Kinetic Energy

1
Kinetic Energy

• Energy due to motion reflects
• the mass
• the velocity
• of the object
• KE 1/2 mv2

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Kinetic Energy

• Units reflect the units of mass v2
• Units KE Units work

3
Calculate Kinetic Energy

• How much KE in a 5 ounce baseball (145 g) thrown
  at 80 miles/hr (35.8 m/s)?

4
Calculate Kinetic Energy

• Table of Variables
• Mass 145 g ? 0.145 kg
• Velocity 35.8 m/s

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Calculate Kinetic Energy

• Table of Variables
• Select the equation and solve

6
Calculate Kinetic Energy

• How much KE possessed by a 150 pound female
  volleyball player moving downward at 3.2 m/s
  after a block?

7
Calculate Kinetic Energy

• Compare KE possessed by
• a 220 pound (100 kg) running back moving forward
  at 4.0 m/s
• a 385 pound (175 kg) lineman moving forward at
  3.75 m/s

Bonus calculate the momentum of each player
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Potential Energy

• Two forms of PE
• Gravitational PE
• energy due to an objects position relative to
  the earth
• Strain PE
• due to the deformation of an object

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Gravitational PE

• Affected by the objects
• weight
• mg
• elevation (height) above reference point
• ground or some other surface
• h
• GPE mgh
• Units Nm or J (why?)

10
Calculate GPE

• How much gravitational potential energy in a 45
  kg gymnast when she is 4m above the mat of the
  trampoline?

Take a look at the energetics of a roller coaster
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Calculate GPE

• How much gravitational potential energy in a 45
  kg gymnast when she is 4m above the mat of the
  trampoline?

Trampoline mat is 1.25 m above the ground
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Calculate GPE
More on this

• GPE relative to mat
• Table of Variables
• m 45 kg
• g -9.81 m/s/s
• h 4 m

• GPE relative to ground
• Table of Variables

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Conversion of KE to GPE and GPE to KE and KE to
GPE and
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Strain PE

• Affected by the objects
• amount of deformation
• greater deformation greater SE
• ?x2 change in length or deformation of the
  object from its undeformed position
• stiffness
• resistance to being deformed
• k stiffness or spring constant of material
• SE 1/2 k?x2

15
Strain Energy

• When a fiberglass vaulting pole bends, strain
  energy is stored in the bent pole
• .

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Strain Energy

• When a fiberglass vaulting pole bends, strain
  energy is stored in the bent pole
• Bungee jumping
• .

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Strain Energy

• When a fiberglass vaulting pole bends, strain
  energy is stored in the bent pole
• Bungee jumping
• Hockey sticks
• .

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Strain Energy

• When a fiberglass vaulting pole bends, strain
  energy is stored in the bent pole
• Bungee jumping
• When a tendon/ligament/muscle is stretched,
  strain energy is stored in the elongated elastin
  fibers (Fukunaga et al, 2001, ref5332)
• k 10000 n /m x 0.007 m (7 mm), Achilles
  tendon in walking
• When a floor/shoe sole is deformed, energy is
  stored in the material
• .

Plyometrics
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Work - Energy Relationship

• The work done by an external force acting on an
  object causes a change in the mechanical energy
  of the object

Click here for a website
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Work - Energy Relationship

• The work done by an external force acting on an
  object causes a change in the mechanical energy
  of the object
• Bench press ascent phase
• initial position 0.75 m velocity 0
• final position 1.50 m velocity 0
• m 100 kg
• g -10 m/s/s
• What work was performed on the bar by lifter?
• What is GPE at the start end of the press?

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Work - Energy Relationship

• Of critical importance
• Sport and exercise ? velocity
• increasing and decreasing kinetic energy of a
  body
• similar to the impulse-momentum relationship

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Work - Energy Relationship

• If more work is done, greater? energy
• greater average force
• greater displacement
• Ex. Shot put technique (121-122).
• If displacement is restricted, average force is
  __________ ? (increased/decreased)
• giving with the ball
• landing hard vs soft

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Gravitational Potential Energy

• Gravitational potential energy
• PE that an object has by virtue of its HEIGHT
  above the ground
• GPE mass x freefall acceleration x height
• GPE mgh (Fd)
• mg weight of the object in Newtons (F)
• h distance above ground (d)
• GPE stored Work done to lift object

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GPE Example - Solved

• A 65 kg rock climber ascends a cliff. What is
  the climbers gravitational potential energy at a
  point 35 m above the base of the cliff?
• Given
• m 65 kg
• h 35 m
• Unknown GPE ? J

• Equation
• PE mgh
• Plug Chug
• PE (65 kg)(9.8 m/s2)(35 m)
• Answer
• GPE 22000 J

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GPE Example - Unsolved

• What is the gravitational potential energy of a
  2.5 kg monkey hanging from a branch 7 m above the
  jungle floor?
• Given
• m 2.5 kg
• h 7 m
• Unknown GPE ? J

• Equation
• GPE mgh
• Plug Chug
• GPE (2.5 kg)(9.8 m/s2)(7m)
• Answer
• GPE 171.5 J

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Kinetic Energy

• Def the energy of a moving object due to its
  motion
• Moving objects will exert a force upon impact
  (collision) with another object.
• KE ½ (mass) (velocity)2
• KE ½ (mv2)

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The Impact of Velocity

• Which variable has a greater impact on kinetic
  energy mass or velocity?
• Velocity! Its SQUARED!
• Velocity as a factor
• Something as small as an apple
• At a speed of 2 m/s 0.2 J
• At a speed of 8 m/s 3.2 J(4 x velocity 16x
  energy)

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KE Example - Solved

• What is the kinetic energy of a 44 kg cheetah
  running at 31 m/s?
• Given
• m 44 kg
• v 31 m/s
• Unknown
• KE ? J

• Equation
• KE ½ mv2
• Plug Chug
• KE ½ (44 kg)(31 m/s)2
• Answer
• KE 21000 J

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KE Example - Unsolved

• What is the kinetic energy of a 900 kg car moving
  at 25 km/h (7 m/s)?
• Given
• m 900 kg
• v 7 m/s
• Unknown KE ? J

• Equation
• KE ½ mv2
• Plug Chug
• KE ½ (900 kg)(7 m/s)2
• Answer
• KE 22050 J

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Work-Energy Theorem

• Imagine a rigid body that does work or has work
  done on it to overcome only inertia (i.e. to
  accelerate it)
• Doesnt experience friction, nor does it rise or
  fall in a gravitational field
• Under these conditions the net work done equals
  the bodys change in kinetic energy.
• W ?KE KEf - KEi

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Conservation of Energy

• Objectives
• Identify and describe transformations of energy
• Explain the law of conservation of energy
• Where does energy go when it disappears?
• Analyze the efficiency of machines

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Conservation of Energy

• The Law of Conservation of Energy
• Energy cannot be created nor destroyed, but can
  be converted from one form to another or
  transferred from one object to another
• Total Energy of a SYSTEM must be CONSTANT!

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Conservation of Energy

• Total Mechanical Energy Kinetic Potential
• TME KE PE
• TME must stay the same!
• If a system loses KE, it must be converted to PE
• In reality some is converted to heat
• We will USUALLY consider frictionless systems ?
  only PE KE

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Energy Conversions in aRoller Coaster

• Energy changes form many times.
• Energy from the initial conveyor
• Work stored Grav. Potential Energy
• Some PE is converted to KE as it goes down
• Some KE is converted to PE as it goes up
• Where does the coaster have max. PE?
• Where does the coaster have min. PE?
• Where does the coaster have max. KE?
• Where does the coaster have min. KE?
• Where could energy be lost?
• Friction, vibrations, air resistance

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Conservation of EnergyExample Problem

• You have a mass of 20 kg and are sitting on your
  sled at the top of a 40 m high frictionless hill.
  What is your velocity at the bottom of the hill?
• Given
• m 20 kg
• h 40 m
• Unknown
• v ? (at bottom)
• Equations
• TME PE KE
• PE mgh
• KE ½ mv2

• Plug Chug
• At Top
• ME mgh
• TME (20 kg)(10 m/s2)(40 m)
• TME 8000 J
• At Bottom
• TME ½ mv2
• 8000 J ½ (20kg)(v2)
• v2 800 m2/s2
• v 28.3 m/s

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Other Forms of Energy

• Mechanical Energy the total energy associated
  with motion
• Total Mechanical Energy Potential Energy
  Kinetic Energy
• Examples roller coasters, waterfalls
• Heat Energy average kinetic energy of atoms
  molecules
• The faster they move, the hotter they get!
• Ex. Boiling water,
• Chemical Energy potential energy stored in
  atomic bonds
• When the bonds are broken, energy is released
• Ex. Combustion (burning), digestion, exercise
• Electromagnetic Energy kinetic energy of moving
  charges
• Energy is used to power electrical appliances.
• Ex. Electric motors, light, x-rays, radio waves,
  lightning
• Nuclear Energy potential energy in the nucleus
  of an atom
• Stored by forces holding subatomic particles
  together
• Ex. Nuclear fusion (sun), Nuclear fission
  (reactors, bombs)