1. Chapter 4 Explaining the Causes of Motion in a Different Way
Work, Power & Energy
Chapter 4
Explaining the Causes of Motion in a Different Way

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
descent phase of the bench press
catching
landing phase of a jump

12. Contemplate
During negative work on the bar, what is the dominant type of activity (contraction) occurring in the muscles?
When positive work is being performed on the bar?

13. EMG during the Bench Press
180 90
On elbow

14. Work performed climbing stairs
Work = Fd
Force
Subject weight
From mass, ie 65 kg
Displacement
Height of each step
Typical 8 inches (20cm)
Work per step
650N x 0.2 m = Nm
Multiply by the number of steps

15. Work on a stair stepper Work = Fd Force Displacement “Work” per step
Push on the step
????
Displacement
Step Height
8 inches
“Work” per step
???N x .203 m = ???Nm

16. Work on a cycle ergometer
Work = Fd
Force
belt friction on the flywheel
mass (eg 3 kg)
Displacement
revolution of the pedals
Monark: 6 m
“Work” per revolution

17. Work on a cycle ergometer
Work = Fd
Force
belt friction on the flywheel
mass (eg 3 kg)
Displacement
revolution of the pedals
Monark: 6 m
“Work” per revolution
3kg x 6 m = 18 kgm

18. Similar principle for wheelchair

19. …and for handcycling ergometer

20. 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

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

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

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

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

25. 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

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

27. 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

28. 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

29. 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

30. 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 =

31. 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

32. 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?)

33. 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

34. 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

35. 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

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

37. 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

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

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

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

41. 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

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

43. 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?

44. 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

45. 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

46. 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)

47. 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

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

49. Calculate & compare power
During the ascent phase of a rep of the bench press, two lifters each exert an average vertical force of 1000 N against a barbell while the barbell moves 0.8 m upward
Lifter A: 0.50 seconds
Lifter B: 0.75 seconds

50. Calculate & compare power
Lifter A
Table of Variables
F = 1000 N
d = 0.8 m
t = 0.50 s
Lifter B

51. Power on a cycle ergometer
Work = Fd
Force: 3kg
Displacement: 6m /rev
“Work” per revolution
3kg x 6 m = 18 kgm
60 rev/min

52. Power on a cycle ergometer
Work = Fd
Force: 3kg
Displacement: 6m /rev
“Work” per revolution
3kg x 6 m = 18 kgm
60 rev/min
1 Watt = 6.12 kgm/min

53. Compare “power” in typical stair stepping
Work = Fd
Force: Push on the step
constant setting
Displacement
Step Height: 5” vs 10”
0.127 m vs m
step rate
56.9 /min vs 28.8 /min
Time per step
60s/step rate
Thesis data from Nikki Gegel
and Michelle Molnar

54. Compare “power” in typical stair stepping
Work = Fd
Force: Push on the step
constant setting
Displacement
Step Height: 5” vs 10”
0.127 m vs m
step rate
56.9 /min vs 28.8 /min

55. Compare “power” in typical stair stepping
Work = Fd
Force: Push on the step
constant setting
Displacement
Step Height: 5” vs 10”
0.127 m vs m
step rate
56.9 /min vs 28.8 /min
Results: VO2 similar fast/short
steps vs slow/deep steps