Linear Kinetics Relationship between force and motion Classification

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) 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 (m. V)

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 mv 2 ) – gravitational potential, energy of position (PE = Weight x height) – elastic potential, or strain, energy of condition (PE = Fd)

Work while pedaling on bicycle: From Mc. Ardle and Katch. Exercise Physiology

Work while running on treadmill: From Mc. Ardle 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 = 980 N 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 (1/2 mv 2) remains constant

Energy conservation – Case II : gravitational potential and kinetic Potential energy (Wh) + kinetic energy (1/2 mv 2) 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