Week 11 – Linear Kinetics – Relationship between force and motion Read Chapter 12 in text 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 Problems –Introductory problems, p 411: 1,3,5,7,8,10 –Additional problems, p 412: 6,8,9

Classification of Forces Action vs reaction Internal vs external Motive vs resistive Force resolution – horizontal and vertical components Simultaneous application of forces – determining the net force through vector summation

Types of external forces encountered by humans Gravitational force (weight = mg) Ground Reaction Force (GRF)(Figure 12-4, p 386) –Vertical –Horizontal (frictional) Frictional force (coefficient of friction) (pp ) Elastic force (coefficient of restitution) (pp ) Free body diagram - force graph (p 63)

Force Plates – Measurement of ground reaction forces

While walking

C fr = Fr f /No f Sample Prob # 2, p 392

Coefficient of restitution: Sample problem #5, p 402

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 Illustrations from Kreighbaum: Figures F.4, F.5, and F.6 (pp )

Force Applied Through a Time: Impulse- Momentum Relationship (pp ) 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 force- time curve Impulse produces a change in momentum (mV) Sample problem #4, p 397

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? Sample prob #3, p 396

Force Applied Through a Distance: Work, Power, Energy (pp ) Work - force X distance (Newton-meters, or Joules) –On a bicycle: W ork = F (2  r X N) –On a treadmill: W ork = W eight d X per cent grade Power - work rate, or combination of strength and speed (Newton-meters/second, or watts) –On a treadmill: P = W eight d 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 McArdle and Katch. Exercise Physiology

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

Homework: 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 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 Sample prob #6, p 405

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 Videodisk on pole vault

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

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

Linear Kinetics Formulae