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

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 = 1/2mv 2 ) 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 Monday, November 14) – Additional problems, p 412: 6,8,9

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

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 ) Elastic force (coefficient of restitution) (pp ) Free body diagram - force graph (p 63)

Force Plates – Measurement of ground reaction forces

Coefficient of friction, resistance to sliding: C fr = Fr f /No f Sample Prob # 2, p 392

Coefficient of Restitution (COR) COR is a measure of the liveliness of an object When 2 objects collide: When one object is stationary, this reduces to: An alternative way to measure COR is to drop a ball and measure the ht bounced compared to ht dropped:

Coefficient of Restitution (COR) COR of balls dropped or thrown at a rigid wooden surface is shown here. COR increases directly with temperature and inversely with impact velocity.

Coefficient of Restitution (liveliness or bounciness)

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 Net impulse (Ft) 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 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 –Running up stairs: W ork = W eight d 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 –Running up stairs: P = W eight d /time (See next slide) 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)

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

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 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

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

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

Falling objects and work-energy relationship Problem: –If a 2 kg object is dropped from a height of 1.5 meters, what will be its velocity and kinetic energy when it hits the ground? Solution: –Kinetic energy at impact (mgh) equals the potential energy at drop height (½ mv 2 ) Potential energy at drop(mgh) = Nm Kinetic energy at impact = Nm; v = 5.42 m/s 5

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 mv 2 ) –Increase distance through which force is applied Force-area, or pressure concept (P = F/a) –Increase area over which force is applied

Linear Kinetics Formulae