1. Work, Power & Energy

2. Work
The product of force and the amount of displacement along the line of action of that force.
Units: ft . lbs (horsepower)
Newton•meter (Joule) e

3. Work = F x d To calculate work done on an object, we need: The Force
The average magnitude of the force
The direction of the force
The Displacement
The magnitude of the change of position
The direction of the change of position

4. Calculate Work
During the ascent phase of a rep of the bench press, the lifter exerts an average vertical force of 1000 N against a barbell while the barbell moves 0.8 m upward
How much work did the lifter do to the barbell?

5. Calculate Work Table of Variables: Force = +1000 N
Displacement = +0.8 m
Force is positive due to pushing upward
Displacement is positive due to moving upward

6. Calculate Work Table of Variables: Force = +1000 N
Displacement = +0.8 m
Select the equation and solve:

7. - & + Work
Positive work is performed when the direction of the force and the direction of motion are the same
ascent phase of the bench press
Throwing a ball
push off (upward) phase of a jump

8. Calculate Work
During the descent phase of a rep of the bench press, the lifter exerts an average vertical force of 1000 N against a barbell while the barbell moves 0.8 m downward

9. Calculate Work Table of Variables Force = +1000 N
Displacement = -0.8 m
Force is positive due to pushing upward
Displacement is negative due to movement downward

10. Calculate Work Table of Variables Force = +1000 N
Displacement = -0.8 m
Select the equation and solve:

11. - & + Work
Positive work
Negative work is performed when the direction of the force and the direction of motion are the opposite

12. Energy Energy (E) is defined as the capacity to do work (scalar)
Many forms
No more created, only converted
chemical, sound, heat, nuclear, mechanical
Kinetic Energy (KE):
energy due to motion
Potential Energy (PE):
energy due to position or deformation

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

14. Kinetic Energy Units: reflect the units of mass * v2
Units KE = Units work

15. Calculate Kinetic Energy
How much KE in a 5 ounce baseball (145 g) thrown at 80 miles/hr (35.8 m/s)?

16. Calculate Kinetic Energy
Table of Variables
Mass = 145 g  kg
Velocity = 35.8 m/s

17. Calculate Kinetic Energy
Table of Variables
Mass = 145 g  kg
Velocity = 35.8 m/s
Select the equation and solve:
KE = ½ m v2
KE = ½ (0.145 kg)(35.8 m/s)2
KE = ½ (0.145 kg)( m/s/s)
KE = ½ (185.8 kg m/s/s)
KE = 92.9 kg m/s/s, or 92.9 Nm, or 92.9J

18. Calculate Kinetic Energy
How much KE possessed by a 150 pound female volleyball player moving downward at 3.2 m/s after a block?

19. Calculate Kinetic Energy
Table of Variables
150 lbs = kg of mass
-3.2 m/s
Select the equation and solve:
KE = ½ m v2
KE = ½ (68.18 kg)(-3.2 m/s)2
KE = ½ (68.18 kg)(10.24 m/s/s)
KE = ½ ( kg m/s/s)
KE = Nm or J

20. 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

21. Calculate Kinetic Energy
Table of Variables
m = 100 Kg
v = 4.0 m/s
Select the equation and solve:
KE = ½ m v2
KE = ½ (100 kg)(4.0 m/s)2
KE = 800 Nm or J
Table of Variables
m = 175 kg
v = 3.75 m/s
Select the equation and solve:
KE = ½ m v2
KE = ½ (175)(3.75)2
KE = 1230 Nm or J

22. Calculate Momentum Momentum = mass times velocity
Player 1 = 100 kg * 4.0 m/s
Player 1 = 400 kg m/s
Player 2 = 175 * 3.75 m/s
Player 2 =

23. 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

24. 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?)

25. 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

26. 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

27. Calculate GPE More on this GPE relative to mat Table of Variables
m = 45 kg
g = m/s/s
h = 4 m
PE = mgh
PE = 45kg * m/s/s * 4 m
PE = J
GPE relative to ground
Table of Variables
m = 45 kg
g = m/s/s
h = 5.25 m
PE = mgh
PE = 45m * m/s/s * 5.25 m
PE = J

28. 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

29. Strain Energy
When a fiberglass vaulting pole bends, strain energy is stored in the bent pole
Pole vault explosion

30. 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

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

32. 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?

33. Work - Energy Relationship
What work was performed on the bar by lifter?
Fd =  KE +  PE
Fd = ½ m(vf –vi)2 + mgh
Fd = 100kg * - 10 m/s/s * 0.75 m
Fd = 750 J
W = Fd
W = 100 kg * .75m
W = 75 kg m
W = 75 kg m (10) = 750 J

34. Work - Energy Relationship
What is GPE at the start & end of the press?
End (ascent)
PE = mgh
PE = 100 kg * -10 m/s/s * 1.50 m
PE = 1500 J
Start (ascent)
PE = 100 kg * -10 m/s/s * 0.75m
PE = 750 J

35. Work - Energy Relationship
Of critical importance
Sport and exercise =  velocity
increasing and decreasing kinetic energy of a body
similar to the impulse-momentum relationship
Ft = m (vf-vi)

36. Power
The rate of doing work
Work = Fd
Units: Fd/s = J/s = watt

37. Newton’s Laws of Motion
1st Law – An object at rest will stay at rest, and an object in motion will stay in motion at constant velocity, unless acted upon by an unbalanced force.
2nd Law – Force equals mass times acceleration.
3rd Law – For every action there is an equal and opposite reaction.

38. 1st Law of Motion (Law of Inertia)
An object at rest will stay at rest, and an object in motion will stay in motion at constant velocity, unless acted upon by an unbalanced force.

39. 1st Law
Inertia is the tendency of an object to resist changes in its velocity: whether in motion or motionless.
These pumpkins will not move unless acted on by an unbalanced force.

40. Friction! There are four main types of friction:
What is this unbalanced force that acts on an object in motion?
Friction!
There are four main types of friction:
Sliding friction: ice skating
Rolling friction: bowling
Fluid friction (air or liquid): air or water resistance
Static friction: initial friction when moving an object

41. 2nd Law
The net force of an object is equal to the product of its mass and acceleration, or F=ma.

42. 2nd Law
When mass is in kilograms and acceleration is in m/s/s, the unit of force is in newtons (N).
One newton is equal to the force required to accelerate one kilogram of mass at one meter/second/second.

43. For every action, there is an equal and opposite reaction.
3rd Law
For every action, there is an equal and opposite reaction.

44. 3rd Law
According to Newton, whenever objects A and B interact with each other, they exert forces upon each other. When you sit in your chair, your body exerts a downward force on the chair and the chair exerts an upward force on your body.