1. Kinetic Energy KE = 1/2 mv2 Energy due to motion reflects
the mass
the velocity
of the object
KE = 1/2 mv2

2. 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  kg
Velocity = 35.8 m/s

5. 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

8. Potential Energy Two forms of PE: Gravitational PE: Strain PE:
energy due to an object’s position relative to the earth
Strain PE:
due to the deformation of an object

9. Gravitational PE Affected by the object’s GPE = mgh
weight mg
elevation (height) above reference point
ground or some other surface h
GPE = mgh
Units = Nm or J (why?)

10. 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?
Take a look at the energetics of a roller coaster

11. Calculate GPE Trampoline mat is 1.25 m above the ground
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

12. Calculate GPE More on this GPE relative to mat Table of Variables
m = 45 kg
g = m/s/s
h = 4 m
GPE relative to ground
Table of Variables

13. Conversion of KE to GPE and GPE to KE and KE to GPE and …

14. Strain PE Affected by the object’s amount of deformation stiffness
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 .

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

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

18. Strain Energy Plyometrics
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 = n /m x = m (7 mm), Achilles tendon in walking
When a floor/shoe sole is deformed, energy is stored in the material .
Plyometrics

19. Work - Energy Relationship
The work done by an external force acting on an object causes a change in the mechanical energy of the object
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20. 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?

21. Work - Energy Relationship
Of critical importance
Sport and exercise =  velocity
increasing and decreasing kinetic energy of a body
similar to the impulse-momentum relationship

22. Work - Energy Relationship
If more work is done, greater energy
greater average force
greater displacement
Ex. Shot put technique ( ).
If displacement is restricted, average force is __________ ? (increased/decreased)
“giving” with the ball
landing hard vs soft

23. 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

24. 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 = J

25. 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 = J

26. 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)

27. 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)

28. 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 = J

29. 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 = J

30. 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

31. 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

32. 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!

33. 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

34. 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

35. 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

36. 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)