Transcript Gravitational Potential Energy

Kinetic Energy
Energy due to motion reflects
– the mass
– the velocity
of the object
KE = 1/2
2
mv
Kinetic Energy
Units: reflect the units of mass * v2
KE 
• Units KE = Units work
KE 
KE 
KE 
KE 
1 2
mv
2
1
(kg)( m / s ) 2
2
1
kg  m  m / s / s
2
1
(kg  m / s / s )  m
2
1
Nm
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 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
Potential Energy
Two 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 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
Calculate GPE
More on this
GPE relative to mat
Table of Variables
m = 45 kg
g = -9.81 m/s/s
h=4m
GPE relative to ground
Table of Variables
Conversion of KE to GPE and
GPE to KE and KE to GPE and
…
Strain PE
Affected 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 kx2
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
in walking
x = 0.007 m (7 mm), Achilles tendon
• 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
Fd  Energy
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a website
Fd  KE  PE
1
2
Fd  mv f  vi   mg (rf  ri )
2
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
Fd  Energy
Fd  KE  PE
1
2
Fd  mv f  vi   mg (rvf  rvi )
2
– similar to the impulse-momentum relationship
Ft  m(vv  vi )
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=7m
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
• Equation:
energy of a 900 kg
– KE = ½ mv2
car moving at 25 km/h
(7 m/s)?
• Plug & Chug:
KE = ½ (900 kg)(7 m/s)2
• Given:
– m = 900 kg
– v = 7 m/s
• Unknown: KE = ? J
• 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 a
Roller 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)