Force and Motion Relationships Instantaneous Effect of force

Force and Motion Relationships • Instantaneous Effect of force on motion is to accelerate the object: F=ma • Force applied through a distance: workenergy relationship • Force applied through a time: impulsemomentum relationship

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)

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

Linear Kinetics Formulae

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

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)

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

Sum of two forces: Sum of two velocities:

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

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?

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

Segmental concept of center of mass

Segmental concept of center of mass