Force and Motion Relationships

1. Force and Motion Relationships • Instantaneous Effect of force on motion is to accelerate the object: F=ma • Force applied through a distance: work-energy relationship • Force applied through a time: impulse-momentum relationship

2. 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 283-284)

6. 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?

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

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

9. 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

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

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

12. 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)

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

14. 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

15. 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

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

17. 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

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

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

20. Linear Kinetics Formulae

21. Vector Resolution Problems • Projectile motion situations • Find horizontal velocity • Find vertical velocity • Friction problems • Find horizontal force component (Friction) • Find vertical component (Normal) • First step in adding, or combining vectors • When more than one force is acting on an object • When adding velocity vectors

22. Vector resolution: Vert comp = F•sin•Θ Horiz comp = F•cos•Θ Θ Θ Vert comp = F•sinΘ Horiz comp = F•cosΘ Θ Θ d Θ Turning comp = F•d•sinΘ Radial comp = F•d•cosΘ (d = d•sinθ)

23. Vector Addition Problems • Combining forces • Net effect of two forces applied to any object • What is maximum safe speed for a curve? • Centrifugal force, frictional force, & gravity • What makes a spitball work? • Wind force and weight • Combining velocities • In crossing a river, what direction is best? • Velocity of water and swimmer • In aviation, correcting for wind • air speed and ground speed

24. Sum of two forces: Sum of two velocities:

25. (May be deleted if your calculator provides resultant angle in a 0-360 deg system)

27. COM Questions • What is COM (or COG) and why is it important? • How is COM location different for infants and how does this affect their movement? • Is COM location different for men vs women? • How is COM different if you lose an arm and how does this affect movement? • How does COM relate to stability? • Why do you lean to one side when carrying a load with one arm? • Can Vince Carter, or any athlete really hang in the air?

28. COM/COG Concept and Calculation Method (Adrian pp 33-41) • Center of Mass (COM) • Concept of balancing segmental torques • Segmental Calculation of COM • General calculation method • Information needed • Proportionate mass of each segment • location of COM of each segment

29. Segmental concept of center of mass

31. Segmental concept of center of mass