Linear Kinetics – Relationship between
force and motion
• Sources:
– Kinetics – Hamill, Ch 10 & 11, secondarily Adrian Ch 6)
– Measurement – Kreighbaum pp 555-558; Adrian pp 145-149
– 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
Classification of Forces
•
•
•
•
Action vs reaction
Internal vs external
Motive vs resistive
Force resolution – horizontal and vertical
components
• Simultaneous application of forces - vector
summation
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)
2
Centripetal force (mv /r)
Buoyant force
Free body diagram - force graph
Ground
reaction
forces
Ground
reaction
forces while
walking
Cfr = Frf /Nof
Centripetal &
Centrifugal forces
2
Cf = mv /r
Free body diagrams:
Free body diagrams
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
Force Applied Through a Time:
Impulse-Momentum Relationship
•
•
•
•
Force applied through a time
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?
Impulse: area
under forcetime curve
Impulse produces
a change in
momentum (mV)
Vertical
impulse
While
Running:
Area under
Force-time
curve
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
Conservation of momentum: when net impulse is zero
(i.e. the system is closed), momentum does not change
Conservation of momentum: is this a closed system?
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)
Work while pedaling on bicycle:
From McArdle and Katch.
Exercise Physiology
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
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
Power running up stairs:
Work rate = (weight X vertical dist) ÷ time
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
Energy conservation – Case I : elastic potential (strain) and kinetic
Potential energy (FD) +
Kinetic energy (1/2mv2)
remains constant
Energy conservation – Case II : gravitational potential and kinetic
Potential energy
(Wh) + kinetic
energy (1/2mv2)
remains constant
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
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
Measurement of Muscle Action
Potentials
Measuring ground
Reaction forces
Measuring forces on bat
handle using strain gages
Measuring
forces on bat
handle using
strain gages
Using strain gages to measure
Bat bending and vibration
Begin swing: 183 ms PC
Bat Vibrations During Swing & Impact
4
Peak 41 ms PC
Begin Swing
233ms PC
3
Horiz Pk 38 ms PC
Strain (v)
2
1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
-1
-2
-3
-4
Time (s)
Horiz Dir
Vert Dir
Magnitude
Horiz Dir
Vert Dir
Magnitude
0.7
Bending Direction During Swing & Impact
250
Beg Sw - 233 ms PC
200
Direction (deg)
150
100
50
0
O is horiz & back - 21 ms PC
0
-50
0
0.1
0.2
0.3
0.4
-100
-150
-200
-250
Time (s)
0.5
0.6
0.7
Approximate position when peak bending and
Peak torque occurs ~ 40 ms PC
Using strain gages to measure force on
Hammer during hammer throw
Pressure under shoulder pads
using piezoresistive transducers
Pressure under
shoulder pads
using
piezoresistive
transducers
Pressure under shoulder pads
using piezoresistive transducers
Capacitance and
piezoresistive transducers