Biomechanical Basis of Biomechanical Basis of MovementMovement

Chapter 12: Linear Kinetics of Chapter 12: Linear Kinetics of Human MovementHuman Movement

Why study Kinetics?Why study Kinetics?

We know how to describe and analyze We know how to describe and analyze movement.movement.

We need to learn something about the forces We need to learn something about the forces that create movements (and injuries).that create movements (and injuries).

Kinetics gives insight into the interactions that Kinetics gives insight into the interactions that occur when bodies (people) contact each occur when bodies (people) contact each other or their environment.other or their environment.

Newton’s LawsNewton’s Laws

1st-law of inertia1st-law of inertia 2nd-law of acceleration2nd-law of acceleration 3rd-law of reaction3rd-law of reaction

Law of InertiaLaw of Inertia

A body will maintain a state of rest or A body will maintain a state of rest or constant velocity unless acted on by an constant velocity unless acted on by an external force that changes the state.external force that changes the state.• I.e: in absence of a net force the state of I.e: in absence of a net force the state of

motion of an object will not change.motion of an object will not change.

Law of AccelerationLaw of Acceleration

A force applied to a body causes an A force applied to a body causes an acceleration of that body of a magnitude acceleration of that body of a magnitude proportional to the force, in the direction proportional to the force, in the direction of the force, and inversely proportional of the force, and inversely proportional to the body’s mass.to the body’s mass.

F=maF=ma

Some important concepts regarding Some important concepts regarding F=maF=ma• cause and effect relationshipcause and effect relationship• ““a” directionally proportional to F and in a” directionally proportional to F and in

same directionsame direction• To produce a given “a” it takes a larger F To produce a given “a” it takes a larger F

for a large objectfor a large object

Law of ReactionLaw of Reaction

For any action, there is an equal and For any action, there is an equal and opposite reaction.opposite reaction.

When one body exerts a force on a When one body exerts a force on a second, the second body exerts a second, the second body exerts a reaction force that is equal in magnitude reaction force that is equal in magnitude and opposite in direction on the first and opposite in direction on the first body.body.

Tennis ball and racquetTennis ball and racquet• Action force applied to the ball by the Action force applied to the ball by the

racquet accelerates the ballracquet accelerates the ball• Reaction force applied to the racquet by Reaction force applied to the racquet by

the ball accelerates the racquet.the ball accelerates the racquet. What about you pushing on a wall?What about you pushing on a wall? You pushing on the earth while You pushing on the earth while

walking?walking?

Law of GravitationLaw of Gravitation

All bodies are attracted to one another All bodies are attracted to one another with a force proportional to the product with a force proportional to the product of their masses and inversely of their masses and inversely proportional to the distance between proportional to the distance between them.them.• FFgg=Gm=Gm11mm22/d/d22

• FFgg=ma=magg

• aagg = -9.81m/s = -9.81m/s22

Ground Reaction Force Curve-Ground Reaction Force Curve-WalkingWalking

FrictionFriction

FrictionFriction-Force acting at the area of -Force acting at the area of contact between two surfaces in the contact between two surfaces in the direction opposite that of motion or direction opposite that of motion or motion tendency.motion tendency.

Forces Affecting MovementForces Affecting Movement

Friction -Friction -

applied force weight

reaction force

friction

Friction Friction Static friction Static friction

• The friction present when a force attempts to slide an The friction present when a force attempts to slide an object on a surface but is not strong enough to actually object on a surface but is not strong enough to actually cause movementcause movement

Dynamic friction Dynamic friction • The friction present once an object starts to move or slide The friction present once an object starts to move or slide

along a surface.along a surface.– Also called kinetic friction (symbol: Fk)Also called kinetic friction (symbol: Fk)

Rolling friction Rolling friction • The friction that resists the movement of an object rolling The friction that resists the movement of an object rolling

on a given surface.on a given surface.

Applied external force

Fric

tion

For static bodies, friction is equal to the applied force.

For bodies in motion, friction is

constant and less than maximum

static friction.

Fa = Applied force parallel to surface (normal force)

Fm = Maximum static friction

R = Reaction force

wt = Object weight

Factors Governing the Factors Governing the Magnitude of FrictionMagnitude of Friction

The coefficient of friction (m)The coefficient of friction (m) General: F = General: F = µµ R R

• R R = wt • cos q where q = deviation from normal = wt • cos q where q = deviation from normal force (if weight). R drawn normal or perpendicular force (if weight). R drawn normal or perpendicular to surfaceto surface

• µµ = Unitless- indicating the relative ease of an = Unitless- indicating the relative ease of an object moves across a surfaceobject moves across a surface

• µµ - Roughness, adherence properties of BOTH - Roughness, adherence properties of BOTH surfacessurfaces

The coefficient of friction (The coefficient of friction ():):Incline, declineIncline, decline

F = F = RR

• R = wt • cosR = wt • cos where where = deviation from normal = deviation from normal force (if weight). R drawn normal or force (if weight). R drawn normal or perpendicular to surfaceperpendicular to surface

• When walking, riding uphill or downhillWhen walking, riding uphill or downhill

• inc, cosinc, cosdecreases, R decreases, friction decreases, R decreases, friction decreasesdecreases wt

R

Types of FrictionTypes of Friction

Maximum Static FrictionMaximum Static Friction-Maximum -Maximum amount of friction that can be generated amount of friction that can be generated between two static surfaces.between two static surfaces.

Kinetic FrictionKinetic Friction-Constant magnitude -Constant magnitude friction generated between two surfaces friction generated between two surfaces in contact during motion.in contact during motion.

Types of FrictionTypes of Friction

Factors that Influence the Factors that Influence the Amount of Friction ForceAmount of Friction Force

Coefficient of FrictionCoefficient of Friction-number that -number that serves as an index of the interaction serves as an index of the interaction between two surfaces in contact.between two surfaces in contact.• 0<0<<1<1

Normal Reaction ForceNormal Reaction Force-force acting -force acting perpendicular to two surfaces in perpendicular to two surfaces in contact.contact.• RR

Calculating the Force of FrictionCalculating the Force of Friction

F=F=RR

RR

wtwtF (applied)F (applied)

FF

Two Types of FrictionTwo Types of Friction

Maximum Static Maximum Static FrictionFriction

FFmm==ssRR

Kinetic FrictionKinetic Friction FFkk==kkRR

**kk<<ss

ExampleExample

Nick Saban has increased his weight to Nick Saban has increased his weight to 1130N by eating cheeseburgers. If he stands 1130N by eating cheeseburgers. If he stands on a 500N blocking sled, how hard must his on a 500N blocking sled, how hard must his linemen push to start the sled moving and linemen push to start the sled moving and keep it moving? The static coefficient of keep it moving? The static coefficient of friction between the sled and the grass is 0.4 friction between the sled and the grass is 0.4 and the kinetic coefficient of friction is 0.25.and the kinetic coefficient of friction is 0.25.

Solution-How hard do the Solution-How hard do the linemen push to start the sled linemen push to start the sled moving?moving?

Solution-How hard do the Solution-How hard do the linemen push to keep the sled linemen push to keep the sled moving?moving?

ExampleExample

A non-Biomechanics student is trying to A non-Biomechanics student is trying to move a desk. He pushes on the desk move a desk. He pushes on the desk with a force of 100N at an angle of with a force of 100N at an angle of 330°. If the desk weighs 75N and the 330°. If the desk weighs 75N and the coefficient of static friction is 0.70, does coefficient of static friction is 0.70, does he move the desk?he move the desk?

Pushing a desk

SolutionSolution

Solution continuedSolution continued

What would happen if he pulled on the What would happen if he pulled on the desk with a 100N at 30°?desk with a 100N at 30°?

Pulling a desk

R = wt - Pv

wt

SUMMARYSUMMARY

SUMMARYSUMMARY

SummarySummary

MomentumMomentum

MomentumMomentum-product of a body’s mass and its -product of a body’s mass and its velocityvelocity

M=mvM=mv units: kgm/sunits: kgm/s

• Particularly useful in collisions as collision Particularly useful in collisions as collision outcome is directly related to momentum of the outcome is directly related to momentum of the colilding bodies just before impact.colilding bodies just before impact.

– Greater momentum of a body, the bigger the effect it will Greater momentum of a body, the bigger the effect it will have on other objects it collides with.have on other objects it collides with.

ExampleExample

A quarterback is chased from the A quarterback is chased from the pocket on a crucial 4th down play. He pocket on a crucial 4th down play. He has a mass of 85kg and is running has a mass of 85kg and is running toward the first down marker at 9m/s. toward the first down marker at 9m/s. The opposing linebacker (mass=100kg) The opposing linebacker (mass=100kg) meets him head-on with a velocity of meets him head-on with a velocity of -8m/s inches from the marker. Does the -8m/s inches from the marker. Does the quarterback make the 1st down?quarterback make the 1st down?

SolutionSolution

Another exampleAnother example

The linebacker wraps up the The linebacker wraps up the quarterback during their collision. What quarterback during their collision. What is their resulting velocity after the is their resulting velocity after the collision?collision?

Hint: Momentum must be conserved; Hint: Momentum must be conserved; the momentum before the impact must the momentum before the impact must be equal to the momentum after the be equal to the momentum after the impact.impact.

Another solutionAnother solution

ImpulseImpulse

ImpulseImpulse-product of a force and the time -product of a force and the time interval over which the force actsinterval over which the force acts

Impulse =F*tImpulse =F*t units: Nsunits: Ns Ft=Ft=MM Ft = mvFt = mv22-mv-mv11

Impulse - ApplicationsImpulse - Applications

Impulse = F•∆t = ∆(m•v)Impulse = F•∆t = ∆(m•v)• We increase an object’s momentum (can apply a large We increase an object’s momentum (can apply a large

force or time exerted or both):force or time exerted or both):• (1) hurling a discus or shot put (1) hurling a discus or shot put • (2) throwing a baseball or softball(2) throwing a baseball or softball• (3) hitting a baseball or tennis ball(3) hitting a baseball or tennis ball• (4) takeoff in a high jump (create vertical momentum (4) takeoff in a high jump (create vertical momentum

without losing forward momentum)without losing forward momentum)• (5) jump for a rebound in basketball(5) jump for a rebound in basketball

– * flexing the hips, knees, and dorsiflexing the ankle allows * flexing the hips, knees, and dorsiflexing the ankle allows for greater force generation (muscle stretch + more force goes for greater force generation (muscle stretch + more force goes to rotating joints) and more time (greater range of motion)to rotating joints) and more time (greater range of motion)

Impulse - ApplicationsImpulse - Applications Impulse = F•∆t = ∆(m•v)Impulse = F•∆t = ∆(m•v)

(4) takeoff in a high jump (4) takeoff in a high jump (create vertical (create vertical momentum without losing forward momentum)momentum without losing forward momentum)

time

Force

Area = F • t

Greater ∆ in momentumin A than B.

Will jump HIGHER

A

B

Impulse - ApplicationsImpulse - Applications Impulse = F•∆t = ∆(m•v) = m•∆vImpulse = F•∆t = ∆(m•v) = m•∆v

We decrease an object’s momentum We decrease an object’s momentum – To reduce impact force we increase the contact To reduce impact force we increase the contact

time (∆t)time (∆t)– This is called CUSHIONING or DAMPINGThis is called CUSHIONING or DAMPING::

(1) design of the front end of an auto (1) design of the front end of an auto crash crash (2) catching a baseball or softball(2) catching a baseball or softball

• flexion of elbow + shoulder and flexion of elbow + shoulder and deformationdeformation of mitt of mitt

(3) cushioning of running shoewear, protective gear by (3) cushioning of running shoewear, protective gear by deformationdeformation

If ∆t is doubled, then F decreases by 50%!If ∆t is doubled, then F decreases by 50%!Injury Prevention Injury Prevention

ExampleExample

A bobsled team begins a downhill run A bobsled team begins a downhill run by pushing their sled to obtain a by pushing their sled to obtain a maximum velocity. Team Jamaica maximum velocity. Team Jamaica pushes their 110kg sled over a 5s time pushes their 110kg sled over a 5s time interval. If they push with a force of interval. If they push with a force of 150N, how fast will the sled be going 150N, how fast will the sled be going after the 5s period?after the 5s period?

SolutionSolution

Another exampleAnother example

During a Gator baseball game, the During a Gator baseball game, the catcher (mass = 90kg) was analyzed to catcher (mass = 90kg) was analyzed to determine the effects of catching fast determine the effects of catching fast balls. He caught a 45m/s pitch over a balls. He caught a 45m/s pitch over a 0.3 second time period. How much 0.3 second time period. How much force was created by the impact of the force was created by the impact of the ball against the glove? The mass of the ball against the glove? The mass of the ball is 0.15kg.ball is 0.15kg.

Another solutionAnother solution

CollisionsCollisions

ImpactImpact-collision characterized by the -collision characterized by the exchange of a large force during a small exchange of a large force during a small time intervaltime interval

Perfectly elastic impactPerfectly elastic impact-impact during -impact during which the velocity of the system is which the velocity of the system is conservedconserved

Perfectly plastic impactPerfectly plastic impact-impact resulting -impact resulting in the total loss of system velocityin the total loss of system velocity

CollisionsCollisions

Coefficient of restitutionCoefficient of restitution-number that -number that serves as an index of elasticity for serves as an index of elasticity for colliding bodiescolliding bodies

0<e<10<e<1

Coefficient of RestitutionCoefficient of Restitution

e = e = (h (hbb/h/hdd))

hhbb = height of bounce = height of bounce

hhdd = height dropped = height dropped

hhbb

hhdd

Tennis ballsTennis balls

A tennis ball actually bounces higher A tennis ball actually bounces higher after 800 hitsafter 800 hits• As long as it has not been out of the can As long as it has not been out of the can

for longfor long When are tennis balls affected?When are tennis balls affected?

• 5 days out of the can5 days out of the can

ExampleExample

A 0.4kg basketball is dropped from a A 0.4kg basketball is dropped from a height of 1.5m. Video analysis is used height of 1.5m. Video analysis is used to determine that the ball bounced to a to determine that the ball bounced to a height of 0.95m. What is the coefficient height of 0.95m. What is the coefficient of restitution between the floor and the of restitution between the floor and the ball?ball?

SolutionSolution

WorkWork

WorkWork-expression of mechanical energy that is -expression of mechanical energy that is calculated as force multiplied by the calculated as force multiplied by the displacement of the resistance in the direction displacement of the resistance in the direction of the forceof the force

W = F*dW = F*d units: Junits: J

Another way of expressing the effects of a Another way of expressing the effects of a force! Force causing a change in position.force! Force causing a change in position.

PowerPower

PowerPower-rate of work production that is -rate of work production that is calculated as work divided by the time calculated as work divided by the time during which the work was doneduring which the work was done

P = W/P = W/tt units: Wunits: W

ExampleExample

A football fan is trying to find his seat. A football fan is trying to find his seat. His seat is in the 90th row. The His seat is in the 90th row. The difference in height between the seats is difference in height between the seats is 35cm. If the fan weighs 800N, how 35cm. If the fan weighs 800N, how much work does he do climbing to the much work does he do climbing to the 90th row? How much power is 90th row? How much power is generated if he climbs to his seat in 90 generated if he climbs to his seat in 90 seconds?seconds?

SolutionSolution

We focused on the the positive work (lifting We focused on the the positive work (lifting the body). What about lowering the body? Is the body). What about lowering the body? Is there work done coming downthere work done coming down• Yes, gravity does work on the body that must be Yes, gravity does work on the body that must be

resisted by the muscles (ie eccentric muscle resisted by the muscles (ie eccentric muscle activity). Thus muscles are doing negative work!activity). Thus muscles are doing negative work!

– It cost energy to do negative work and eccentric activity It cost energy to do negative work and eccentric activity is a major contributor to fatigue and DOMS.is a major contributor to fatigue and DOMS.

EnergyEnergy

EnergyEnergy-the ability or capacity to do work-the ability or capacity to do work• units: Junits: J

Types of EnergyTypes of Energy

Kinetic energyKinetic energy-capacity to do work by virtue -capacity to do work by virtue of a body’s motionof a body’s motion• KE=1/2mvKE=1/2mv22

Potential energyPotential energy-capacity to do work by -capacity to do work by virtue of a body’s positionvirtue of a body’s position• PE=mghPE=mgh

Strain energyStrain energy-capacity to do work by virtue of -capacity to do work by virtue of a deformed body returning to its original a deformed body returning to its original shapeshape• SE=1/2kxSE=1/2kx22

Energy, Work, and PowerEnergy, Work, and Power

An alternative analysis to the dynamic analysis of F=ma for understanding the mechanics of physical systems

Provides insight into motion in terms of a combination of kinematics (displacement) and kinetics (force)

Provides insight into muscle mechanics in terms of contraction types, roles of muscles, sources of movement

EnergyEnergy

Energy has many forms – chemical, nuclear, electrical, mechanical, and more

Energy is often transformed from one form to another:

Electricity is used to spin CDsChemical energy in ATP is used to produce the “power stroke” and slide actin over myosin

Energy is a scalar variable that reflects the “energetic state” of the object

EnergyEnergy

Mechanical energy is the capacity to do work and work is the product of force and displacement

Work = Force * Displacement

Mechanical energy is the capacity to move objects

Energy = Zero or positive value (a scalar), Joules = J

1 J is very small – move fingers a few centimeters?

133 J lifts 150 lb (666 N) person up one step (20 cm)

Forms of Mechanical EnergyForms of Mechanical Energy

Three basic forms of mechanical energy

Potential – position

Kinetic – velocity

Strain - elastic stretch

(or two forms with PE gravitational & strain)

Potential Energy Potential Energy (or Gravitational (or Gravitational

Potential Energy)Potential Energy)

Potential Energy = energy of position = energy associated with the weight of an object and its height above the floor

P.E. = mgh in kgm2 / s2 = J

Runner’s body has some P.E.: P.E. = 50 kg (9.81 m/s2) (1 m) = 490 J

Vaulter has more P.E. P.E. = 80 kg (9.81 m/s2) (3 m) = 2,354 J

1 m

3 m

Potential Energy and WorkPotential Energy and Work

How does Potential Energy have the capacity to do work?

Hold a bowling ball 1 m above floor P.E. = 71 kg (9.81 m/s2) (1 m) = 698 J

Drop the ball on your foot.

Did your foot move by the force applied from the bowling ball?

1 m

Potential Energy and WorkPotential Energy and Work

The potential to do work from the Potential Energy is simply held in check by a supporting force onto the object.

The potential to do work inherent within P.E. is a function of the weight of the object and its velocity at impact

(No P.E. in zero gravity)

1 m

Linear Kinetic EnergyLinear Kinetic Energy

Kinetic Energy = energy of motion = energy associated with the mass and velocity of an object

Linear K.E. = ½ mv2 in kgm2 / s2 = J

Jumper’s body has Linear K.E.: K.E. = ½ (65 kg) (7.4 m/s)2 = 1,780 J

Related to linear momentum = mv

Kinetic Energy and WorkKinetic Energy and Work

How does Kinetic Energy have the capacity to do work?

Step in front of the jumper and find out.

The large kinetic energy in her body will cause you to move.

The large kinetic energy in her body will enable her to exert force on you which will cause you to move.

Conservation of Mechanical Conservation of Mechanical EnergyEnergy

When gravity is the only acting external When gravity is the only acting external force, a body’s mechanical energy force, a body’s mechanical energy remains constant.remains constant.• C = PE + KEC = PE + KE• C = mgh + 1/2mvC = mgh + 1/2mv22

ExampleExample

A 9kg dumbell is being held by the A 9kg dumbell is being held by the persons side (1.5m above the ground). persons side (1.5m above the ground). What is the velocity of the dumbell What is the velocity of the dumbell immediately before impacting the lifters immediately before impacting the lifters toe if dropped?toe if dropped?

SolutionSolution

Principle of Work and EnergyPrinciple of Work and Energy

W = W = KEKE W = W = PEPE *Non-projectile motion*Non-projectile motion

• Example:Example:• How much mechanical work is required to How much mechanical work is required to

catch a .5kg hockey puck traveling at a catch a .5kg hockey puck traveling at a velocity of 50 m/s?velocity of 50 m/s?