Work, Power

1
Work, Power Energy

• Chapter 7
• Explaining the Causes of Motion Without Newton
• (sort of)

2
Work

• The product of force and the amount of
  displacement along the line of action of that
  force.
• Units ft . lbs (horsepower)
• Newtonmeter (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

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
• push off phase of a jump

8
- Work

• Positive work is performed when the direction of
  the force and the direction of motion are the
  same
• Negative work is performed when the direction of
  the force and the direction of motion are the
  opposite

9
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
• How much work did the lifter do to the barbell?

10
Calculate Work

• Table of Variables
• Force 1000 N
• Displacement -0.8 m

11
Calculate Work

• Table of Variables
• Force 1000 N
• Displacement -0.8 m
• Select the equation and solve

12
- 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

13
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?

14
EMG during the Bench Press
15
Work on a cycle ergometer

• Work Fd
• Force
• belt friction on the flywheel
• mass ie 3 kg
• Displacement
• revolution of the pedals
• Monark 6 m
• Work per revolution
• 3kg x 6 m 18 kgm

16
Work on a stair stepper

• Work Fd
• Force
• Push on the step
• ????
• Displacement
• Step Height
• 8 inches
• Work per step
• ???N x .203 m ???Nm

17
Energy

• Energy (E) is defined as the capacity to do work
• 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

18
Kinetic Energy

• Energy due to motion reflects
• the mass
• the velocity
• of the object
• KE 1/2 mv2

19
Kinetic Energy

• Units reflect the units of mass v2
• Units KE Units work

20
Calculate Kinetic Energy

• How much KE in a 5 ounce baseball (145 g) thrown
  at 80 miles/hr (35.8 m/s)?

21
Calculate Kinetic Energy

• Table of Variables
• Mass 145 g ? 0.145 kg
• Velocity 35.8 m/s

22
Calculate Kinetic Energy

• Table of Variables
• Mass 145 g ? 0.145 kg
• Velocity 35.8 m/s
• Select the equation and solve

23
Calculate Kinetic Energy

• How much KE possessed by a 150 pound female
  volleyball player moving downward at 3.2 m/s
  after a block?

24
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
25
Potential Energy

• Two forms of PE
• Gravitational PE
• energy due to an objects position relative to
  the earth
• Strain PE
• due to the deformation of an object

26
Gravitational PE

• Affected by the objects
• weight
• mg
• elevation (height) above reference point
• ground or some other surface
• h
• GPE mgh
• Units Nm or J (why?)

27
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
28
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
29
Calculate GPE

• GPE 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
• m 45 kg
• g -9.81 m/s/s
• h 5.25 m

30
Strain PE

• Affected by the objects
• 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

31
Strain Energy

• When a fiberglass vaulting pole bends, strain
  energy is stored in the bent pole
• When a tendon/ligament/muscle is stretched,
  strain energy is stored in the elongated elastin
  fibers (Fukunaga et al, 2001, ref5332)
• 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
• .

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

33
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?

34
Work - Energy Relationship

• Of critical importance
• Sport and exercise ? velocity
• increasing and decreasing kinetic energy of a
  body
• similar to the impulse-momentum relationship

35
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

36
Power

• The rate of doing work
• Work Fd
• Units Fd/s J/s watt

37
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

38
Calculate compare power

• Lifter A
• Table of Variables
• F 1000 N
• d 0.8 m
• t 0.50 s

• Lifter B

39
Power on a cycle ergometer

• Work Fd
• Force 3kg
• Displacement 6m /rev
• Work per revolution
• 3kg x 6 m 18 kgm
• 60 rev/min

40
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 (How so??)
41
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 0.254 m
• step rate
• 56.9 /min vs 28.8 /min
• Time per step
• 60s/step rate

Thesis data from Nikki Gegel and Michelle Molnar
42
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 0.254 m
• step rate
• 56.9 /min vs 28.8 /min

43
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 0.254 m
• step rate
• 56.9 /min vs 28.8 /min

Results VO2 similar fast/short steps vs
slow/deep steps