is the energy
  stored due to height.
• Work can change the height of the Boulder
• Work can change the potential energy of the
  Boulder

116
Potential energy changes to kinetic energy due to
work done by gravity
PE
117
Work to PEor PE to work

• a force acts upon it and changes the height

118
Measurement of Horsepower

• The maximum horsepower developed by a human being
  over a few seconds time can be measured by timing
  a volunteer running up the stairs in the lecture
  hall.
• If a person of weight W runs up height h in time
  t, then h.p. Wh/t X 1/550 ft-lbs/sec.
• A person in good shape can develop one to two
  horsepower. It will be entertaining to the
  students if the professor tries it too.
• Should the person be allowed a running start?

http//www.physics.ucla.edu/demoweb/demomanual/mec
hanics/energy/faith_in_physics_pendulum.html
119
A bouncing basketball captured with a
stroboscopic flash at 25 images per second.
Ignoring air resistance, the square root of the
ratio of the height of one bounce to that of the
preceding bounce gives the coefficient of
restitution for the ball/surface impact.
120
Bouncing of ball

• If a soccer ball is dropped on a hard surface, it
  will bounce back to a height lower than its
  initial position. Such kind of motion is called
  the bouncing of the soccer ball, which plays an
  important role in the motion of the ball. Let us
  study the mechanism of the bouncing of the ball
  in details.

• The relative bounciness of different types of
  balls

121

• The coefficient of restitution is how you
  quantify bounciness or give bounciness a number,
  and you do that by dividing the bounce height by
  the drop height, then finding the square root of
  that. When... Read more http//wiki.answers.com
  /Q/What_is_the_Coefficient_of_Restitution_of_bounc
  ing_a_basketballixzz1JW73FiKE

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• As a result, a ball with smaller coefficient of
  restitution rebounds to lower height in
  successive bounces and a shorter time is required
  for the ball to stop.
• For example, grass reduces the coefficient of
  restitution of a soccer ball since the bending of
  blades causes further loss of its kinetic energy.
• Therefore, it would take a shorter time for the
  soccer ball to stop if it is kicked on grass
  instead of hard floor.

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changing its temperature.

• We can also change the bounciness of a ball by
  changing its temperature. Take two baseballs that
  bounce to about the same height. Put one in the
  freezer for an hour and leave the other at room
  temperature. Then compare their bounciness again.
  You should notice that the room temperature ball
  bounces a little bit higher. The cold ball would
  bounce about 80 percent as high as the room
  temperature ball. Although the difference of
  bounciness is not dramatic, it's enough to see
  that temperature can be a factor it could make
  the difference between a home run and a pop fly.
• However, the change in bounciness due to the
  change in temperature is taken for granted for
  some sport. For example, squash player rely on
  the pre-game warm up to warm up the ball as well
  as the players.

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Surface bounced on

• Examplegrass reduces the coefficient of
  restitution of a soccer ball since the bending of
  blades causes further loss of its kinetic energy.
  Therefore, it would take a shorter time for the
  soccer ball to stop if it is kicked on grass
  instead of hard floor.

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COR

• Coefficient of restitution of a tennis ball is
  0.712. Thanks ...

127
                                                1910 soccer ball ii                                                    1950 soccer ball ii                                                    2004 Euro Cup ball ii

• 1910 soccer ball ii 1950 soccer ball ii
  2004 Euro Cup ball ii
• In the late 1980s, the leather casing ball was
  replaced by totally synthetic ball in soccer
  competitions. The covering material of the
  totally synthetic ball is synthetic leather made
  from polymer. For high quality ball, the casing
  is made of the synthetic leather panels stitched
  together through pre-punched holes by waxed
  threads. The bladder of a totally synthetic ball
  is usually latex or butyl bladder. The ball is
  then inflated by pumping air into its bladder
  through a tiny hole on the casing. The totally
  synthetic ball could resist water absorption and
  reliably maintain its shape.
• The Internal structure of a totally synthetic
  soccer ball ii
• Nowadays, the official soccer rules called the
  "Laws of the game", which are maintained by the
  International Football Association Board (IFAB),
  specify the qualities of the ball used in soccer
  matches. According to the laws, the soccer ball
  should satisfy the following descriptions
• it is spherical in shape,
• its casing is made of either leather or other
  suitable material,
• its circumference is not more than 70 cm and not
  less than 68 cm,
• its weight is not more than 450 g and not less
  than 410 g at the start of the match.
• its pressure inside equal to 0.6 - 1.1 atmosphere
  at sea level.

128
Figure explaining the extra pressure inside the
soccer ball.
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The relative bounciness of different types of
balls iii
130

• Energy change in the falling ball after release
  until hitting on the ground.(Note that here
  "G.P.E." and "K.E." stand for the gravitational
  potential energy and kinetic energy
  respectively.)

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Work must be done in order to distort an elastic
object

• . Therefore, if you pull a spring outward so that
  it become longer, some energy must have been
  transferred from yourself to the spring. The
  energy stored in an distorted object due to its
  deformation is called the elastic potential
  energy. So, when talking about the elasticity of
  the ball, we are indeed talking about the
  spring-like behavior of the ball. In other words,
  we are considering the tendency of the ball to
  return to its original spherical shape when it is
  being squeezed. Where does the elasticity of the
  ball come from? The elasticity of a solid ball
  arises from the elasticity of the constituting
  material which is due to the interatomic or
  intermolecular force inside. In contrast, for
  air-filled ball like soccer ball, its elasticity
  is resulted from the extra air pressure inside
  the ball. What happens to a ball after you
  dropped it above a hard floor? The gravity pulls
  the ball toward the ground and thus the ball
  falls leading to the lost of its gravitational
  potential energy. By the law of conservation of
  energy, the ball must gain kinetic energy and so
  it falls towards the ground with an increasing
  speed. Subsequently, the ball hits the hard floor
  with a high speed. (Note that the ball always
  moves with the downward acceleration of g 9.8
  m/s2 as it falls.)

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The elasticity of an object means

• the tendency of the object to return to its
  equilibrium shape, the natural shape of the
  object with no net force applied on it, when it
  is being deformed. And the force for the object
  to restore to its equilibrium shape is called the
  restoring force, which is always directed in
  opposite to the deformation of the object. Almost
  all real rigid body are elastic, i. e. having
  certain extent of elasticity. A trivial example
  of an elastic object is the spring. You probably
  have the experience that a spring would tend to
  restore to its original size when you stretch it
  to be longer. Scientist found that, providing the
  deformation is not too large, the relationship
  between the distortion and the restoring force is
  given by the Hooke's law"The restoring force
  exerted by an elastic object is proportional to
  how far it has been distorted from its
  equilibrium shape." The restoring force Fs on a
  spring in case of different extension.

133
Law of conservation of energy

• In the law of conservation of energy, it was
  stated that"Energy can neither be created or
  destroyed but can only be changed from one form
  to another."Therefore, the amount of total
  energy in an isolated system must be constant.
  For example, let us consider a piece of charcoal
  placed in an isolated room. If we burn the
  charcoal, the chemical energy inside the charcoal
  is changed into the thermal energy of the room.
  Then the temperature inside the room would be
  increased. When the ball hits the ground, the
  ball exerts force on it. By the Newton's 3rd law
  of motion, the ground exerts a force on the ball
  as well. The motion of the ball would be stopped
  by the (stationary) hard floor resulting in the
  compression of the ball. So the work done on the
  ball leads to the increase of the elastic
  potential energy of the ball. That means some of
  the kinetic energy of the ball (which is
  converted from the gravitational potential energy
  of the ball) is converted into the elastic
  potential energy when the ball hits the ground.
  On the other hand, some of the kinetic energy is
  lost as thermal energy during the impact due to
  either the internal friction of the ball or the
  heating of the surface.
• Energy change in the falling ball during the
  impact

134
After losing all the kinetic energy, the ball
becomes momentarily at rest.

• The squashed ball would simply act like a
  compressed spring. The ball pushes the ground
  with a restoring force proportional to its
  displacement from the equilibrium position
  (Hooke's law). In consequence, the ground pushes
  back the ball with a force of equal magnitude but
  opposite in direction. Thus the ball bounces back
  in upward direction. During the rebound, the
  stored elastic potential energy is released as
  the kinetic energy of the ball which is then
  converted to gravitational potential energy as
  the ball moves up. Moreover, some of the elastic
  potential energy is lost again due to friction or
  heat which results in slight heating of the ball.
  The ball keeps on going upward until it comes to
  rest after losing all its kinetic energy again.
  Due to the lost of some of the initial
  gravitational potential energy into thermal
  energy, the ball cannot bounce back to the
  original height.

135
What is the Coefficient of Restitution?(also
called Elastic Coefficient)

• What is the slope of each of the graphs?
• Use the slope of the graphs to find the
  Coefficient of Restitution, just like we did for
  the Spring Constant.
• The Coefficient of Restitution tells us how
  springy the ball is.
• The slope of the graph represents this constant.
  The constant will be the same for a given ball.

136
PE Bouncing Ball Lab

• Work and Potential Energy and Problems
• Patterns in graphs
• Increasing/decreasing/ no change
• Linear or curved line of best fit.

137
Bouncing ball labmeasure height at the first
bounce up and the second bounce
138
Work to PEor PE to work

• a force acts upon it and changes the height

139
Measurement of Horsepower

• The maximum horsepower developed by a human being
  over a few seconds time can be measured by timing
  a volunteer running up the stairs in the lecture
  hall.
• If a person of weight W runs up height h in time
  t, then h.p. Wh/t X 1/550 ft-lbs/sec.
• A person in good shape can develop one to two
  horsepower. It will be entertaining to the
  students if the professor tries it too.
• Should the person be allowed a running start?

http//www.physics.ucla.edu/demoweb/demomanual/mec
hanics/energy/faith_in_physics_pendulum.html
140
Bouncing Ball

141
Bouncing a Ball

• What you need
• a tennis ball
• a basketball
• a room without breakables
• InstructionsDrop the tennis ball from waist
  height and see how high it bounces.Drop the
  basketball from the same height and see how high
  it bounces.Put the tennis ball on top of the
  basketball and drop them both at arms length from
  waist height.
•  Results ExplanationThe tennis ball should
  bounce a lot higher than before. When the balls
  hit the ground, momentum from the basketball was
  transferred to the tennis ball making it go much
  higher than before.

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Mechanical Work Equals ZEROno change in motion ?
no workForce is - to motion ?no Work
90
F
d

• WFd 1 N m 1 Joule
• W 0! Carrying a weight corresponds to W 0.
• F is perpendicular to d, ? 90
• W 0. IF you are pushing against an immovable
  object, d 0 so W 0!!

d 0
150
Which Path Requires the Most Energy?

• Suppose that a car traveled up three different
  roadways (each with varying incline angle or
  slope) from the base of a mountain

151
Vertical distance only affects the PE

• The PE at the top of each is 30 J,
• The work to move up each would be 30 J.
• How can this be????
• For Work use Force to displacement!!

Fg UP d
Fg UP d
Fg UP d
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Work F d Using the force and the distance
along the ramp

• The amount of work done by a force on any object
  is given by the equation
• Work F d cosT
• F is the Applied force,
• d is the displacement
• ? is the angle between the F d

153
Force not in same direction as displacementwe
use the component in the direction of the motion
154
Concepts Involving Work

• Let be an unbalanced force applied to an
  object, and let d be a resulting displacement.

F F cos T
If F is the component of F along d, then the
WORK done by F, is given by W F x d
Work F cos T d
Work F d cos T
155

• Work is of the nature of a force times a distance
  !
• Work F d
• But if Force not Parallel to motion
• Work done by a force parallel to the displacement
  is

Work F d cos T
156
Add Mechanical Work Equations
Page 7 section 1
157
Work on incline

• Answer the following about the above picture
• Draw the three forces acting on the object.
• If the object slides down the incline, what work
  was done with gravity?
• What work is done against the motion?
• What is the net work done?
• Predict the final velocity of the object.

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Units of Work

• Whenever a new quantity is introduced in physics,
  the standard metric units associated with that
  quantity are discussed. In the case of work (and
  also energy), the standard metric unit is the
  Joule (abbreviated J). One Joule is equivalent to
  one Newton of force causing a displacement of one
  meter. In other words,
• The Joule is the unit of work.
• 1 Joule 1 Newton 1 meter
• 1 J 1 N m
• In fact, any unit of force times any unit of
  displacement is equivalent to a unit of work.
  Some nonstandard units for work are shown below.
  Notice that when analyzed, each set of units is
  equivalent to a force unit times a displacement
  unit.
•                                                 
                                                    
                 

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• A trolley of mass 10 kg is pulled along the
  floor. The pulling force is 36 N, at an angle of
  30? above the horizontal. Ignore friction.
• What other forces are acting on the trolley?
• Gravity and normal reaction force.
• What is the total vertical force acting on the
  trolley? Why can we say this?
• Zero.
• No vertical motion ? zero vertical acceleration ?
  Fy 0.
• What is the magnitude of the normal force?
• The vertical forces are gravity, the normal
  force, and the vertical component of the pulling
  force.
• Let's find the horizontal and vertical components
  of the pulling force
• Px P cosq 36 cos30 31 N Py P sinq 36
  sin30 18 N
• The gravitational force (ie the weight of the
  trolley) is w mg 10 9.8 98 N
• Now we either say that the total vertical force
  is zero Fy w N Py 0 -98 N 18 80 N
  N or we can say that the forces up equal the
  forces down (but be careful with sign and
  direction!) up down N Py w N 18 98 N
  80 N
• What is the total force acting on the trolley?
• The vertical forces add to zero, the total force
  must be the horizontal pulling force, equal to
  31 N horizontally.
• What is the acceleration of the trolley?
• F ma 31 10 a 3.1 m/s2 a
• The acceleration is 3.1 m/s2 horizontally, in the
  direction the trolley is being pulled.

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diagram showing the forces acting on a block that
is resting on an inclined plane
164
Measuring the coefficient of friction on a flat
surface
165
Measuring the coefficient of friction on an
inclined surface.
http//en.wikibooks.org/wiki/How_To_Build_a_Pinewo
od_Derby_Car/Physics
166
FRICTION VS. PULLING ANGLE

• PURPOSE To demonstrate how pulling angle affects
  the frictional force, and to show that the
  minimum force required to pull an object occurs
  when pulling at the angle of repose a, where the
  coefficient of friction utana.
• DESCRIPTION A wooden board of weight w, lying on
  a sandpaper surface, is pulled at an angle a by a
  string connected to a spring scale. The force F
  required to move the board is given by F w /
  (1/u)cosa sina. Differentiating F with respect
  to a, the minimum force is seen to occur at the
  angle of repose, utana. Pulling horizontally is
  definitely not the most efficient angle!
• SUGGESTIONS Pull horizontally to determine u,
  then check the angle of repose by tilting the
  sandpaper surface. Then pull at a variety of
  angles to demonstrate that pulling at the angle
  of repose requires the least force.

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Moving objects can do work (bowling ball
displaces pins hammer pushes in nail car creams
cow) energy of motion kinetic energy.Energy is
the ability to do work

• Suppose a "bullet" of mass m moving at vo mushes
  into a block of soft clay and experiences a
  constant force F (decelerating at a constant
  rate, a).
•                        
• The force required to slow down the bullet is F
  ma, where a is the deceleration. The work done
  through the distance s, W Fs mas.
• During the deceleration, v2 vo2 2as or as
  1/2(v2 - vo2)
• or Work done ON OBJECT . (would get same
  result for non-constant F and a).

169
Potential energy changes to kinetic energy due to
work done by gravity
PE
170
A boulder resting at the top of a hill has
potential energy.

• Gravitational Potential Energy is the energy
  stored due to height.
• Work can change the height of the Boulder
• Work can change the potential energy of the
  Boulder

171
Example PE?KE

• You are standing on the edge of a cliff and
  decide to push a rock that has a mass of 2kg off
  the edge with your foot. Using conservation of
  mechanical energy, determine how fast the rock is
  going just before it impacts the ground 75m
  below. Assume that there is no air resistance. If
  you dropped a 20kg rock from the same spot would
  the velocity be the same?

172
Drivers Training and braking

• Speed of a car increased by 50. By what factor
  will minimum braking distance be increased
  (ignore reaction time)?
•         
• Braking force same. Therefore
• Distance 2.25times original

173
Mechanical Energy traditional definition the
ability to do work.

• Work done in stopping a car

174
The mechanical work done on the object the
change in kinetic energy  

•   If W is positive, KE increases IF W is
  negative, KE decreases.                         
          
•   -- often called Work-Energy Theorem (Net work
  done change in kinetic energy

175
Work done by gravity

• Suppose a car of mass 1200 kg falls vertically a
  distance of 24 m (starting from rest i.e., voy
  0).
• (a) What is the work done by gravity on the car?
• Fgrav mg Dy 24 m Force and displacement in
  same direction (down).
•                                                 
                                                   
•    
•     
•                                         
• Fgrav Fnet
• because gravity is only force acting on car.

176
Using Work-Energy Theorem

• (b) Find final velocity of car.
• Using constant acceleration (g)
• Using Work-Energy Theorem
•                                               
•                     
• Plug in v 22 m/s.

177
A mass m is moving in a straight line at velocity
vo. It comes into contact with a spring with
force constant k. How far will the spring
compress in bringing the mass to rest?A spring
exerts F proportional to x in both compression
and extension (for reasonable x).
178
Drivers Training and braking

• Speed of a car increased by 50. By what factor
  will minimum braking distance be increased
  (ignore reaction time)?
•         
• Braking force same. Therefore Distance 2.25
  times original

179
Both cases body uses chemical energy for muscles
to exert these forces (you get tired, need more
Twinkies to keep going)--in terms of mechanical
work performed ZIP!Work done holding the box up
180
Work, PE, KE

• In the diagram at left no work is done moving an
  object along a horizontal direction when there is
  no friction (recall Galileo's principle of
  inertia. No force is required to keep an object
  moving. A small amount of work is necessary to
  start it moving and an equal amount is "given
  back" when it is stopped.)

181
Work, PE, KE

• Whether the motion is circular (as with the
  pendulum), up a series of steps, or in one
  horizontal movement followed by lifting the
  height h, the work done is the same to raise the
  object to a height h.This is what we mean by
  "Path Independence".

182
The spring has more mechanical (elastic)
potential energy when compressed.
183
Pendulumgraph with low friction

• Energy slowly "leaks away" from mechanical system

184
Pendulum --graph with high friction
185
KE -- PE

• Assume the track is frictionless and the car
  starts from rest.
• 1. At what position is kinetic energy the
  greatest?
• 2. When placed in order of least amount of
  kinetic energy to greatest, positions of the
  roller coaster are 3. At what position does ET
  EP only?

186
Work, KE,PE

• 4. A 50.0 kg crate is pushed 4.00 m across a
  level frictionless surface with a force of 58.0
  N. The kinetic energy of the moving crate is?
• 5. An object is dropped from rest a certain
  height above the floor. Its speed at the moment
  before it hits the floor is independent of
• 6. When work done on a frictionless horizontal
  surface, all the work is transformed into

187
Work, KE,PE

• 7. A sled slides down a snowy hill. As the sled
  descends the hill the total mechanical energy
• 8. A boy rides up a hill on his bike. As he
  ascends the hill his kinetic energy
• 9.Friction makes molecules vibrate with
• 10. As potential energy of a closed or isolated
  system increases, __________ decreases

188
Work, KE,PE

• 11. This type of energy is called "energy of
  position"? 12. This type of energy is called the
  energy of motion?
• 13. Which of the following is a unit for work?
• 14. A figure skater exerts an upward force of
  25.0 N on his skating partner while he glides
  35.0 m on the ice. How much work is done on the
  lifted skater?

189
Work, KE,PE

• 15. Work is done when a rubber band is stretched.
  Energy is then stored in the band until it snaps
  back. The stored energy is best known as
  ___________ energy
• 16. A crane raises a 20.0 N object above the
  ground in 2.50 seconds. The work done by the
  crane is 500 N. What is the power output of the
  crane?

190
Work, KE,PE

• 17. For a free falling object, the ratio of the
  force of gravity to the acceleration is
• 18. Which two quantities are measured in the same
  units? 19. A moving body must undergo a change
  of 20. Two objects of equal mass are a fixed
  distance apart. If the mass of each object would
  be tripled, the gravitational force between the
  objects would?

191
Gravitational Potential Energy
192
Elastic Potential Energy The Potential Energy in
figures a, b, and c are
193
The Kinetic Energy is the energy an object has by
virtue of its motion. The kinetic energy of an
object of mass m moving at a velocity v is , for
pure transitional motion.
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II. Total Mechanical Energy

• The Total Mechanical Energy of an object is the
  sum of its kinetic and potential energies, .

196
total mechanical energy of the system is conserved

• Law of Conservation of Energy When the work done
  on a system by non-conservative forces is zero,
  then the total mechanical energy of the system is
  conserved (i.e., constant).

197
Energy Transformation for a PendulumKE?? PE No
friction!!

• The conservation of mechanical energy is
  demonstrated in the animation below. Observe the
  KE and PE bars of the bar chart their sum is a
  constant value.

198
Read each description and indicate whether energy
is transformed from KE ? PE or from PE ? KE

• A ball falls from a height of 2 meters in the
  absence of air resistance.

199
Read each description and indicate whether energy
is transformed from KE ? PE or from PE ? KE

• A skier glides from location A to location B
  across the friction free ice.

200
Read each description and indicate whether energy
is transformed from KE ? PE or from PE ? KE

• A baseball is traveling upward towards a man in
  the bleachers.

201
Read each description and indicate whether energy
is transformed from KE ? PE or from PE ? KE

• A bungee chord begins to exert an upward force
  upon a falling bungee jumper.

202
Read each description and indicate whether energy
is transformed from KE ? PE or from PE ? KE

• The spring of a dart gun exerts a force on a dart
  as it is launched from an initial rest position.

203
The following descriptions involve external
forces indicate whether the gain or loss of
energy resulted in a change in the object's
kinetic energy, potential energy, or both

• Megan drops the ball and hits an awesome
  forehand. The racket is moving horizontally as
  the strings apply a horizontal force while in
  contact with the ball.

204
Read each description and indicate whether energy
is transformed from KE to PE or from PE to KE

• A baseball player hits the ball into the outfield
  bleachers. During the contact time between ball
  and bat, the bat is moving at a 10 degree angle
  to the horizontal.

205
Read each description and indicate whether energy
is transformed from KE to PE or from PE to KE

• Rusty Nales pounds a nail into a block of wood.
  The hammer head is moving horizontally when it
  applies force to the nail.

206
Read each description and indicate whether energy
is transformed from KE to PE or from PE to KE

• The frictional force between highway and tires
  pushes backwards on the tires of a skidding car.

207
Read each description and indicate whether energy
is transformed from KE to PE or from PE to KE

• A diver experiences a horizontal reaction force
  exerted by the blocks upon her feet at start of
  the race.

208
Read each description and indicate whether energy
is transformed from KE to PE or from PE to KE

• A weightlifter applies a force to lift a barbell
  above his head at constant speed.

209
law of conservation of the total mechanical energy

• (i.e. if Wnc0 then ET constant).
• And then,

210
Work - Energy Theorem

• Let be the total mechanical energy of an
  object at position one (1).
• Let be its total mechanical energy at
  position two (2). The change in the total
  mechanical energy, from position one to position
  two, is .

211
non-conservative forces.

• Work - Energy Theorem The change in the total
  mechanical energy of a system (or object), from
  position one to position two, is equal to the
  work done on the system (or object) by the
  non-conservative forces.

212
How Far Will It Skid?

• This mathematical relationship between initial
  speed and stopping distance is depicted in the
  animation

213
Work and Energy--Energy Transformation for a Dart

• The animation shows that the energy of the
  dart/gun system is initially present in the form
  of the elastic potential energy (PEs) and
  gravitational potential energy (PEg). The springs
  of the dart gun are compressed which accounts for
  the elastic potential energy. Furthermore, the
  dart is initially elevated at a height of 1-meter
  above the ground which accounts for the
  gravitational potential energy. The presence of
  these two initial forms of energy are shown by
  the PEg and PEs bars of the bar chart.

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External-internal forces

• We categorize a force as internal or external
  because
• internal forces conserve mechanical energy (keep
  same)
• external forces either add or remove mechanical
  energy

Internal Forces External Forces
FgFsp FAFfrFairFTF-
215
The Work-Energy Theorem Internal vs. External
Forces

• Forces can be categorized as internal forces or
  external forces.

216
External-internal forces

• The significance of categorizing a force as
  internal or external is related to the ability of
  that type of force to change an object's total
  mechanical energy when it does work upon an
  object.
• When work is done upon an object by an external
  force, the total mechanical energy changes of
  that object is changed

217
conservation of mechanical energy-practice

• Example 1
• You are standing on the edge of a cliff and
  decide to pus