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Kinetic EnergyEnergy due to motion reflects
– the mass – the velocity
of the object
KE = 1/2 mv2
Kinetic EnergyUnits: reflect the units of mass * v2
• Units KE = Units work
NmKE
mssmkgKE
ssmmkgKE
smkgKE
mvKE
2
1
)//(2
1
//2
1
)/)((2
12
1
2
2
Calculate Kinetic Energy
How much KE in a 5 ounce baseball (145 g) thrown at 80 miles/hr (35.8 m/s)?
Calculate Kinetic Energy
Table of Variables
Mass = 145 g 0.145 kg
Velocity = 35.8 m/s
Calculate Kinetic Energy
Table of Variables
Select the equation and solve:
Calculate Kinetic Energy
How much KE possessed by a 150 pound female volleyball player moving downward at 3.2 m/s after a block?
Calculate Kinetic EnergyCompare 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 momentumof each player
Potential EnergyTwo forms of PE:
• Gravitational PE:–energy due to an object’s position
relative to the earth
• Strain PE:–due to the deformation of an object
Gravitational PE• Affected by the object’s
– weight • mg
– elevation (height) above reference point• ground or some other surface• h
GPE = mgh
Units = Nm or J (why?)
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
Calculate GPEHow much gravitational potential energy in a
45 kg gymnast when she is 4m above the mat of the trampoline?
Trampoline mat is 1.25 mabove the ground
Calculate GPEGPE 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
Conversion of KE to GPE and GPE to KE and KE to GPE and
…
Strain PEAffected by the object’s• 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 kx2
Strain Energy• When a fiberglass vaulting pole bends,
strain energy is stored in the bent pole
.
Strain Energy• When a fiberglass vaulting pole bends,
strain energy is stored in the bent pole
• Bungee jumping
.
Strain Energy• When a fiberglass vaulting pole bends,
strain energy is stored in the bent pole
• Bungee jumping
• Hockey sticks
.
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, ref#5332)– 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
Work - Energy Relationship
• The work done by an external force acting on an object causes a change in the mechanical energy of the object
)(2
1 2ifif rrmgvvmFd
PEKEFd
EnergyFd
Click here fora website
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?
Work - Energy Relationship
• Of critical importance
• Sport and exercise = velocity– increasing and decreasing kinetic energy of a
body
– similar to the impulse-momentum relationship
)(2
1 2vivfif rrmgvvmFd
PEKEFd
EnergyFd
) (i vv v m Ft
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
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
GPE Example - Solved
• A 65 kg rock climber ascends a cliff. What is the climber’s 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
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
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)
The Impact of Velocity
• Which variable has a greater impact on kinetic energy: mass or velocity?– Velocity! It’s 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)
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
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
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)
• Doesn’t experience friction, nor does it rise or fall in a gravitational field
• Under these conditions the net work done equals the body’s change in kinetic energy.
• W = ΔKE = KEf - KEi
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
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!
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
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
Conservation of Energy:Example 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
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)