Linear Kinetics – Relationship between force and motion Classification of forces Types of forces...
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Transcript of Linear Kinetics – Relationship between force and motion Classification of forces Types of forces...
Linear Kinetics – Relationship between force and motion
• 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)
• Centripetal force (mv2/r) • Buoyant force • Free body diagram - force graph
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?
Anterioposterior(frictional) component of GRF: impulseIs area under Force-time curvePositive andNegative impulseAre equal ifHorizontal compOf velocity isconstant
Conservation of momentum: when net impulse is zero (i.e. the system is closed), momentum does not change
Force Applied Through a Distance: Work, Power, Energy
• Work - force X distance (Newton-meters, or Joules)– On a bicycle: Work = F (2r 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 (2r 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 running on treadmill:
Note that %grade = tan θ X 100,and tan θ and sin θ are very similar below 20% grade
From McArdle and Katch. Exercise Physiology
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
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) + kineticenergy (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
Bat Vibrations During Swing & Impact
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Time (s)
Str
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Horiz DirVert DirMagnitudeHoriz DirVert DirMagnitude
Begin Swing 233ms PC
Peak 41 ms PC
Horiz Pk 38 ms PC
Bending Direction During Swing & Impact
-250
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Time (s)
Dir
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de
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Beg Sw - 233 ms PC
O0 is horiz & back - 21 ms PC