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 = 1/2mv2)• 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 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 389-395)
• Elastic force (coefficient of restitution) (pp 399-402)
• Free body diagram - force graph (p 63)
Force Plates – Measurement of ground
reaction forces
Coefficient of friction, resistance to sliding:
Cfr = Frf /Nof
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 283-284)
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?
Impulse: areaunder force-time curve
Net impulse (Ft) produces a change in momentum (mV)
Sample problem #4, p 397
Vertical impulse While Running: Area underForce-timecurve
Anterioposterior(frictional) component of GRF: impulseIs area under Force-time curvePositive andNegative impulseAre equal ifHorizontal compOf velocity isconstant
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 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– 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 (2r 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)
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 (1/2mv2) remains constant
Energy conservation – Case II : gravitational potential and kinetic
Potential energy(Wh) + kineticenergy (1/2mv2) 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 mv2)
• Potential energy at drop(mgh)= 29.43 Nm
• Kinetic energy at impact = 29.43 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 mv2)– 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