1. Linear Kinetics – Relationship between force and motion
Sources:
Kinetics – Hamill, Ch 10 & 11, secondarily Adrian Ch 6)
Measurement – Kreighbaum pp ; Adrian pp
Research methods – Robertson Ch 4
Classification of forces
Types of forces encountered by humans
Force and motion relationships
Instantaneous effect – Newton’s law of acceleration (F=ma)
Force applied through time (Impulse-momentum)
Conservation of Momentum
Force applied through distance (work-energy)
Conservation of Energy

2. Classification of Forces
Action vs reaction
Internal vs external
Motive vs resistive
Force resolution – horizontal and vertical components
Simultaneous application of forces - vector summation

3. Types of external forces encountered by humans
Gravitational force (weight = mg)
Ground Reaction Force (GRF)
Vertical
Horizontal (frictional)
Frictional force (coefficient of friction)
Elastic force (coefficient of restitution)
Centripetal force (mv2/r)
Buoyant force
Free body diagram - force graph

4. Ground reaction forces

5. Ground reaction forces while
walking

6. Cfr = Frf /Nof

8. Centripetal &
Centrifugal forces
Cf = mv2/r

9. Free body diagrams:

10. Free body diagrams

11. Instantaneous Effect of Force on an Object
Remember the concept of net force?
Need to combine, or add forces, to determine net force
Newton’s third law of motion (F = ma)
Inverse dynamics – estimating net forces from the acceleration of an object

12. Force Applied Through a Time: Impulse-Momentum Relationship
Impulse - the area under the force-time curve
Momentum - total amount of movement (mass x velocity)
An impulse applied to an object will cause a change in its momentum (Ft = mv)
Conservation of momentum (collisions, or impacts)
in a closed system, momentum will not change
what is a closed system?

13. Impulse: area
under force-
time curve
Impulse produces
a change in
momentum (mV)

14. Vertical
impulse
While
Running:
Area under
Force-time
curve

15. Anterioposterior
(frictional)
component
of GRF: impulse
Is area under
Force-time curve
Positive and
Negative impulse
Are equal if
Horizontal comp
Of velocity is
constant

16. Conservation of momentum: when net impulse is zero
(i.e. the system is closed), momentum does not change

17. Conservation of momentum: is this a closed system?

18. Force Applied Through a Distance: Work, Power, Energy
Work - force X distance (Newton-meters, or Joules)
On a bicycle: Work = F (2r X N)
On a treadmill: Work = Weightd X per cent grade
Power - work rate, or combination of strength and speed (Newton-meters/second, or watts)
On a treadmill: P = Weightd X per cent grade/ time
On a bicycle: P = F (2r X N) / time
What about kilogram-meters/min?
Energy - capacity to do work
kinetic, the energy by virtue of movement (KE = 1/2 mv2 )
gravitational potential, energy of position (PE = Weight x height)
elastic potential, or strain, energy of condition (PE = Fd)

19. Work while pedaling on bicycle:
From McArdle and Katch.
Exercise Physiology

20. Work while running on treadmill:
From McArdle and Katch. Exercise Physiology
Note that %grade = tan θ X 100,
and tan θ and sin θ are very
similar below 20% grade

21. Calculating Power on a Treadmill
Problem: What is workload (power) of a 100 kg man running on a treadmill at 10% grade at 4 m/s?
Solution:
Power = force x velocity
Force is simply body weight, or 100 x 9.8 = 980 N
Velocity is vertical velocity, or rate of climbing
Rate of climbing = treadmill speed x percent grade = 4 m/s x .1 = .4 m/s
Workload, workrate, or power = 980N X .4 m/s = 392 Watts
Note: 4 m/s = 9 mph, or a 6 min, 40 sec mile
Homework: Calculate your workload if you are running on a treadmill set at 5% grade and 5 m/s.
Answer for 200 lb wt is: 223 Watts

22. Power running up stairs:
Work rate = (weight X vertical dist) ÷ time

23. Conservation of Energy
In some situations, total amount of mechanical energy (potential + kinetic) does not change
Stored elastic energy converted to kinetic energy
diving board
bow (archery)
bending of pole in pole vault
landing on an elastic object (trampoline)
Gravitational potential energy converted to kinetic energy
Falling objects

24. Energy conservation – Case I : elastic potential (strain) and kinetic
Potential energy (FD) +
Kinetic energy (1/2mv2)
remains constant

25. Energy conservation – Case II : gravitational potential and kinetic
Potential energy
(Wh) + kinetic
energy (1/2mv2)
remains constant

26. Electronic Load Measurement
Sensor or transducer - the heart & soul of the measurement system
Properties of transducer often sets limits on the usefulness of the measurement system
Electrodes for EMG – polarity between them
Strain gauge – bonded to an elastic material, such as steel beam, it transforms bending into resistance
Piezoelectric – transforms force into electrical charge
Piezoresistive – transforms pressure into electrical resistance (shoulder pad study)
Capacitance – transforms load into electrical energy storage
Signal conduction
Telemetry or wired

27. Electronic load measurement (cont’d)
Signal conditioning – converts output from transducer into an analog signal +10 VDC
Amplifier
Cutoff filters to eliminate noise (low frequency cutoff, high frequency cutoff, notch filters)
Electric circuitry to change resistance to current
Balance potentiometer
Analog-digital conversion, acquisition and analysis board and software
Output
Visual display of data, graphs, charts
Hard copy of data, graphs, chartgs

28. Measurement of Muscle Action Potentials

29. Measuring ground
Reaction forces

32. Measuring forces on bat handle using strain gages

33. Measuring forces on bat handle using strain gages

34. Using strain gages to measure
Bat bending and vibration

38. Begin swing: 183 ms PC

39. Peak 41 ms PC
Begin Swing
233ms PC
Horiz Pk 38 ms PC

40. Beg Sw ms PC
O0 is horiz & back - 21 ms PC

41. Approximate position when peak bending and
Peak torque occurs ~ 40 ms PC

42. Using strain gages to measure force on
Hammer during hammer throw

43. Pressure under shoulder pads using piezoresistive transducers

44. Pressure under shoulder pads using piezoresistive transducers

45. Pressure under shoulder pads using piezoresistive transducers

46. Capacitance and piezoresistive transducers