Linear Kinetics Objectives

1. Linear Kinetics Objectives • Identify Newton’s laws of motion and gravitation and describe practical illustrations of the laws • Explain what factors affect friction and discuss the role of friction in daily activities and sports • Define impulse and momentum and explain the relationship between them • Explain what factors govern the outcome of a collision between two bodies • Discuss the interrelationship among mechanical work, power, and energy • Solve quantitative problems related to kinetic concepts

2. Linear Kinetics Outline - The Relationship between force and motion • Read Chapter 12 in text • Classification of forces • Types of forces encountered by humans • Force and motion relationships – three ways to look at it: • Instantaneous effect – Newton’s law of acceleration (F=ma) • Force applied through time (Impulse-momentum)(Ft = mv) • Conservation of Momentum • Force applied through distance (work-energy) (Fd = 1/2mv2) • Conservation of Energy • Self-study problems • Sample problems: #2 p 392; #3 p 396, #4 p 397, #5 p 402, #6 p 405, #7 p 408 • Introductory problems, p 411: 1,3,5,7,8,10 • Homework problems (Due Wednesday, April 13) • Additional problems, p 412: 6,8,9

3. Effect of forces on the system (can be total human body, or a part of the body) • 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

4. External forces commonly 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 389-395) • Elastic force (coefficient of restitution) (pp 399-402) • Free body diagram - force graph (p 63)

5. Force Plates – Measurement of ground reaction forces

6. Coefficient of friction, resistance to sliding: Cfr = Frf /Nof Sample Prob # 2, p 392

7. Coefficient of Restitution (liveliness or bounciness)

8. Coefficient of restitution (liveliness or bounciness)

9. Free body diagrams:

10. 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)

14. Force Applied Through a Time: Impulse-Momentum Relationship (pp 295-399) • 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?

15. Impulse: area under force- time curve Net impulse (Ft) produces a change in momentum (mV) Sample problem #4, p 397

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

17. 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

18. Conservation of momentum: when net impulse is zero (i.e. the system is closed), momentum does not change Sample prob #3, p 396

19. Force Applied Through a Distance: Work, Power, Energy (pp 403-409) • 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 • Running up stairs: Work = Weightd • 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 • Running up stairs: P = Weightd /time (See next slide) • 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)

20. Sample prob #6, p 405 Power running up stairs: Work rate = (weight X vertical dist) ÷ time

21. 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

22. 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 (91 kg) is: 223 Watts

23. 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

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

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

26. Conservation of energy: gravitational potential and kinetic Sample problem #7, p 408

27. Three ways to minimize impact force of 2 colliding objects • Force-time, or impulse-momentum relationship (Ft = mv) • Increase time through which force is applied • Force-distance, or work-energy relationship (FD = ½ mv2) • Increase distance through which force is applied • Force-area, or pressure concept (P = F/a) • Increase area over which force is applied

28. Linear Kinetics Formulae