week 11 – linear kinetics – relationship between force and motion read chapter 12 in text...
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Week 11 – Linear Kinetics – Relationship between force and motion
• Read Chapter 12 in text• Classification of forces• Types of forces encountered by humans• Force and motion relationships
– Instantaneous effect – Newton’s law of acceleration (F=ma)– Force applied through time (Impulse-momentum)
• Conservation of Momentum
– Force applied through distance (work-energy) • Conservation of Energy
• Problems– Introductory problems, p 411: 1,3,5,7,8,10– Additional problems, p 412: 6,8,9
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Classification of Forces
• 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
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Types of external forces 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)
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Force Plates – Measurement of ground
reaction forces
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While walking
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Cfr = Frf /Nof
Sample Prob# 2, p 392
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Coefficient of restitution: Sample problem #5, p 402
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Free body diagrams:
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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)
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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?
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Impulse: areaunder force-time curve
Impulse produces a change in momentum (mV)
Sample problem #4, p 397
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Vertical impulse While Running: Area underForce-timecurve
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Anterioposterior(frictional) component of GRF: impulseIs area under Force-time curvePositive andNegative impulseAre equal ifHorizontal compOf velocity isconstant
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Conservation of momentum: when net impulse is zero (i.e. the system is closed), momentum does not change
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Conservation of momentum: is this a closed system?
Sample prob#3, p 396
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Force Applied Through a Distance: Work, Power, Energy (pp 403-409)
• Work - force X distance (Newton-meters, or Joules)– On a bicycle: Work = F (2r 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 (2r 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)
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Work while pedaling on bicycle:
From McArdle and Katch.Exercise Physiology
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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
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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 is: 223 Watts
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Power running up stairs: Work rate = (weight X vertical dist) ÷ time
Sample prob#6, p 405
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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
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Energy conservation – Case I : elastic potential (strain) and kinetic
Potential energy (FD) + Kinetic energy (1/2mv2) remains constant
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Energy conservation – Case II : gravitational potential and kinetic
Potential energy(Wh) + kineticenergy (1/2mv2) remains constant
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Linear Kinetics Formulae